Question

Factorise 3x³+18x²-21x

Answer 1

Answer:

3x • (x + 1) • (x - 7)

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

((3 • (x3)) - (2•32x2)) - 21x

STEP

2

:

Equation at the end of step

2

:

(3x3 - (2•32x2)) - 21x

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

3x3 - 18x2 - 21x = 3x • (x2 - 6x - 7)

Trying to factor by splitting the middle term

4.2 Factoring x2 - 6x - 7

The first term is, x2 its coefficient is 1 .

The middle term is, -6x its coefficient is -6 .

The last term, "the constant", is -7

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

Step-2 : Find two factors of -7 whose sum equals the coefficient of the middle term, which is -6 .

-7 + 1 = -6 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and 1

x2 - 7x + 1x - 7

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

x • (x-7)

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

1 • (x-7)

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

(x+1) • (x-7)

Which is the desired factorization

Answer 2

3x³+18x²-21x

3x³+21x²-3x²-21x

3x²(x+7)-3x(x+7)

(x+7)(3x²-3x)

(x+7)3x(x-1)

3x(x+7)(x-1)

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