Question

1. which of the following expressions is equivalent to $x^2 - 11x + 24$?

a. $(x - 3)(x + 8)$
b. $(x + 3)(x - 8)$
c. $(x - 3)(x - 8)$
d. $(x + 3)(x + 8)$

1. which of the following is a factor of the polynomial $9a^2 - 49$

a. $(3a + 7)(3a + 7)$
b. $(3a - 7)(3a + 7)$
c. $(7a + 3)(7a + 3)$
d. $(7a - 3)(7a + 3)$

Explanation:

(Question 9):

Step1: Find pair summing to -11

We need two numbers that add to $-11$ and multiply to $24$: $-3$ and $-8$.

Step2: Factor the quadratic

Write the quadratic as product of binomials:
$(x - 3)(x - 8)$

Step3: Verify by expanding

$$\begin{align*} (x-3)(x-8)&=x^2 -8x -3x +24\\ &=x^2 -11x +24 \end{align*}$$

(Question 10):

Step1: Recognize difference of squares

$9a^2-49=(3a)^2-(7)^2$

Step2: Apply difference of squares rule

Use $a^2-b^2=(a-b)(a+b)$:
$(3a-7)(3a+7)$

Answer:

Question 9: C. $(x - 3)(x - 8)$
Question 10: B. $(3a - 7)(3a + 7)$