FACTORING TRINOMIALS with leading coefficient ax2 + bx + c to (ax + b)(cx + d)

Now we need to factor trinomials with other leading coefficients! For example: THE FIRST STEP IS TO ALWAYS CHECK IF YOU CAN FACTOR OUT A GCF Example 1: Example 2: 2x2 – 4x – 70 What is the GCF? 2(x2 – 2x – 35) Factor as normal! So 2x2 – 4x – 70 = 2(x + 5)(x – 7). 3x2 – 33x + 72 What is the GCF? 3(x2 – 11x +24) Factor as normal! So 3x2 – 33x + 72 = 3(x - 3)(x – 8).

First check to see if there is a GCF we can factor out… is there? Step 1: Multiply the first and last terms’ coefficients. (21)(-4) =-84 Step 2: Find factors of -84 that add to -5 -84 means one factor is + one factor is - Step 3: Replace the middle term with these factors. Step 4: Factor by grouping. First check to see if there is a GCF we can factor out… is there? No, so we expand it to make 4 terms then factor by grouping! Factors of -84 (larger is - ) Difference of factors = -5

First check to see if there is a GCF we can factor out… is there? Step 1: Multiply the first and last terms’ coefficients. (25)(9) =225 Step 2: Find factors of 225 that add to -30 225 means both factors are + or both are - Step 3: Replace the middle term with these factors. Step 4: Factor by grouping. First check to see if there is a GCF we can factor out… is there? No, so we expand it to make 4 terms then factor by grouping! Sum of factors = -30 Factors of 225

First check to see if there is a GCF we can factor out… is there? Step 1: Multiply the first and last terms’ coefficients. (2)(9) =18 Step 2: Find factors of 18 that add to -9 18 means one factor is + one factor is - Step 3: Replace the middle term with these factors. Step 4: Factor by grouping. First check to see if there is a GCF we can factor out… is there? No, so we expand it to make 4 terms then factor by grouping! Factors of 18 (both are - ) Sum of factors = -9

First check to see if there is a GCF we can factor out… is there? Step 1: Multiply the first and last terms’ coefficients. (12)(5) =60 Step 2: Find factors of 60 that add to 19 60 means both factors are + or both are - Step 3: Replace the middle term with these factors. Step 4: Factor by grouping. First check to see if there is a GCF we can factor out… is there? No, so we expand it to make 4 terms then factor by grouping! Factors of 60 (both are + ) Sum of factors = 19

Put in descending order first!! What's different here? It's out of order... Put in descending order first!! Now follow the same steps! Sum of factors = +33 Factors of 200 (both are + )

Put in descending order first!! What's different here? It's out of order... Put in descending order first!! Now follow the same steps! Sum of factors = +3 Factors of -40 (larger is + )

Using grouping with trinomials Multiply the first and last coefficients. 4(7) = 28 Find the factors of 28 that add to -1 None of the factors will ADD to give -1 Using grouping with trinomials DOES NOT FACTOR!!! Sum of factors = -1 Factors of 28 (both are - )

Using grouping with trinomials Multiply the first and last terms. 3(-5) = -15 Find the factors of -15 that add to 7 None of the factors will SUBTRACT to give +7 Using grouping with trinomials DOES NOT FACTOR!!! Factors of -15 (larger is + ) Sum of factors = +7