Question

PLEASE HELP In your answer, write a polynomial that cannot be factored further. Explain in detail how you know it can’t be factored further. Describe the factoring techniques that might work with this polynomial, and show why they don’t work.

Answer 1

Explanation:

(x-m)

comp w. (x-a)

a=m

f(X) = a * q(X)

Answer 2

I explained a lot bc I’m not sure how in detail you want, so only pay attention to what you need :)

x^2 + 9x + 4

There is not way this could be factored further, because no two numbers have a product of 4 and a sum of 9. (No two numbers can be multiplied together to equal 4 and added together to give nine).

Because of this, the typical factoring technique that you would use for a polynomial in this form (ax^2 + bx + c) wouldn’t work:

Using the equation y= ax^2 + bx +c, you would typically multiply a with c. Then, you would try to find 2 numbers that can be multiplied together to equal a times c, but added together to equal b.

Using the equation I gave above, I’ll explain why this doesn’t work:

x^2 + 9x + 4

In this example, a times c is 1 times 4, which is 4. And b is 9. Therefore, you need 2 numbers that multiply to give 4 and add to give nine. But, the only numbers that multiply to give 4 are: 1,2,4.

1 + 4 = 5
2 + 2 = 4

Therefore, this polynomial is not able to be factored.