Question

Let P be a polynomial where P(x) = (x+6)(x+3)(x-5)

1. Rewrite the polynomial in standard form.
2. Identify the degree and the constant term.​

Answer 1

1. P(x) = x^3 +4x^2 -27x -90

2. degree: 3; constant: -90

Explanation:

1. You can multiply the factors 2 at a time using the distributive property.

P(x) = (x +6)(x(x -5) +3(x -5)) = (x +6)(x^2 -5x +3x -15)

= (x +6)(x^2 -2x -15) = x(x^2 -2x -15) +6(x^2 -2x -15)

= x^3 -2x^2 -15x +6x^2 -12x -90

P(x) = x^3 +4x^2 -27x -90

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2. The degree is 3, the highest power. The constant term is the one without any variables: -90.