Question

32+7x+2
$32 + 7x + 2$
​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

((0 - 7x2) + 32x) - 33

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

-7x2 + 32x - 33 = -1 • (7x2 - 32x + 33)

Trying to factor by splitting the middle term

3.2 Factoring 7x2 - 32x + 33

The first term is, 7x2 its coefficient is 7 .

The middle term is, -32x its coefficient is -32 .

The last term, "the constant", is +33

Step-1 : Multiply the coefficient of the first term by the constant 7 • 33 = 231

Step-2 : Find two factors of 231 whose sum equals the coefficient of the middle term, which is -32 .

-231 + -1 = -232

-77 + -3 = -80

-33 + -7 = -40

-21 + -11 = -32 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -21 and -11

7x2 - 21x - 11x - 33

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

7x • (x-3)

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

11 • (x-3)

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

(7x-11) • (x-3)

Which is the desired factorization

Final result :

(3 - x) • (7x - 11