Question

a) factor the trinomial.
$3x^2 + 5x + 2 = 0$
enter one root into each box,
whole numbers or fractions only:
b) find roots=

Explanation:

Step1: Split middle term

$3x^2 + 3x + 2x + 2 = 0$

Step2: Group and factor pairs

$3x(x+1) + 2(x+1) = 0$

Step3: Factor out common binomial

$(3x+2)(x+1) = 0$

Step4: Solve for x (first root)

$3x+2=0 \implies x=-\frac{2}{3}$

Step5: Solve for x (second root)

$x+1=0 \implies x=-1$

Answer:

A) $(3x+2)(x+1)$
B) $-\frac{2}{3}$, $-1$