f(x) = 4x^4 + 5x^3 + 2x^2 - 1

Are the following binomials factor of f(x)? x + l? , x - 1?

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The given polynomial is `f(x)=4x^4 + 5x^3 + 2x^2 - 1.`

To find if (x+1) is a factor of the given function, we have to use the factor theorem which states that (x-a) is a factor of f(x), if f(a)=0.

Here, `f(-1)=4(-1)^4 + 5(-1)^3 + 2(-1)^2 - 1.`

`=4-5+2-1=0`

Hence, (x+1) is a factor of the given f(x).

Again `f(1)=4(1)^4 + 5(1)^3 + 2(1)^2 - 1.`

` =4+5+2-1=10`

f(1)`!=` 0, so, (x-1) is not a factor of the given f(x).

**Therefore, of the given binomials, (x+1) is the factor of f(x).**

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