Question

Use the graph of the polynomial function to find the factored form of the related polynomial. Assume it has no constant factor.

Answer 1

Answer with explanation:

I will use cubic polynomial to explain this.Let the graph of the polynomial cuts the X axis at , a, b and c.Suppose all the three roots of the cube are Real.

So, it has three roots equal to a, b and c.

Equation of Cubic Polynomial is given by:

= (x-a)(x-b)(x-c)

= [x² - (a+b)x + a b](x-c)

= x²(x -c)-x(a+b)(x-c)+ab(x-c)

= x³-x²c- (x²-xc)(a+b)+a b x - a b c

= x³ - x² c-x² a - x² b+a c x + b c x+a b x - a b c

=x³-x²(a+b+c)+x(a b+b c+ca)-a b c

The factors a, b and c can be any rational number in the form of
`(p)/(q), q\\eq 0.`

For example ,the roots of the cubic polynomial are 1, -1 and 3.

Polynomial Function = (x -1)[x-(-1)](x-3)

=(x-1)(x+1)(x-3)

Answer 2

See example below.

Explanation:

The factored from of a polynomial can be found from the zeros or x-intercepts of the graph.

The x-intercepts here are x= -3 and x= 3.

Then the factors are x+3 and x-3.

So the factored form is (x+3)(x-3).