Question

d: factor by gcf and grouping
factor the following quadratic expression:
$15x^2 + 35x$
a $3x(5x - 1)$
b $5x(3x + 7)$
c $7x(5x - 6)$
d not factorable

Explanation:

Step1: Find GCF of coefficients and variables

The coefficients are 15 and 35. GCF of 15 and 35 is 5. For the variable part, \(x^2\) and \(x\) have GCF \(x\). So overall GCF is \(5x\).

Step2: Factor out GCF from the expression

Factor out \(5x\) from \(15x^2 + 35x\): \(5x(3x + 7)\).

Answer:

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