Title: Unit 12 Quiz
Course: Technical Math for Industry

Q: Find the greatest common factor of and .
A: (a choice with no text)
If wrong: Incorrect. This is a factor of the first monomial, but it is not a factor of the second one. The GCF should have as factors each prime they have in common and each variable they have in common. The variable b is not a factor of , so it should not appear in the GCF.
If wrong: Incorrect. This is a common factor, but not the greatest common factor. To find the GCF of two monomials, factor each into primes and variables. Find each prime they have in common and each variable they have in common. For each of those, count how many times they have that factor in common. The GCF should have that many.
If wrong: Incorrect. This is a factor of the first monomial, but it is not a factor of the second one. The GCF should have as factors each prime they have in common and each variable they have in common. The variable b is not a factor of , so it should not appear in the GCF.
If right: Correct. GCF

Q: Factor out the GCF:
A: (a choice with no text)
If right: Correct. GCF
If wrong: Incorrect. This is a factorization of the given expression, but is not the GCF. You may have thought that you needed only to factor out the different factors that occur. However, they have the variable c in common six times, so is part of the GCF, and they have the prime 3 in common two times, so or 9 is part of the GCF.
If wrong: Incorrect. This is a factorization of the given expression, but is not the GCF. You may have subtracted the two exponents to obtain the as part of your common factor. Factor both terms. They have the variable c in common six times, so is part of the GCF.
If wrong: Incorrect. is a common factor, but not the GCF. Also, this is an incorrect factorization. You may have incorrectly thought that the exponents get multiplied when you multiply the variables. If you used the distributive property to multiply , you would get , not .

Q: Factor:
A: (a choice with no text)
If wrong: Incorrect. Using FOIL: This is not equal to the given expression. First group terms into pairs and factor out the GCF of each pair. Then factor out the common binomial factor.
If wrong: Incorrect. This is not a factorization. You have factored out a common term for the first three terms instead of factoring by grouping. First group terms into pairs and factor out the GCF of each pair. Then factor out the common binomial factor.
If wrong: Incorrect. Using FOIL: This is not equal to the given expression. First group terms into pairs and factor out the GCF of each pair. Then factor out the common binomial factor.
If right: Correct. The GCF of the first two terms is x and the GCF of the last two terms is 7. Factor those out. The resulting terms have a common factor .

Q: Factor .
A: (a choice with no text)
If wrong: Incorrect. , not . You first need to find two numbers whose product is 30 and whose sum is 11.
If right: Correct. . The factors whose sum is 11 are 5 and 6. Now rewrite the trinomial and use grouping:
If wrong: Incorrect. , not . You first need to find two numbers whose product is 30 and whose sum is 11.
If wrong: Incorrect. , not . You first need to find two numbers whose product is 30 and whose sum is 11.

Q: Factor out the GCF of the three terms, then complete the factorization of  .
A: (a choice with no text)
If wrong: Incorrect. You may have correctly factored out the GCF, but then incorrectly factored . It appears that you used 3 and 6 because their sum is 9, but their product is not 14.
If wrong: Incorrect. You correctly factored out the GCF, but you still need to factor . Use the method that you learned to rewrite , and factor by grouping.
If wrong: Incorrect. You factored the GCF out of only the first two terms. This is not a factorization because you have not written the entire expression as a product. First find the GCF of the three terms and factor it out of the trinomial. Then factor the remaining trinomial into the product of two binomials.
If right: Correct. The GCF of the three terms is , so . Factor by grouping:

Q: Factor:
A: (a choice with no text)
If wrong: Incorrect. This is a sum, not a product. After you factor each pair of terms, you need to use the distributive property in reverse:
If right: Correct.
If wrong: Incorrect. You may have correctly factored each pair of terms, but then made a mistake in the last step. You need to use the distributive property in reverse:
If wrong: Incorrect. You may have correctly rewritten as , but while factoring by grouping you made a mistake with signs. If you have an expression like and you factor out a negative number, the signs of all the terms will change.

Q: Factor:
A: (a choice with no text)
If wrong: Incorrect. Although the product of the first terms is , and the product of the last terms is 9, the outer and inner products do not add up to . The first step is to determine if this a perfect square trinomial. Then you can use the fact that a trinomial in the form can be factored as .
If right: Correct. This expression is a perfect square trinomial because , , and . Therefore, .
If wrong: Incorrect. Although the product of the first terms is , the product of the last terms is , not 9, and the outer and inner products do not add up to . The first step is to determine if this a perfect square trinomial. Then you can use the fact that a trinomial in the form can be factored as .
If wrong: Incorrect. You probably recognized that the first and last terms are perfect squares, but you used the wrong sign. If you multiply this answer out, you will get a middle term of , not . A trinomial in the form can be factored as .

Q: Factor:
A: (a choice with no text)
If wrong: Incorrect. , not . The given expression is a difference of squares, which can be factored using .
If wrong: Incorrect. You may have been thinking about factoring a perfect square trinomial, but the given expression is a difference of squares. This expression can be factored using .
If wrong: Incorrect. You may have been thinking about factoring a perfect square trinomial, but the given expression is a difference of squares. This expression can be factored using .
If right: Correct. and , so this a difference of squares. Use to get .

Q: Factor:
A: (a choice with no text)
If wrong: Incorrect. You correctly factored out an 8, but then made a mistake with the signs. A binomial in the form can be factored as .
If right: Correct. First, you can factor out a common factor of 8. Then, a binomial in the form can be factored as .
If wrong: Incorrect. It appears that you mixed up the placement of the minus signs. A binomial in the form can be factored as .
If wrong: Incorrect. You probably did the correct first step, , but then made a mistake. A binomial in the form can be factored as . The second factor in this answer is missing its middle term. Check your answer by multiplying out.

Q: Factor:
A: (a choice with no text)
If wrong: Incorrect. You may have correctly done the first step: . Now is in the form and can be factored as . You are missing a term inside the last factor. Whenever you factor, remember to check your answer by multiplying the factors back together.
If wrong: Incorrect. It appears that you used the formula for the sum of two cubes instead of the difference. A binomial in the form can be factored as . Whenever you factor, remember to check your answer by multiplying the factors back together.
If right: Correct. A binomial in the form can be factored as .
If wrong: Incorrect. You may have correctly done the first step: . Now is in the form and can be factored as . Since and , you should have replaced a by and b by 3. Whenever you factor, remember to check your answer by multiplying the factors back together.

Q: Solve for x:
- or (Incorrect. You may have looked at each factor and thought that all you had to do was reverse the sign of the constant term. To solve an equation in factored form, set each factor equal to 0 and solve each equation.)
- or (Correct. To solve an equation in factored form, set each factor equal to 0 and solve each equation. or or or)
- or (Incorrect. You reversed the signs of the solutions. To solve an equation in factored form, set each factor equal to 0 and solve each equation. Remember that when you solve an equation you must add the same number to both sides, or subtract the same number from both sides.)
A: or
If wrong: Incorrect. To solve an equation in factored form, set each factor equal to 0 and solve each equation. This is not the same as setting x equal to 0. If you substitute the value of 0 into the left side you will get , not 0. So is not a solution.

Q: Solve for x.
- or (Incorrect. You have reversed the signs either while factoring or while solving the equations. When you are solving equations you must add the same number to both sides or subtract the same number from both sides.)
- or (Correct. Rewrite as , as , and . Then factor by grouping to get: or or)
A: or
If wrong: Incorrect. This is a solution to the equation, but not the complete solution. To solve a quadratic equation, factor it, set each factor equal to 0, and solve each equation. You may have thought that could not be equal to 0, because you were thinking of the addition of two positive numbers. However, x could be positive or negative.
If wrong: Incorrect. Although the product of the two factors in this equation is equal to 0, this is not the same as x being equal to 0. If you substitute 0 for x in the left side of the equation, you will get , not 0. So is not a solution.

Q: Solve for x:
- or (Incorrect. You may have made a mistake with signs while factoring or while solving the two equations you got after using the Zero Product Property.)
- or (Correct. Subtract x and 2 from both sides of the equation to get 0 on one side: or or)
- or (Incorrect. You may have solved the equation correctly until the last step, when you forgot to divide by the coefficients of the x terms.)
A: or
If wrong: Incorrect. You may have ignored the exponent on the term, and solved the equation . Subtract x and 2 from both sides of the equation to get 0 on one side, then factor and solve.