# Precalculus

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I'm sorry I'm posting so many questions, I promise this is the last one tonight :)

The leading coefficient of a cubic polynomial P is 2, and the coefficient of the linear term is -5. If P(0)=7 and P(2)=21, find P(3).

I DO NOT understand how to even start this one. I thought as you write out the equation, you also have to add the constant at the end that makes the equation comply with the P(0)=... terms above, but that doesn't work. ANY help is greatly appreciated! :D

• Precalculus - ,

Let the cubic polynomial be
P(x)=Ax³ + Bx² + Cx + D

"The leading coefficient of a cubic polynomial P is 2", so A=2.

"and the coefficient of the linear term is -5.", so C=-5

P(0)=7, i.e. when x=0, P(0)=7, so D=7.

The only unknown is B.
Thus
P(x)= 2x³ + Bx² -5x + 7

"P(2)=21". If we substitute x=2, we obtain P(2)=4B+13 = 21
Therefore
B=(21-13)/4=2

The polynomial is now completely determined:
P(x)= 2x³ + 2x² -5x + 7
P(3)= 2*3³+2*²-5*(3)+7
=54+18-15+7
=64

• Precalculus - ,

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