SOLUTION: I don't understand how to get the final answer to this type of problem. Fourth degree, zeros of -5,-2,1, and 3, and y-intercept of 15. p(x)=a(x+5)(x+2)(x-1)(x-3) p(0)=a(5)(2

Question 167067This question is from textbook College Algebra
: I don't understand how to get the final answer to this type of problem.
Fourth degree, zeros of -5,-2,1, and 3, and y-intercept of 15.
p(x)=a(x+5)(x+2)(x-1)(x-3)
p(0)=a(5)(2)(-1)(-3)=30a
30a=15 a=1/2
p(x)=1/2(x+5)(x+2)(x-1)(x-3) How do you mutiply out the four linear factors and the constant?
This question is from textbook College Algebra

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Distributive property
Let's look at Z(C+D)=ZC+ZD.
What if Z=A+B?
Then
Z(C+D)=(A+B)(C+D)=ZC+ZD=(A+B)C+(A+B)D=AC+BC+AD+BD
So then,

and

This is the FOIL method for expanding quadratic equations from factors.
.
.
.
Now the problem becomes,

Let's look at the product of the two quadratics,
.
.
.
We again have to use the distributive property and make sure we account for each term.
There are nine terms in all.

Now we'll put that back in our original function.

.
.
.
Check, as an exercise, that we didn't make any mistakes and that x= -5,-2,1, and 3 are in fact zeros of this polynomial.

So that checks out.
RELATED QUESTIONS
Find a polynomial f(x) of degree 3 that has the indicated zeros -2 1 5 and satisfies the... (answered by stanbon)

Hey, If you could help me remember how to do this type of problem it would be AWESOME! (answered by John10)

I have a question on polynomials with prescribed zeros. The problem is find polynomial... (answered by ankor@dixie-net.com)

my math teacher taught us how to do this but i don't understand (3,2), y = x + 5 (answered by josgarithmetic)

Solve for y, x+5y=25, I need to know how to work this type of problem out. I have tried... (answered by Fombitz)

Information is given about a polynomial f(x) whose coefficients are all real numbers.... (answered by ikleyn)

What is the radius of a circle with an area of 144 pi? The correct answer is 12 but when (answered by ewatrrr)

f(x)=3X+2 and g(x)=-2X+1 find g(f(-2)) I don't understand how to solve this... (answered by ikleyn)

9{[5(c-4)+15]-[3(5c-2)+4]}= I have been working on problems lke this one for the last... (answered by arallie)