Question

PLEASE ANSWER!! 25 POINTS

2. What is the product of -2 x^3+x-5 and x^3-3 x-4?

(a)Show your work.

(b) equal to the product of -2 x^3+x-5 and x^3-3 x-4 ?
Explain your answer.

Answer:

Answer 1

-2x^6 +7x^4 +3x^3 -3x^2 +11x +20

Explanation:

(a) I wrote the coefficients down as ...

-2 0 1 -5

1 0 -3 -4

and used a progressive patterns of Xs to compute the product.

• x^6 term: (-2)(1) ⇒ -2x^6
• x^5 term: (-2)(0) + (1)(0) = 0
• x^4 term: (-2)(-3) + (1)(1) + (0)(0) ⇒ 7x^4
• x^3 term: (-2)(-4) + (1)(-5) + (0)(-3) + (0)(1) ⇒ 3x^3
• x^2 term: (0)(-4) + (0)(-5) + (1)(-3) ⇒ -3x^2
• x term: (1)(-4) + (-3)(-5) ⇒ 11x
• constant: (-5)(-4) ⇒ 20

So, the result is ...

-2x^6 +7x^4 +3x^3 -3x^2 +11x +20

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(b) The factors are the same, so the product will be the same.