Question

Complete the steps to factor 56x2 – 8x – 7x + 1 by grouping.

Answer 1

Step-by-step explanation:

The first term is, 56x2 its coefficient is 56 .

The middle term is, -15x its coefficient is -15 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 56 • 1 = 56

Step-2 : Find two factors of 56 whose sum equals the coefficient of the middle term, which is -15 .

-56 + -1 = -57

-28 + -2 = -30

-14 + -4 = -18

-8 + -7 = -15 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and -7

56x2 - 8x - 7x - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

8x • (7x-1)

Add up the last 2 terms, pulling out common factors :

1 • (7x-1)

Step-5 : Add up the four terms of step 4 :

(8x-1) • (7x-1)

Which is the desired factorization

Final result :

(7x - 1) • (8x - 1)