Factor by grouping (sometimes called the ac-method) 11x^2+15x+4

Question

Factor by grouping (sometimes called the ac-method).

11x²+15x+4

Specify the correct form.

Then, fill in the blanks with numbers to be used for grouping.

Finally, show the factorization.

Answer 1

11x^2 + 15x + 4

a=11, c= 4

ac =11(4) =44

find two factors of 44 that sum to 15

11 and 4. 15x = 11x +4x

11x^2 +15x + 4

11x^2 + 11x +4x +4

group the 1st two terms and the last two terms

(11x^2 + 11x) + (4x+4)

factor out 11x from the 1st grouping and 4 from the 2nd grouping

= 11x(x+1) = 4(x+1)

= (11x +4)(x+1)

using FOIL

= 11x^2 + 11x + 4x + 4

= 11x^2 + 15x + 4