Week 5- Precalc11

The new chapter began in this week is “Factoring Polynomial Expressions”, the steps to decompose a polynomial can be divided into five: CDPEU.

C: common

D: difference of squares( binomials)

P: pattern(trinomials)

E: easy( the coefficient of highest power is equal to 1)

U: ugly( the coefficient of highest power is not equal to 1)

 

EX: factor each polynomial expression

1) 2x^2-50y^2=2(x^2-25y^2)=2(x+5y)(x-5y)

In this case, find the common is 2 so that take the 2 out and put it on the outside.Each of the terms of the original equation is divided by two and it’s just the expression of difference of squares, and the result can be simplified directly to is equal to 2(x+5y)(x-5y).

2)(x+1)^2+4(x+1)-32=(x+1+8)(x+1-4)=(x+9)(x-3)

In this case, view (x+1) as “A”, so this term become toA^2+4A-32.You can simplify it to (A+8)(A-4) by multiplying the cross, then replace (x+1) back into the formation, so that we can find the answer is (x+9)(x-3).

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