# Can I get some assistance on this function in precalculus?Use the remainder theorem to find the remainder when f(x) is divided by x+5. Then use the factor theorem to determine whether x+5 is a...

Can I get some assistance on this function in precalculus?

Use the remainder theorem to find the remainder when f(x) is divided by x+5. Then use the factor theorem to determine whether x+5 is a factor of f(x).

f(x) = x^4 + 5x^3 - 7x^2 - 32x + 15

### 2 Answers | Add Yours

Given `x^4+5x^3-7x^2-32x+15` :

The remainder theorem states that the remainder when f(x) is divided by (x-c) is f(c).

**Thus the remainder of `f(x)=x^4+5x^3-7x^2-32x+15` when divided by (x+5) is f(-5)=0.**

The factor theorem states that if the remainder when f(x) is divided by (x-c) is zero, then (x-c) is a factor.

**Thus (x+5) is a factor.**

`f(x)= x^4 + 5x^3 - 7x^2 -32x + 15 `

`==gt f(x)= (x^4+5x^3)- (7x^2 +32x -15)`

Now we will factor x^3 from the first two terms and then factor the quadratic equation ( last 3 terms.).

`==gt f(x)= x^3(x+5) - (7x-3)(x+5).`

`` Now we will factor (x+5) .

`==gt f(x)= (x+5) (x^3-(7x-3)) `

`==gt f(x)= (x+5)(x^3 -7x+3)`

`` We notice that (x+5) is a factor of f(x).

**Then the remainder when f(x) is divided by (x+5) is zero because (x+5) is a factor of f(x).**