Answer:
- x^2 + 12x + 4x + 48
- (x +12)(x +4)
Explanation:
The X-method chart is supposed to help you find factors of the polynomial constant that have a sum equal to the linear term coefficient.
Chart
An X-method chart is shown in the attachment. The numbers at the sides of the chart are chosen to have the product at the top and the sum at the bottom. One way to find these side numbers is to look at the ways that the product can be factored:
48 = (1)(48) = (2)(24) = (3)(16) = (4)(12) = (6)(8)
The sums of these factor pairs are 49, 26, 19, 16, 14. The one of interest is the factor pair (4)(12), which factors have a sum of 16.
4-Term polynomial
The factors at the sides of the chart can be used to write the middle term of the 3-term polynomial as a sum of two terms. That is ...
16 = 12 + 4
so
16x = 12x +4x
and the 4-term equivalent polynomial is ...
x^2 +12x +4x +48
Complete factorization
The utility of the 4-term equivalent polynomial is that terms can be factored in pairs:
(x^2 +12x) +(4x +48) = x(x +12) +4(x +12)
These factor pairs will have a common factor that lets you complete the factorization as ...
= (x +4)(x +12)
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Additional comment
If the leading coefficient is not 1, then the value at the top of the X chart is the product of the leading coefficient and the constant. Factoring can be completed using the 4-term polynomial in the same way as shown here.