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Write the cubic function y=(6-x)(5-x)(x+1) in standard form.

User Eckes
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1 Answer

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Explanation:

First, let's multiply the factors using the distributive property.

(y = (6 - x)(5 - x)(x + 1))

= (6 - x)(5 - x)x + (6 - x)(5 - x)(1)

Next, we can simplify each term separately.

(6 - x)(5 - x)x = (30 - 6x - 5x + x^2)x

= 30x - 6x^2 - 5x^2 + x^3

(6 - x)(5 - x)(1) = (30 - 6x - 5x + x^2)(1)

= 30 - 6x - 5x + x^2

Now, we can combine the simplified terms.

y = (30x - 6x^2 - 5x^2 + x^3) + (30 - 6x - 5x + x^2)

= x^3 - 11x^2 + 19x + 30

Therefore, the cubic function y = (6 - x)(5 - x)(x + 1) in standard form is y = x^3 - 11x^2 + 19x + 30.

User Mohamed F
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