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2 years ago

Simplify the following polynomial expression.

Mathematics

1 answer:

victus00 [196]2 years ago

7 0

Answer:

5x^4 -37x^3 -6x^2 +41x -6

Step-by-step explanation:

We simplify this expression by removing parentheses and combining like terms. Parentheses are removed using the distributive property.

<h3>Form the product</h3>

The product of the final pair of polynomials in parentheses is ...

(-4x^3 +5x -1)(2x -7) = (-4x^3 +5x -1)(2x) +(-4x^3 +5x -1)(-7)

= -8x^4 +10x^2 -2x +28x^3 -35x +7

= -8x^4 +28x^3 +10x^2 -37x +7

<h3>Combine with remaining sums</h3>

= (5x^4 -9x^3 +7x -1) + (-8x^4 +4x^2 -3x +2) - (-8x^4 +28x^3 +10x^2 -37x +7)

= (5 -8 -(-8))x^4 +(-9 -28)x^3 +(4 -10)x^2 +(7 -3 -(-37))x +(-1 +2 -7)

= 5x^4 -37x^3 -6x^2 +41x -6

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