Posted by **Emily** on Tuesday, September 1, 2009 at 9:44pm.

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 -
**MathMate**, Tuesday, September 1, 2009 at 9:55pm
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 -
**Linda**, Thursday, September 10, 2009 at 3:21pm
how do you convert 18 miles to meters?

## Answer This Question

## Related Questions

- Math - 1. Identify the degree, leading term and leading coefficient of each ...
- Math - Determine whether the following statement makes sense or does not make ...
- POLYNOMIALS - The cubic polynomial f(x) is such that the coefficient of x^3 is -...
- Math (polynomial functions) - Hi there, Can someone please help me understand ...
- Maths - Check my answer please? Not sure if I did this right. Let y = f(x) be a ...
- math algebra 2 - polynomial complete the table for -7x^4+8x^3-3x^2+5x-9 not sure...
- algebra - A cubic polynomial function f(x) has leading coefficient -2 and ...
- Pre Calculus - 1. Find all rational zeros of the polynomial. Then determine any ...
- Algebra - Sketch the graph of a polynomial of degree 2 with a leading ...
- Algebra - Sketch the graph of a polynomial of degree 3 with a positive leading ...

More Related Questions