UNIT 6-OBJECTIVE 4- FACTORING TRINOMIALS

An algebraic expression that has three terms is called a trinomial, not all trinomials can be factorized using real numbers.

The general quadratic trinomial is of the form:

where a, b, c represent real numbers.

Examples when a=11.

You are looking for two numbers that multiply together that equal 10 and add together to equal 3. The numbers would be 5 and 2 because

(-5)(2)= -10

-5+2= -3

The solution would be:

2.

You are looking for two numbers that multiply together that equal 16 and add together to equal 10. The numbers would be 8 and 2 because

(8)(2)=16

(8+2)=10

The solution would be (x+8) (x+2)

Examples where a is not equal to 11.

You would use trial and error method or you can use graphical method. You are looking for two numbers that multiply together to equal 120 ((6)(-20)) and add together to equal 7. The numbers would be 15 and 8 as the coefficients for x.

(Notice that 15x-8x=7x)

We now apply factoring by grouping we have used in objective 3.

(We can now factor out the quantity (2x+5))

2.

We are looking for two numbers that multiply together to equal 10 and add together to equal 13. We cannot find any numbers that satisfy this so we cant factor this trinomial.

3.

We are looking for two numbers that multiply together to equal 35 and add together to equal 12. The numbers would be 7 and 5. We can now rewrite the polynomial using 7 and 5 as the coefficient for y.

(notice that 7y -5y = -12y)

We now apply factoring by grouping we used in objective 3.

(We can now factor out quantity (y-1))

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