P is of degree 2; P(0)= 12; zeros: 2,3

Write a polynomial function, P, in factored form and in standard form by using the given information. Please show work. :-)

2(x - 2)(x - 3).

2x^2 - 10x + 12.

Step-by-step explanation:

Degree 2 means that the highest degree is 2 and we may write it as:

ax^2 + bx + c  where a, b and c are constants to be found.

As p(0)  = 12, the first 2 terms in the above are zero so c = 12.

The zeros are 2, 3 so we may write it as

a(x - 2)(x - 3) = 0

The last term in the expansion is 12 so:

a*(-2)*(-3) = 12

thus a = 12/6 = 2.

In factored form our polynomial is:

2(x - 2)(x - 3).

Standard form:

2(x - 2)(x - 3)

= 2(x^2  - 5x + 6)

= 2x^2 - 10x + 12.

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