February 4th

February 4th

Steps in Factoring

1) Factor out the greatest common factor (GCF). (There will not always be one).

2) Count the number of terms.

Two terms: Look to see if you have a difference of squares or a sum or difference of cubes.

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Difference of squares: X -Y => (X+Y)(X-Y)

X + Y => PRIME

Difference of cubes: X - Y=>(X-Y)(X +XY +Y )

Sum of cubes: X + Y => (X+Y)(X -XY + Y )

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Three terms: Look for two binomials.

A. Trial and error method:

2x - x -10

*Remember! (A-C)(B+D) = AB+AD-BC-CD.

The factors of 10 take the place of C and D.

The factors of 2x (2x and x) take the place of A and B.

Try: (2x 5)(x 2) or (2x 10)(x 1)

At this point, you must use trial and error to arrange the factors and signs so that the original trinomial can be obtained by combining the binomials in the FOIL manner.

(2x-5)(x+2) =2x +4x-5x-10 combine like terms to get = 2x -x-10

Clues for factoring trinomials by trial and error.

If the sign of the last term is +, the middle sign of the binomials will have the same sign as the second term in the trinomial.

Example: x -3x +2 = (x- 2)(x- 1) or x +5x+6= (x+3)(x+2)

If the sign of the last term is -, the middle sign of the binomials will be + and-.

Example: x -5x-6= (x-6)(x+1) or x +x -56= (x+8)(x-7)

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B. Grouping number method:

3x -10x+8 1. Multiply the a term of the coefficient x with the constant

( ax + bx + c ) c term. You are looking for two numbers that multiply together to get 24 and add together to get 10 in this case.

3x -4x-6x+8 2. Rewrite the problem. Replace the middle term ( bx ) with -4x and -6x.

3x -4x -6x+8 3. Solve by grouping.

a. Pull out a GCF from each group.

x(3x-4) -2(3x-4)

b. Collect like groups and combine remaining terms.

(x-2)(3x-4)

Four terms: Factor by grouping method.

A. Grouping Method

am + an + bm + b 1. Count the terms. Group the first two terms and the last two terms together.

(am + an) + (bm + bn)

a(m + n) + b(m + n) 2. Take out the common factor in the first group and the common factor in the second group.

(m + n)(a + b) 3. Factor out the common factor.

3) Check to be sure each factor is prime, if not, repeat 1-3.

4) Check by multiplying the factors out to see if you get the original polynomial.

REMEMBER!! FACTORING IS UNMULTIPLYING!!