For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response

Question

Part A: If the result of a division problem is as x^3+2x^2+3x-4=(x^2+3x+6)(x-1)+2, identify the dividend, quotient, divisor, and remainder. What do you know about the function at x=1?

Part B: When the polynomial P(x)=3x^3+22x^2+38x+15 is divided by (x+2), the remainder is 3. What is known about the function?

Part C: If P(-5)=0, what is known about the function?

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Answer 1

Part A

If you plug in x=1, you will get 2 as a result because 1-1=0 and the whole product except the +2 at the end becomes 0.

Part B

Since the remainder is not 0, then x+2 is not a factor of the polynomial P(x).

Part C

P(-5)=0 tells us that we have a remainder of zero when we divide the polynomial P(x) by x+5, which means x+5 is a factor of the polynomial.

Hope the explanations helped!