Question

factorize 8x^3-2x^2+6x-1​

Answer 1

Step-by-step explanation:

8x3-2x2-6x

Final result :

2x • (x - 1) • (4x + 3)

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((8 • (x3)) - 2x2) - 6x

Step 2 :

Equation at the end of step 2 :

(23x3 - 2x2) - 6x

Step 3 :

Step 4 :

Pulling out like terms :

4.1 Pull out like factors :

8x3 - 2x2 - 6x = 2x • (4x2 - x - 3)

Trying to factor by splitting the middle term

4.2 Factoring 4x2 - x - 3

The first term is, 4x2 its coefficient is 4 .

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

The last term, "the constant", is -3

Step-1 : Multiply the coefficient of the first term by the constant 4 • -3 = -12

Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -1 .

-12 + 1 = -11

-6 + 2 = -4

-4 + 3 = -1 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 3

4x2 - 4x + 3x - 3

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

4x • (x-1)

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

3 • (x-1)

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

(4x+3) • (x-1)

Which is the desired factorization

Final result :

2x • (x - 1) • (4x + 3)