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How do you use the remainder theorem to find the remainder for each division #(2x^3-3x^2+x)div(x-1)#?

Answer 1

Lincoln Anderson

#0#

The remainder theorem states that if you divide #P(x)# by #(x-a)#

the remainder will be #P(a)#

so dividing #P(x)=(2x^3-3x^2+x)" "#by #" "(x-1)#

will give a remainder of #P(1)#

#P(1)=2xx1^3-3xx1^2+1#

#P(1)=2-3+1=0#

which means that in this case #(-1)# is a factor of #P(x)#

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Answer 2

Chloe Alexander

To use the remainder theorem, substitute the value of the divisor (x - 1) into the polynomial (2x^3 - 3x^2 + x) to find the remainder. When x equals 1, the polynomial becomes (2(1)^3 - 3(1)^2 + 1), which simplifies to (2 - 3 + 1) or 0. Therefore, the remainder for the division is 0.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.