question\nfactor the trinomial:\n$5x^{2}+9x + 4$

Explanation:

Step1: Multiply the coefficient of (x^{2}) and the constant term

For the trinomial (5x^{2}+9x + 4), (a = 5), (b=9), (c = 4). Calculate (a\times c=5\times4 = 20).

Step2: Find two numbers that multiply to (20) and add up to (b = 9)

The numbers are (5) and (4) since (5\times4=20) and (5 + 4=9).

Step3: Rewrite the middle term

(5x^{2}+9x + 4=5x^{2}+5x+4x + 4)

Step4: Group the terms

((5x^{2}+5x)+(4x + 4))

Step5: Factor out the common factors from each group

(5x(x + 1)+4(x + 1))

Step6: Factor out the common binomial factor

((x + 1)(5x+4))

Answer:

((x + 1)(5x + 4))