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see explanation

Step-by-step explanation:

3x² + 5x + 2 = 0

(a)

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × 2 = 6 and sum = 5

The factors are + 3 and + 2

Use these factors to split the x- term

3x² + 3x + 2x + 2 = 0 ( factor the first/second and third/fourth terms )

3x(x + 1) + 2(x + 1) = 0 ← factor out (x + 1) from each term

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

(b)

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = -

20

step-by-step explanation: