Polynomials in the Form ax^2 + bx + c

You had previously factored polynomials in the form x^2 + bc + c, but with this kind of polynomial, you will add another value in front of the first term. You may have touched upon this type of polynomial last year, but you would likely have been asked to guess the values. This year, you will be taught to solve properly, without any guesswork.

Example:

3x^2 + 7x + 4

You will begin by breaking the middle value (b value), in this case 7x, into two other values that fulfill certain parameters. However, you must first find these parameters, which you will do by multiplying the coefficients of the first and last values (a and c). You will then find the two numbers that will add to the b value and multiply to the ac value.

3x^2 + 7x + 4

(3)(4) = 12

This means that the numbers you split 7x into will add to 7 and multiply to 12, meaning the answer is 3 and 4.

3 + 4 = 7

(3)(4) = 12

Splitting the b value:

3x^2 + 3x + 4x + 4 = 0

From here, factor by grouping and you will have your answer.

= 3x(x + 1) + 4(x + 1)

= (x + 1)(3x + 4)