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If f(x)=5x 2 +3, then what is the remainder when f(x) is divided by x−6?

User Tim Jahn
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Final answer:

To find the remainder when f(x) is divided by x-6, substitute x-6 into f(x)=5x^2+3 and evaluate it. The remainder is

5x^2 - 60x + 183.

Step-by-step explanation:

To find the remainder when f(x) is divided by x-6, we can use the remainder theorem.

According to the remainder theorem, if we substitute the divisor x-6 into f(x) and evaluate it, the result will be the remainder.

So, substituting x-6 into f(x)=5x^2+3, we get:

f(x-6) = 5(x-6)^2 + 3

To simplify further, we can expand the binomial term:

f(x-6) = 5(x^2 - 12x + 36) + 3

Now, distribute the 5:

f(x-6) = 5x^2 - 60x + 180 + 3

Combine like terms:

f(x-6) = 5x^2 - 60x + 183

Therefore, the remainder when f(x) is divided by x-6 is 5x^2 - 60x + 183.

User Raja Asthana
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