ℓ(x)=x^(4)+36x^(2)-10,000 The polynomial function ℓ is defined. What is the remainder of ℓ(x) when divided by x+10 ?

Use Remainder Theorem: To find the remainder of ℓ(x) when divided by x + 10, we can use the Remainder Theorem. The Remainder Theorem states that the remainder of a polynomial f(x) divided by x - k is f(k). Since we are dividing by x + 10, we will find ℓ(-10).Substitute x = -10: Substitute x = -10 into the polynomial ℓ(x). ℓ(-10) = (-10)^4 + 36(-10)^2 - 10,000Calculate value of ℓ(-10): Calculate the value of ℓ(-10). ℓ(-10) = (10000) + 36(100) - 10,000 ℓ(-10) = 10000 + 3600 - 10000Simplify expression: Simplify the expression to find the remainder. ℓ(-10) = 10000 + 3600 - 10000 ℓ(-10) = 3600

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ℓ(x)=x^(4)+36x^(2)-10,000
The polynomial function
ℓ is defined. What is the remainder of
ℓ(x) when divided by
x+10 ?

$\ell(x)=x^{4}+36 x^{2}-10,000$ $\newline$ The polynomial function $\ell$ is defined. What is the remainder of $\ell(x)$ when divided by $x+10$ ?

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Math Problems

Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

\ell(x)=x^{4}+36 x^{2}-10,000

\newline

The polynomial function

\ell

is defined. What is the remainder of

\ell(x)

when divided by

x+10

Use Remainder Theorem: To find the remainder of $\ell(x)$ when divided by $x + 10$ , we can use the Remainder Theorem. The Remainder Theorem states that the remainder of a polynomial $f(x)$ divided by $x - k$ is $f(k)$ . Since we are dividing by $x + 10$ , we will find $\ell(-10)$ .
Substitute $x = -10$ : Substitute $x = -10$ into the polynomial $\ell(x)$ . $\ell(-10) = (-10)^4 + 36(-10)^2 - 10,000$
Calculate value of $\ell(-10)$ : Calculate the value of $\ell(-10)$ . $\ell(-10) = (10000) + 36(100) - 10,000$ $\ell(-10) = 10000 + 3600 - 10000$
Simplify expression: Simplify the expression to find the remainder. $\newline$ $\ell(-10) = 10000 + 3600 - 10000$ $\newline$ $\ell(-10) = 3600$