Answer:
2x - 7
Explanation:
4x² - 2x - 42 ( factor out 2 from each term )
= 2(2x² - x - 21) ← factor the quadratic
consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 21 = - 42 and sum = - 1
the factors are+ 6 and - 7
use these factors to split the x- term
2x² + 6x - 7x - 21 ( factor the first/second and third/fourth terms )
= 2x(x + 3) - 7(x + 3) ← factor out (x + 3) from each term
= (x + 3)(2x - 7)
then
4x² - 2x - 42 = 2(x + 3)(2x - 7) ← in factored form
with 2x - 7 as a factor