Question

factor completely: $4x^2 + 4xy - 3x - 3y$
$\bigcirc (4x - 3)(x - y)$
$\bigcirc (4x - 3)(x + y)$
$\bigcirc 4x(x + y) - 3(x + y)$
$\bigcirc x(4x + 4y - 3) - 3y$
question 28
one of the factors of $2x^2 + x - 6$ is:
$\bigcirc 2x - 3$
$\bigcirc 2x - 6$
$\bigcirc 2x + 3$
$\bigcirc 2x + 6$

Explanation:

Step1: Group terms for factoring

$4x^2 + 4xy - 3x - 3y = (4x^2 + 4xy) + (-3x - 3y)$

Step2: Factor out GCF from each group

$= 4x(x + y) - 3(x + y)$

Step3: Factor out common binomial

$= (4x - 3)(x + y)$

Step4: Factor quadratic expression

For $2x^2 + x - 6$, use AC method:
$2x^2 + 4x - 3x - 6 = 2x(x + 2) - 3(x + 2)$

Step5: Extract common binomial factor

$= (2x - 3)(x + 2)$

Answer:

1. $(4x - 3)(x + y)$
2. $2x - 3$