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PLEASE HELP!! please do all steps! i’ll mark as brainliest!!!

Answer the following questions using what you've learned from this unit. Write your
responses in the space provided.
1. Factor the polynomial. (2 polnts)
-3x4 - 9x3 + 15x2
2. Use the grouping method to factor the polynomial below completely. (4 points)
10x3 - 35x2 + 6x - 21

PLEASE HELP Please Do All Steps Ill Mark As Brainliest Answer The Following Questions Using What Youve Learned From This Unit Write Your Responses In The Space class=

Sagot :

Answer: 1. 3x^2(-x^2-3x+5). 2. (2x-7)(5x^2+3)

Step-by-step explanation:

(1) Find the greatest common factor - 3x^2. Simplify as much as possible.

(2) Split 10x^3 - 35x^2 and 6x-21 into two separate groups. Factor each group separately to get 5x^2(2x-7) and 3(2x-7). The numbers in the parentheses should be the same for each group - (2x-7). Take the numbers outside of the parentheses and put them together to get (5x^2+3). Your final answer will be (2x-7)(5x^2+3).

1. The required factor of the polynomial is

(-3x²)(x²+3x-5).

2. The required factor of the polynomial using grouping method, the answer is (5x²+3)(2x-7).

What is a polynomial?

"A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables."

What is factorization of a polynomial?

"The factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.

There are six different methods to factorizing polynomials. One of those methods is factorization of a polynomial by grouping method."

1. The given polynomial is

[tex]-3x^{4} - 9x^{3} + 15x^{2} \\= - 3x^{2}(x^{2}+3x-5)\\[/tex]

Therefore, by factorizing the given polynomial, we get:

[tex]- 3x^{2}(x^{2}+3x-5)[/tex].

2. The given polynomial is

[tex]10x^{3}-35x^{2} +6x-21[/tex]

We need to factorize it using grouping method.

Therefore,

[tex]10x^{3}-35x^{2} +6x-21\\= 5x^{2}(2x-7)+3(2x-7)\\= (5x^{2} +3)(2x-7)[/tex]

Hence,

1. The required factor of the polynomial is

(-3x²)(x²+3x-5).

2. The required factor of the polynomial using grouping method, the answer is (5x²+3)(2x-7).

Learn more about the factorization of a polynomial here: https://brainly.com/question/10499871

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