Factoring Polynomials by Grouping Practice — Grade 9 math

Lesson 87: Factoring Polynomials by Grouping — Practice Questions

1. Which expression is equivalent to $4p(q - 2) + 9(2 - q)$ after applying the sign change rule to the second term?
- A. $4p(q - 2) + 9(q - 2)$
- B. $4p(q - 2) - 9(q - 2)$
- C. $-4p(2 - q) + 9(2 - q)$
- D. $4p(q - 2) - 9(2 + q)$
2. Factor the polynomial $3ab - 12a + 8 - 2b$ completely. Your answer should be in the form $(...)(...)$. Answer: ___
3. After factoring the GCF from each group, which expression would require factoring out a $-1$ to proceed?
- A. $m(n - 5) + 2(n - 5)$
- B. $5x(2 - y) + 3(y - 2)$
- C. $a(x + 2) + b(x + 2)$
- D. $k(j + 1) - 4(j + 1)$
4. Factor the polynomial $20 - 5mn + 2m^2n - 8m$ completely. Your answer should be in the form $(...)(...)$. Answer: ___
5. What is the completely factored form of the expression $5xy - 10x + 20 - 10y$?
- A. $(y - 2)(5x - 10)$
- B. $5(y - 2)(x + 2)$
- C. $5(y - 2)(x - 2)$
- D. $(5y - 10)(x - 2)$
6. To factor the trinomial $3x^2 - 10x - 8$ by grouping, what is the required product $ac$ and sum $b$ for the two numbers used to split the middle term?
- A. Product: -24, Sum: -10
- B. Product: 24, Sum: -10
- C. Product: -8, Sum: 3
- D. Product: 30, Sum: -10
7. Factor the expression $2x^2 + 7x + 3$ completely. One of its factors is $(x+3)$. The other factor is ___.
8. To factor $4m^2 - 5m - 6$, the term $-5m$ is rewritten as the sum of two terms. What are the coefficients of these two new terms?
- A. 6 and -1
- B. -8 and 3
- C. 2 and -7
- D. 4 and -9
9. The trinomial $3y^2 - 11y + 10$ can be factored into the form $(3y-5)(\_\_\_)$. What is the missing factor?
10. Which expression is the completely factored form of the trinomial $p^2 + 2p - 15$?
- A. (p - 5)(p + 3)
- B. (p + 5)(p - 3)
- C. (p - 1)(p + 15)
- D. (p + 1)(p - 15)