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Please help me with these questions , thank you​

Please help me with these questions , thank you​-example-1

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Answer:

1. 4
x^(3) + 26x² + 4x - 48

2. 2
x^(3) - 23x² + 60x - 32

3.
x^(5) + 7
x^(3) - 4x + 2
x^(4) + 14x² - 8

4. 2
x^(7) +
x^(6) - 28
x^(5) + 3x + 12

Explanation:

To multiply polynomials, simply distribute whatever's outside the largest set of parenthesis, then combine like terms.

1) Distribute the parenthesis (x + 6):

x(4x² + 2x - 8) + 6(4x² + 2x - 8)

4
x^(3) + 2x² -8x + 6(4x² + 2x -8)

4
x^(3) + 2x² -8x + 24x² + 12x - 48

Combine like terms:

4
x^(3) + 26x² + 4x - 48

2) Distribute the parenthesis (x - 8):

x(2x² - 7x + 4) + (-8)(2x² - 7x + 4)

2
x^(3) - 7x² + 4x + (-8)(2x² - 7x + 4)

2
x^(3) - 7x² + 4x + -16x² + 56x - 32

Combine like terms:

2
x^(3) - 23x² + 60x - 32

3) Distribute the parenthesis (x + 2):

x(
x^(4) + 7x² - 4) + 2(
x^(4) + 7x² - 4)


x^(5) + 7
x^(3) - 4x + 2(
x^(4) + 7x² - 4)


x^(5) + 7
x^(3) - 4x + 2
x^(4) + 14x² - 8

No like terms to combine, so:


x^(5) + 7
x^(3) - 4x + 2
x^(4) + 14x² - 8

4) Distribute the parenthesis (x + 4):

x(2
x^(6) - 7
x^(5) + 3) + 4(2
x^(6) - 7
x^(5) + 3)

2
x^(7) - 7
x^(6) + 3x + 4(2
x^(6) - 7
x^(5) + 3)

2
x^(7) - 7
x^(6) + 3x + 8
x^(6) - 28
x^(5) + 12

Combine like terms:

2
x^(7) +
x^(6) - 28
x^(5) + 3x + 12

hope this helps!

User Zstefanova
by
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