Question

Is (x + 5) a factor of f(x) = x3 − 4x2 + 3x + 7? Use either the remainder theorem or the factor theorem to explain your reasoning. This is worth 100 points. Will mark brainliest. Whatever you want. Please answer this.

Answer 1

Answer:

(x + 5) is not a factor of, $f(x) = x^ 3 − 4x^2 + 3x + 7$

Step-by-step explanation:

$f(x) = x^ 3 − 4x^2 + 3x + 7 \\ \\ let \: x + 5 = 0 \\ \implies \: x = - 5 \\ \\ plug \: x = - 5 \: in \: f(x) \\ \\ f( - 5) = ( - 5)^ 3 − 4( - 5)^2 + 3( - 5) + 7 \\ \\ f( - 5) = - 125 − 4(25) - 3( 5) + 7 \\ \\ f( - 5) = - 125 − 100 - 15 + 7 \\ \\ f( - 5) =7 - 240 \\ \\ f( - 5) = - 233 \\ \\ \because \: f( - 5) \neq 0 \\ \implies \: remainder\: is\: not\: zero\\ \therefore \: (x + 5) \: is \: not \: a \: factor \: of \: \\ f(x) = x^ 3 − 4x^2 + 3x + 7$

Answer 2

I’m gonna use the remainder theorem so if a polynomial p(x) is divided by x-a the remainder obtained is p(a) therefore

X= -5

Then just plug in -5 in the function and if the result is 0 then is a factor

(-5)^3 - 4(-5)^2 + 3(-5) + 7 = -233

Therefore x+5 is not a factor