Question

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Answer 1

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Step by step solution :

STEP

1

:

Equation at the end of step 1

((2•3m2) - 13m) - 5 = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 6m2-13m-5

The first term is, 6m2 its coefficient is 6 .

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

The last term, "the constant", is -5

Step-1 : Multiply the coefficient of the first term by the constant 6 • -5 = -30

Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is -13 .

-30 + 1 = -29

-15 + 2 = -13 That's it

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

6m2 - 15m + 2m - 5

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

3m • (2m-5)

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

1 • (2m-5)

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

(3m+1) • (2m-5)

Which is the desired factorization

Equation at the end of step

2

:

(2m - 5) • (3m + 1) = 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 prod