Question

factorize by splitting middle term 12x² + 13x - 35. please tell me fast
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Answer 1

Answer:

Step by step solution :

STEP

1

:

Equation at the end of step 1

((22•3x2) - 13x) - 35 = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 12x2-13x-35

The first term is, 12x2 its coefficient is 12 .

The middle term is, -13x its coefficient is -13 .

The last term, "the constant", is -35

Step-1 : Multiply the coefficient of the first term by the constant 12 • -35 = -420

Step-2 : Find two factors of -420 whose sum equals the coefficient of the middle term, which is -13 .

-420 + 1 = -419

-210 + 2 = -208

-140 + 3 = -137

-105 + 4 = -101

-84 + 5 = -79

-70 + 6 = -64

-60 + 7 = -53

-42 + 10 = -32

-35 + 12 = -23

-30 + 14 = -16

-28 + 15 = -13 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -28 and 15

12x2 - 28x + 15x - 35

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

4x • (3x-7)

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

5 • (3x-7)

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

(4x+5) • (3x-7)

Which is the desired factorization

Equation at the end of step

2

:

(3x - 7) • (4x + 5) = 0

STEP

3

:

Theory - Roots of a product

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well

Step-by-step explanation:

I HOPE THAT IT'S HELPFUL FOR YOU.

Answer 2

Step-by-step explanation:

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