Factoring Part 3. FACTORING #1: Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 6x How to do it…. Find what is in common in each term and put in front. See what.

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Presentation transcript:

Factoring Part 3

FACTORING #1: Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 6x How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing. Solution:

FACTORING #1: Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 6x How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing. Solution: 2x( )

FACTORING #1: Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 6x How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing. Solution: 2x(x 3 )

FACTORING #1: Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 6x How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing. Solution: 2x(x 3 – 4x 2 )

FACTORING #1: Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 6x How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing. Solution: 2x(x 3 – 4x 2 + 2x )

FACTORING #1: Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 6x How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing. Solution: 2x(x 3 – 4x 2 + 2x – 3)

FACTORING #1: Take out the GCFEX: 15xy 2 – 10x 3 y + 25xy 3 How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing out. Solution:

FACTORING #1: Take out the GCFEX: 15xy 2 – 10x 3 y + 25xy 3 How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing out. Solution: 5xy( )

FACTORING #1: Take out the GCFEX: 15xy 2 – 10x 3 y + 25xy 3 How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing out. Solution: 5xy(3y )

FACTORING #1: Take out the GCFEX: 15xy 2 – 10x 3 y + 25xy 3 How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing out. Solution: 5xy(3y – 2x 2 )

FACTORING #1: Take out the GCFEX: 15xy 2 – 10x 3 y + 25xy 3 How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing out. Solution: 5xy(3y – 2x 2 + 5y 2 )

FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 5x + 6 How to do it…. Make a table of factors of the last number. Pick the factors that add up to the middle number. Solution:

FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 5x + 6 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. Solution:

FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 5x + 6 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. Solution:

FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 5x + 6 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. Solution: (x + 2)(x + 3)

FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 5x + 6 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. Solution: (x + 2)(x + 3) Check with FOIL

FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 12 How to do it…. Make a table of factors of the last number. Pick the factors that add up to the middle number. Solution:

FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 12 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. Solution:

FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 12 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. Solution:

FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 12 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. Solution: (x + 3)(x + 4)

FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 12 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. Solution: (x + 3)(x + 4) Check with FOIL.

FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 6 How to do it…. Make a table of factors of the last number. Pick the factors that add up to the middle number. Solution:

FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 6 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. Solution:

FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 6 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. Solution:

FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 6 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. Solution: (x + 6)(x + 1)

FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 6 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. Solution: (x + 6)(x + 1) Check with FOIL.

FACTORING #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 - 5x + 4 How to do it…. Make a table of factors of the last number. Pick the factors that add up to the middle number. Solution:

FACTORING #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 - 5x + 4 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. Solution:

FACTORING #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 - 5x + 4 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. None of these work! Solution:

FACTORING #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 - 5x + 4 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. None of these work! TRY negatives Solution:

FACTORING #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 - 5x + 4 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. None of these work! TRY negatives Solution:

FACTORING #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 - 5x + 4 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. None of these work! TRY negatives Solution:

FACTORING #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 - 5x + 4 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. None of these work! TRY negatives Solution: (x – 1)(x – 4)

FACTORING #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 - 5x + 4 How to do it…. Make a table of factors of the last number Pick the factors that add up to the middle number. None of these work! TRY negatives Solution: (x – 1)(x – 4) Check with FOIL.

x 2 + 6x + 5 =

x 2 + 6x + 5 = (x + 5)(x + 1)

x x + 16 =

x x + 16 = (x + 2)(x + 8)

a 2 – 5a + 6 =

a 2 – 5a + 6 = (a – 2)(a – 3)

#2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 + 2x - 15 How to do it…. Make a table of factors of the last number. Pick the numbers that add to be the middle number. Solution:

#2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 + 2x - 15 How to do it…. Make a table of factors of the last number Pick the numbers that add up to be the middle number. Solution:

#2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 + 2x - 15 How to do it…. Make a table of factors of the last number Pick the numbers that add up to be the middle number. Solution:

#2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 + 2x - 15 How to do it…. Make a table of factors of the last number Pick the numbers that add up to be the middle number. Solution: (x + 5)(x – 3)

#2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 + 2x - 15 How to do it…. Make a table of factors of the last number Pick the numbers that add up to be the middle number. Solution: (x + 5)(x – 3) Check with FOIL.

y 2 + 3y - 10 =

10

y 2 + 3y - 10 =

y 2 + 3y - 10 =

y 2 + 3y - 10 = (x + 5)(x – 2)