Friday

January 30, 2015

January 30, 2015

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

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 9:55pmLet 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 3:21pmhow do you convert 18 miles to meters?

**Answer this Question**

**Related Questions**

Math - 1. Identify the degree, leading term and leading coefficient of each ...

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 ...

Math - Determine whether the following statement makes sense or does not make ...

Pre Calculus - 1. Find all rational zeros of the polynomial. Then determine any ...

Math - Write a polynomial function in standard form that has the given zeros and...

Pre Calc - Use the Leading Coefficient Test to determine the end behavior of the...

algebra 2 - write a polynomial function of least degree that has real ...

math 8 - how do the degree and the sign of the leading coefficient correspond to...

algebra!!!! please help me!!!! - A number is called algebraic if there is a ...