Question

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Answer 1

2n2 - 10n) - 28 = 0

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

2n2 - 10n - 28 = 2 • (n2 - 5n - 14)

Trying to factor by splitting the middle term

3.2 Factoring n2 - 5n - 14

The first term is, n2 its coefficient is 1 .

The middle term is, -5n its coefficient is -5 .

The last term, "the constant", is -14

Step-1 : Multiply the coefficient of the first term by the constant 1 • -14 = -14

Step-2 : Find two factors of -14 whose sum equals the coefficient of the middle term, which is -5 .

-14 + 1 = -13

-7 + 2 = -5 That's it

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

n2 - 7n + 2n - 14

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

n • (n-7)

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

2 • (n-7)

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

(n+2) • (n-7)

Which is the desired factorization

Equation at the end of step

3

:

2 • (n + 2) • (n - 7) = 0

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Answer 2

Answer:

${2n}^{2} - 10n - 28 = 0$

${2n}^{2} - 10n = 28$

${2n}^{2} - 10n - 28 = 2( {n}^{2} - 5n - 14 )$

The first term is, n2 its coefficient is 1 .

The middle term is, -5n its coefficient is -5 .

The last term, "the constant", is -14

Step-1 : Multiply the coefficient of the first term by the constant 1 • -14 = -14

Step-2 : Find two factors of -14 whose sum equals the coefficient of the middle term, which is -5 .

-14 + 1 = -13

-7 + 2 = -5 That's it

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

n2 - 7n + 2n - 14

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

n • (n-7)

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

2 • (n-7)

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

(n+2) • (n-7)

Which is the desired factorization