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Ghella [55]
3 years ago
13

What is the factored form of the function f(x)=x^3+8x^2+5x−50?

Mathematics
1 answer:
Inga [223]3 years ago
3 0

Answer:

the factors of  f(x)=x^3+8x^2+5x-50 are (x-2)(x+5)(x+5)

Step-by-step explanation:

We need to factorise the function f(x)=x^3+8x^2+5x-50

If a number is a factor of this function than it must be completely divisible by last co-efficient. Our last co-efficient is -50

Checking few numbers:

f(1)=(1)^{3}+8(1)^2+5(1)-50\\f(1)=1+8+5-50\\f(1)=-32\\Now \ putting \ x= 2 \\f(2)=(2)^{3}+8(2)^2+5(2)-50\\f(2)=8+8(4)+10-50\\f(2)=8+32+10-50\\f(2)=0

So, f(2)=0 which means x-2 is a factor of the given function. Now we will perform long division of x^3+8x^2+5x-50 by (x-2) to find other factors

The long division is shown in figure attached.

After long division we get: x^2+10x+25

The equation x^2+10x+25 can be further simplified as: (x+5)(x+5) or (x+5)^2

So, the factors of  f(x)=x^3+8x^2+5x-50 are (x-2)(x+5)(x+5)

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