Homework Help

f(x) = 4x^4 + 5x^3 + 2x^2 - 1 Are the following binomials factor of f(x)?     x + l?...

user profile pic

kristenmarieb... | Student, Grade 10 | Valedictorian

Posted July 24, 2013 at 4:55 AM via web

dislike 1 like

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

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

Tagged with algebra2, math

1 Answer | Add Yours

user profile pic

llltkl | College Teacher | Valedictorian

Posted July 24, 2013 at 5:40 AM (Answer #1)

dislike 1 like

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).

 

 

Sources:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes