Factoring ax2 + bx + c

3x² + 5x - 2• This is a little harder. • I would start with the “first”: (3x )(x )• Your “last” needs to multiply to give you a -2 (#’s will have different signs)

• Place them in a way that your “outside” and “inside” combine to get 5.

• OR• Now multiply “a” and “c” (3 and –2). You get negative six. • Your “outside” answer and your “inside” answer multiply to get negative

six AND combine (subtract because the signs must be different) to get 5. Try 6 and –1.

• You must place numbers so that the “inner” and “outer” products will be 6 and –1.

• (3x - 1)(x + 2)

3x2 – 19x + 20

• Factor

Answer: (3x – 4)(x – 5)

8x2 + 27x + 9

• Factor:

Answer: (8x + 3)(x + 3)

Another Way—The Box

• When factoring trinomials, you could use the box again.

• Put the first term in the top left of a 2 by 2 box.• Put the last term in the bottom right square.• Multiply them (“a” and “c”) together. That is your

“magic number”.• In f1= in the calculator, enter your magic number

(#) f1 = #/x• In f2 = #/x + x

Another Way—The Box

• Go to the table. In the f2 column find the “b” number (the middle term).

• In the two remaining boxes, enter the numbers next to that “b” number (the numbers in the “X” column and the y1 column). Be sure to put an x after each number.

• Going across the top row find the GCF. Write it to the left of the box.

• Then find the GCF of the bottom row and write it to the left of the box.

Another Way—The Box

• Then find the GCF of the first column and write it above that row.

• Last find the GCF of the second column and write it above that row.

• You now have the binomial factors of this trinomial.

Example 1

• Factor 6x² + 13x – 5

•Multiply them to get the magic number.

•Now enter in f1 -30/x

•In f2 enter -30/x + x

Example 1

• Go to the table and look in the f2 column and look for 13.

• It is next to the 15 and –2

• So, write 15x and –2x in the remaining boxes.

Example 1

• Find the GCF of each row and write it next to the row.

• Find the GCF of each column and write it above the column.

So it is (2x + 5)(3x – 1)

Try these…

Factor each trinomial. Check your answer.

1. 5x2 + 17x + 6

2. 2x2 + 5x – 12

3. 6x2 – 23x + 7

4. 4x2 - 11x - 20

5. 2x2 - 7x + 3

(x - 4)(4x + 5)

(3x – 1)(2x – 7)

(2x– 3)(x + 4)

(5x + 2)(x + 3)

(2x - 1)(x - 3)