Factoring Trinomials of the Form Ax2 + Bx + C

8.03 Factoring Trinomials

Factoring Trinomials of the form ax2 + bx + c

Factoring Trinomials of the Form ax2 + bx + c

Step 1: Check for a ______.

Step 2: Split the ______term.

 Multiply the ______coefficient and the ______term of the trinomial.  Find factors of this ______that ______to give you the ______of the middle term.  Rewrite the polynomial with those factors replacing the ______of the trinomial. Step 3: Factor by ______.

Step 4: Check your ______. Example 2: Factor 2x2 - 7x + 6

Steps Work  Step 1 – Find a GCF

 Step 2a – Split the middle term – multiply the first coefficient and the last term of the trinomial.

 Step 2b – Split the middle term – Find factors of this product that add to give you the coeffiecnt of the middle term.

 Step 2c – Split the middle term – Rewrite polynomial with those factors replacing the middle term of the trinomial.

 Step 3 – Factor by grouping

 Step 4 – Check your factors. Example 3: Factor 5x2 + 8xy - 4y2

 Step 3 – Factor by grouping

 Step 4 – Check your factors.

Example 4: Factor 8x2 – 14x + 5

 Step 3 – Factor by grouping  Step 4 – Check your factors.

Factoring Trinomials of the form x2 + bx + c

Factoring Trinomials of the Form x2 + bx + c (when a=1)

Step 1: Check for a ______.

Step 2: Write the x’s as the ______term of each binomial factor: (x )(x ).

Step 3: Find the pair of numbers that ______to give you the last term ‘c’ and ______to give you the coefficient of the middle term ‘b.’

Step 4: Fill in the ______term of each binomial.

Step 5: Check your ______using the ______method. Example 1: Factor x2 + 6x + 8

Steps Work  Step 1 – Check for a GCF.

 Step 2 – Write the x’s as the first term of each binomial factor.

 Step 3 – Find the pair of numbers that multiply to give you the last term ‘c’ and add to give you the coefficient of the middle term ‘b’.

 Step 4 – Fill in the last term of each binomial.

 Step 5 – Check your factors using the distribution method.

Example 2: Factor x2 - 12x + 35 Steps Work  Step 1 – Check for a GCF

 Step 2 – Write the x’s as the first term of each binomial factor

 Step 3 – find the pair of numbers that multiply to give you the last term ‘c’ and add to give you the coefficient of the middle term ‘b’.

Example 3: Factor x2 - 3x - 18

Steps Work  Step 1 – Check for a GCF

 Step 3 – find the pair of numbers that multiply to give you the last term ‘c’ and add to give you the coefficient of the middle term ‘b’

 Step 5 – Check your factors using the distribution method. Example 4: Factor x2 + 2xy + y2

Steps Work  Step 1 – Check for a GCF

 Step 3 – find the pair of numbers that multiply to give you the last term ‘c’ and add to give you the coefficient of the middle term ‘b’

Sign Rules for Factoring Trinomials

If the last term in the trinomial is positive, the signs in the factored answer will be the same. If the middle term is positive, the signs in the factored answer will both be positive. If the middle term is negative, the signs in the factored answer will both be negative. If the last term in the trinomial is negative, the signs in the factored answer will be different.