Factor each of the algebraic expressions completely. 12x^{3}-52x^{2}-40x



Answered question


Factor each of the algebraic expressions completely. 12x352x240x

Answer & Explanation



Beginner2021-12-27Added 33 answers

We find factor of 12x352x240x
We find factor of 12x352x240x
Now 12x352x240x
Hence 12x352x240x=4x(x5)(3x+2)
Karen Robbins

Karen Robbins

Beginner2021-12-28Added 49 answers

Factor 4x out of 12x352x240x


Expert2022-01-08Added 669 answers

((12 * (x3))-(22 * 13x2))-40x
((22 * 3x2)-(22 * 13x2))-40x
12x3-52x2-40x=4x * (3x2-13x-10)
Factoring 3x2-13x-10
The first term is, 3x2 its coefficient is 3.
The middle term is, -13x its coefficient is -13.
The last term, "the constant", is -10
Step-1 : Multiply the coefficient of the first term by the constant 3 * -10 = -30
Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is -13.
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 2.
3x2 - 15x + 2x - 10
Step-4 : Add up the first 2 terms, pulling out like factors :
3x * (x-5)
Add up the last 2 terms, pulling out common factors:
2 * (x-5)
Step-5 : Add up the four terms of step 4:
(3x+2) * (x-5)
Which is the desired factorization
Answer: 4x * (x-5) * (3x+2)

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