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.

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!