Question

factor the polynomial. 32p² - 20p + 32 32p² - 20p + 32 = □

Explanation:

Step1: Find GCF of coefficients

The coefficients are 32, -20, 32. The greatest common factor (GCF) is 4.

Step2: Factor out the GCF

Divide each term by 4 and factor it out.
$32p^2 - 20p + 32 = 4(8p^2 - 5p + 8)$

Step3: Check quadratic factor

The quadratic $8p^2 -5p +8$ has discriminant $\Delta = (-5)^2 - 4(8)(8) = 25 - 256 = -231 < 0$, so it cannot be factored over real numbers.

Answer:

$4(8p^2 - 5p + 8)$