Question

factor completely. $5x^2 - 24x + 27$

Explanation:

Step1: Find product of a and c

$a=5, c=27$, so $ac=5×27=135$

Step2: Find factors of 135 summing to -24

Factors: -15 and -9 (since $-15×-9=135$, $-15+(-9)=-24$)

Step3: Split middle term

$5x^2 -15x -9x +27$

Step4: Factor by grouping

$5x(x - 3) -9(x - 3)$

Step5: Factor out common binomial

$(5x - 9)(x - 3)$

Answer:

$(5x - 9)(x - 3)$