Precalculus
posted by Emily on .
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

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=(2113)/4=2
The polynomial is now completely determined:
P(x)= 2x³ + 2x² 5x + 7
P(3)= 2*3³+2*²5*(3)+7
=54+1815+7
=64 
how do you convert 18 miles to meters?