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VladimirAG [237]
3 years ago
14

What is the product of the polynomials below?

Mathematics
1 answer:
Irina-Kira [14]3 years ago
3 0

Answer:

B

(x+4)(x2−8x+3)

=(x+4)(x2+−8x+3)

=(x)(x2)+(x)(−8x)+(x)(3)+(4)(x2)+(4)(−8x)+(4)(3)

=x3−8x2+3x+4x2−32x+12

=x3−4x2−29x+12

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If x+a is a factor of 2x²+2ax+5x+10,find a.
vazorg [7]

If x+a is a factor of the polynomial, it means that -a is a root of the polynomial.

In fact, if a polynomial p(x) has a root x_0 (i.e. p(x_0)=0), then the polynomial is divisible by (x-x_0)

In your case, you know that the polynomial is divisible by (x+a)=(x-(-a)), so -a is a solution.

Let's evaluate p(-a) and set it to zero:

2(-a)^2+2a(-a)+5(-a)+10 = 0 \iff 2a^2-2a^2-5a+10=0 \iff -5a+10 = 0 \iff a = 2

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And we're claiming that -a=-2 is a root of this polynomial:

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Step-by-step explanation:

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