Question

Is X +10 a factor of F(x)= 5X^3 +60X^2+109X+90?

Answer 1

To check if X+10 is a factor of F(x), we can use the factor theorem. We need to check if F(-10) equals to zero. If it does, then X+10 is a factor of F(x).

F(-10)=5(-10)^3+60(-10)^2+109(-10)+90 = -5000+6000-1090+90 = -10

Since F(-10) is not equal to zero, X+10 is not a factor of F(x).

Answer 2

FACTOR OF A POLYNOMIAL

`\mathbb{ANSWER:}`

We can use the factor theorem which states that
`\sf (x - a)` is a factor of
`\sf f(x)`, then
`\sf f(a) = 0`.

Solve for f(-10).

`\sf \rightarrow f(x)=5x^3 + 60x^2 + 109x + 90`

`\sf \rightarrow f(-10)=5(-10)^3 + 60(-10)^2 + 109(-10) + 90`

`\sf \rightarrow f(-10)=5(-1000) + 60(100) + 109(-10) + 90`

`\sf \rightarrow f(-10)=(-5000) + (6000) + (-1090) + 90`

`\sf \rightarrow f(-10)=0`

Hence, (x + 10) is a factor since the remainder is zero.