Question

8n^2-4n-180
(factories)
​

Answer 1

Answer:

Step by step solution :

STEP

1

:

Equation at the end of step 1

(23n2 - 4n) - 180 = 0

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

8n2 - 4n - 180 = 4 • (2n2 - n - 45)

Trying to factor by splitting the middle term

3.2 Factoring 2n2 - n - 45

The first term is, 2n2 its coefficient is 2 .

The middle term is, -n its coefficient is -1 .

The last term, "the constant", is -45

Step-1 : Multiply the coefficient of the first term by the constant 2 • -45 = -90

Step-2 : Find two factors of -90 whose sum equals the coefficient of the middle term, which is -1 .

-90 + 1 = -89

-45 + 2 = -43

-30 + 3 = -27

-18 + 5 = -13

-15 + 6 = -9

-10 + 9 = -1 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 9

2n2 - 10n + 9n - 45

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

2n • (n-5)

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

9 • (n-5)

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

(2n+9) • (n-5)

Which is the desired factorization

Equation at the end of step

3

:

4 • (n - 5) • (2n + 9) = 0

STEP

4

:

Theory - Roots of a product

4.1 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.

Equations which are never true:

4.2 Solve : 4 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Answer 2

Answer:

$the \: answer \: is \: 0$

Step-by-step explanation:

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