factor the following expression.\n8x² + 22x + 5\n(4x + ?)( x + )

Explanation:

Step1: Multiply leading and constant terms

$8\times5 = 40$.

Step2: Find two numbers for 40 that sum to 22

The numbers are 20 and 2 since $20\times2=40$ and $20 + 2=22$.

Step3: Rewrite middle - term

$8x^{2}+22x + 5=8x^{2}+20x+2x + 5$.

Step4: Group the terms

$(8x^{2}+20x)+(2x + 5)$.

Step5: Factor out common factors from each group

$4x(2x + 5)+1(2x + 5)$.

Step6: Factor out the common binomial factor

$(4x + 1)(2x+5)$.

Answer:

$(4x + 1)(2x + 5)$