Question

Based on the polynomial reminder theorem, what is the value of the function when x= -5

Answer 1

Answer:

-15

Step-by-step explanation:

Given is a polynomial in x

$F (x)= x^4 + 12x^3 + 30x^2 - 12x + 70$

We have to find the remainder when the above polynomial is divided by x+5

Remainder theorem says that f(x) gives remainder R when divided by polynomial x-a means f(a) = R

Applying the above theorem we can say that value of the function when x =-5

= Remainder when f is divided by x+5

= F(-5)

Substitute the value of -5 in place of x

= (-5)^4 + 12(-5)^3 + 30(-5)^2 - 12(-5) + 70

= 625-1500+750+60+70

= 5

Hence answer is 5

Answer 2

Answer:

$f(-5)=$ 5

Step-by-step explanation:

According to the polynomial remainder theorem, when a polynomial f(x) is divided by a linear polynomial (x - a), the remainder of that division will be equal to f(a).

Therefore, substituting the value of x as -5 in the given function to find its value:

$f(x)$ = $x^4 + 12x^3 + 30x^2 - 12x + 70$

$f(-5)$ = $(-5)^4 + 12(-5)^3 + 30(-5)^2 - 12(-5) + 70$

$f(-5)$ = $625+(-1500)+750-(-60)+70$

$f(-5)$ = $5$

Therefore, the value of the given function when x = -5 is 5.