Question

Which polynomial is prime?
A. 7x^2 – 35x + 2x – 10
B. 9x^3 + 11x^2 + 3x – 33
C. 10x^3 – 15x^2 + 8x – 12
D. 12x^4 + 42x^2 + 4x^2 + 14

Answer 1

Answer:

C.$9x^{3}+11 x^{2} +3x-33$

Step-by-step explanation:

A polynomial is prime if it can't be factored in polynomials of lower degree. Let's factorize:

A. $7x^{2} -35x+2x-10$

In this case we have 4 terms, so we can use Grouping:

Part a:

$7x^{2} -35x$

We're going to use Greatest common factor:

$=7x^{2} -7.5x\\=7x(x-5)$

Part b:

$2x-10$

In this part we also use greatest common factor:

$2x-10=2x-2.5\\=2(x-5)$

Then,

$7x^{2} -35x+2x-10=\\ 7x(x-5)+2(x-5)=\\ =(7x+2)(x-5)$

This polynomial is not prime.

B. $9x^3 + 11x^2 + 3x-33$

This polynomial cannot be factorized then it's prime.

C.$10x^3-15x^2 + 8x-12$

In this polynomial we can use grouping too:

Part a:

$10x^3 -15x^2=2.5x^3-3.5x^2\\=5x^2(2x-3)$

Part b:

$8x-12=4.2x-4.3\\=4(2x-3)$

Then,

$10x^3-15x^2 + 8x-12=\\=5x^2(2x-3)+4(2x-3)\\=(5x^2+4)(2x-3)$

This polynomial isn't prime.

D. $12x^4 + 42x^2 + 4x^2 + 14$

First we're going to use Greatest common factor:

$12x^4 + 42x^2 + 4x^2 + 14=\\2.6x^4+2.21x^2+2.2x^2+2.7=2(6x^4+21x^2+2x^2+7)$

Now we're going to apply grouping on the terms inside of the parenthesis:

$6x^4+21x^2+2x^2+7$

Part a:

$6x^4+2x^2=2.3x^4+2x^2=2x^2(3x^2+1)$

Part b:

$21x^2+7=7.3x^2+7=7(3x^2+1)$

Then,

$6x^4+21x^2+2x^2+7=2x^2(3x^2+1)+7(3x^2+1)\\=(2x^2+7)(3x^2+1)$

Remember that at the beginning we use Greatest common factor:

$12x^4 + 42x^2 + 4x^2 + 14=\\=2.(6x^4+21x^2+2x^2+7)\\=2(2x^2+7)(3x^2+1)$

This polynomial isn't prime.

Answer 2

Answer:

B not C  9x^3 + 11x^2 + 3x - 33

Step-by-step explanation: