1

Problem

Find the product of the following polynomials:
\$(4x^3 − 3x^2+ 2x −1)(x^4− 2x^3 + 3x^2 − 4x + 5)\$

2

Step

Now, let’s First compute the \$4x^3\$ multiplication:

\$4x^3(x^4 − 2x^3 + 3x^2 − 4x + 5)\$

=\$4x^7 - 8x^6 + 12x^5 - 16x^4 + 20x^3\$

3

Step

Then compute the \$- 3x^2\$ multiplication:

\$-3x^2 (x^4 −2x^3 + 3x^2 − 4x + 5)\$

=\$-3x^6 + 6x^5 - 9x^4 + 12x^3 -15x^2\$

4

Step

Next compute the 2x multiplication:

\$2x (x^4 − 2x^3 + 3x^2 − 4x + 5)\$

=\$ 2x^5 - 4x^4 + 6x^3 - 8x^2 + 10x\$

5

Step

Then compute the -1 multiplication:

\$-1(x^4−2x^3+3x^2−4x+5)\$

=\$-1x^4 + 2x^3 - 3x^2 + 4x - 5\$

6

Step

Now, sum up all the results:

\$4x^7 - 8x^6 + 12x^5 - 16x^4 +20x^3 - 3x^6 + 6x^5 - 9x^4 + 12x^3 -15x^2 + 2x^5 - 4x^4 + 6x^3 - 8x^2 + 10x -1x^4 + 2x^3 - 3x^2 + 4x -5\$

7

Step

Make it simplify the expression

\$4x^7 - 11x^6 + 20x^5 - 30x^4 + 40x^3 - 26x^2 + 14x - 5\$

8

Solution

So, the product of the given polynomials is \$4x^7 - 11x^6 + 20x^5 - 30x^4 + 40x^3 - 26x^2 + 14x - 5\$.

9

Sumup

Please Summarize Problem, Hint, Clue, Formula and Steps

Choices

10

Choice-A

This option is correct. It performed the accurate calculation.

Correct \$4x^7 -11x^6 + 20x^5 - 30x^4 + 40x^3 - 26x^2 + 14x - 5\$

11

Choice-B

Wrong due to different signs for some terms, so it’s incorrect

Wrong \$4x^7 - 11x^6 - 20x^5 - 27x^4 + 40x^3 - 26x^2 +14x - 5\$

12

Choice-C

It is wrong because it has a different combination of coefficients for the terms

Wrong \$4x^7 -11x^6 + 20x^5 - 30x^4 - 40x^3 + 26x^2 + 14x - 5\$

13

Choice-D

This is inaccurate due to incorrect signs across multiple terms

Wrong \$4x^7 + 11x^6 - 20x^5 + 27x^4 + 40x^3 + 26x^2 + 14x + 5\$

14

Step

Option

A

5

Sumup

Please Summarize Choices