Factoring x2 + bx + c ax2 + bx + c when a=1

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Presentation transcript:

Factoring x2 + bx + c ax2 + bx + c when a=1

Factor x² + 7x + 12 Notice that there is not a number in front of x2. (This means that a is 1 in ax2 + bx + c.) You will come up with two binomials. What could you multiply together to get x²? x times x So I start the two binomials like this: (x + )(x + ) What would I multiply together to get +12 that will also add to get +7 3 and 4 (x + 4)(x + 3)

Try: x² - 3x + 2 Start with (x )(x ) Now I need to find two numbers that multiply to get +2, but add to give –3. The signs will be the same because “c” is positive. (-2, and –1) Put those in the parentheses (x – 1)(x – 2)

Try: x² - 2x – 8 You can start with (x )(x ) This time I know the signs in the parentheses will be different because the last term “c” is negative. So, I need two numbers that will multiply to give –8, and add to give –2 (remember the signs are different!) -4 and +2 So, (x – 4)(x + 2)

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

The Box continued… 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.

The Box continued…. 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 x² + 7x +6 Multiply them to get the magic number. Now enter in f1 6/x In f2 enter 6/x + x

Example 1: x² + 7x +6 Go to the table, go to the f2 column and look for 7. It is next to the 6 and 1 So, write 6x and 1x in the remaining boxes. 6x 1x 6

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. X 6 So it is (x + 6)(x + 1) X 1 6x 1x 6

Try these… x2 + 8x + 7 x2 + 6x + 5 x2 + x – 6 Take out common factors first. x3 + 5x2 + 6x 2x3 + 8x2 - 10x (x + 1)(x + 7) (x + 1)(x + 5) (x + 3)(x – 2) x (x + 2) (x + 3) 2x (x – 1) (x + 5 )