Math Help Please

Question

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.

Third-degree, with zeros of −3,−1, and 2, and a y-intercept of −7.

Answer 1

Hi Ty,

If -3,-1, and 2 are zeroes, then (x+3) is a factor, (x+1) is a factor, and (x-2) is a factor, respectively.

So we have P(x)= a(x+3)(x+1)(x-2), where a is a constant.

It's given that the y-intercept is -7. This means that p(0)=-7.

-7=a(0+3)(0+1)(0-2) or -7=-6a. So a=7/6.

∴P(x)=(7/6)(x+3)(x+1)(x-2)

I left it in intercept form. You may use lattices to expand it.

I hope this helps!

Answer 2

a[(x+3)(x+1)(x-2) = -7 when x= 0

a(3)(1)(-2) = -7

a = -7/-6 = 7/6

(7/6)(x+3)(x+1)(x-2)

= (7/6)(x^2+4x+3)(x-2)

= (7/6)(x^3+ +2x^2 -5x -6)

=7x^3/6 + 7x^2/3 - 35x/6 -7