Mathematics: The quotient of (x^4 + 5x^3– 3x – 15) and a polynomial is (x^3 - 3). what is the polynomia

The quotient of (x^4 + 5x^3– 3x – 15) and a polynomial

Ответ:

hailiemanuel930

14.01.2022

The missing polynomial must be of degree 1, since the dividend has degree 4 and the divisor has degree 3. So we're looking for a polynomial ax+b such that

(x^3-3)(ax+b)=x^4+5x^3-3x-15

Expanding the left hand side gives

ax^4+bx^3-3ax-3b

We need to have

$\begin{cases}ax^4=x^4\\bx^3=5x^3\\-3ax=-3x\\-3b=-15\implies a=1,b=5$

so that the missing polynomial is $\boxed{x+5}$ .

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Ответ:

CelesteN64

03.06.2021

Mathematics

$- ( - 6.8k + 8) \\ = + 6.8k - 8 \\ thank \: you$

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The quotient of (x^4 + 5x^3– 3x – 15) and a polynomial is (x^3 - 3). what is the polynomia

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