Question

The quotient of (x^4 + 5x^3 – 3x – 15) and a polynomial is (x^3 – 3). What is the polynomial?

Answer 1

a. x7 + 5x6 – 6x4 – 30x3 + 9x + 45
b. x – 5
c. x + 5
d. x7 + 5x6 + 6x4 + 30x3 + 9x + 45

Answer 2

Hey dear

Answer 3

so what did you do so far?

Answer 4

we use long division, synthetic

Answer 5

I'm not really sure how to solve it.

Answer 6

but for me I would go for another way

Answer 7

let P(x) be the missing polynomial

Answer 8

so P(x) (x^3-3)=x^4 + 5x^3 – 3x – 1

Answer 9

since we have power 4 in the right
our P(x) cannot be more that degree 1 polynomial

Answer 10

knowing that we rewrite it as Ax+B
so our goal is to find A and B

Answer 11

\((Ax+B)(x^3-3)=x^4 + 5x^3 – 3x – 15\)
\(Ax^4-3Ax+Bx^3-3B=x^4 + 5x^3 – 3x – 15\)
\(Ax^4+Bx^3-3Ax-3B=x^4 + 5x^3 – 3x – 15\)

Answer 12

for left to equal right
the coefficients must equal

Answer 13

you can find A and B now

Answer 14

good luck