Question

factor the expression.
$3x^2 + 26x + 35$
a. $(3x + 5)(x + 7)$
b. $(x + 5)(3x + 7)$
c. $(3x + 7)(x - 5)$
d. $(3x + 5)(x - 7)$

Explanation:

Step1: Expand Option A

Multiply \((3x + 5)(x + 7)\) using distributive property:
\(3x \cdot x + 3x \cdot 7 + 5 \cdot x + 5 \cdot 7 = 3x^2 + 21x + 5x + 35 = 3x^2 + 26x + 35\).

Step2: Check Other Options (Optional)

Expanding Option B: \((x + 5)(3x + 7) = 3x^2 + 7x + 15x + 35 = 3x^2 + 22x + 35\) (not matching).
Options C and D have negative signs, leading to negative linear terms (not matching \(+26x\)).

Answer:

A. \((3x + 5)(x + 7)\)