Quadratic Expressions - How to Factor Them When A = 1

Quadratic Expressions How to Factor When A = 1 - How it Works - Video

Notation

Notation:

Here we have the notation. A and B are coefficients and C is constant.

Example 1

Example 1:

Here we have the expression x² + 8x + 12. A = 1 and B = 8 and C = 12.

We need to find two numbers that add to 8 and multiply to 12. These two numbers must be the same.

So we need to write down all the factor pairs of C, in this case 12. So we have 1 and 12; 2 and 6; and 3 and 4 as well as their negative pairs, since a negative times a negative is a positive: -1 and -12; -2 and -6; and -3 and -4.

Now we need to add each pair. The pair that is B, in this case 8, will be our the pair that we want.

1 + 12 = 13; -1 + -12 = -13; 2 + 6 = 8; -2 + -6 = -8; 3 + 4 = 7; -3 + -4 = -7

So 2 and 6 is the factor pair that we want.

So the result of factoring x² + 8x + 12 is (x + 2)(x + 6).

Example 2

Example 2:

Here we have the expression x² - 5x + 6. A = 1 and B = -5 and C = 6.

We need to find two numbers that add to -5 and multiply to 6. These two numbers must be the same.

So we need to write down all the factor pairs of C, in this case 6. So we have 1 and 6; and 2 and 3 as well as their negative pairs, since a negative times a negative is a positive: -1 and -6; and -2 and -3.

Now we need to add each pair. The pair that is B, in this case 8, will be our the pair that we want.

1 + 6 = 7; -1 + -6 = -7; 2 + 3 = 5; -2 + -3 = -5

So -2 and -3 is the factor pair that we want.

So the result of factoring x² - 5x + 6 is (x - 2)(x - 3).

Example 3

Example 3:

Here we have the expression x² + 2x - 8. A = 1 and B = 2 and C = -8.

We need to find two numbers that add to 2 and multiply to -8. These two numbers must be the same.

So we need to write down all the factor pairs of C, in this case -8. So we have 1 and -8; and 2 and -4 as well as the the factor pair if we switch the negative, -1 and 8; and -2 and 4.

Now we need to add each pair. The pair that is B, in this case 8, will be our the pair that we want.

1 + -8 = -7; -1 + 8 = 7; 2 + -4 = -2; -2 + 4 = 2

So -2 and 4 is the factor pair that we want.

So the result of factoring x² + 2x - 8 is (x - 2)(x + 4).

Example 4

Example 4:

Here we have the expression x² - 3x - 4. A = 1 and B = -3 and C = -4.

We need to find two numbers that add to -3 and multiply to -4. These two numbers must be the same.

So we need to write down all the factor pairs of C, in this case -4. So we have 1 and -4; and 2 and -2 as well as the the factor pair if we switch the negative, -1 and 4; and -2 and 2.

Now we need to add each pair. The pair that is B, in this case 8, will be our the pair that we want.

1 + -4 = -3; -1 + 4 = 3; 2 + -2 = 0; -2 + 2 = 0

So 1 and -4 is the factor pair that we want.

So the result of factoring x² - 3x - 4 is (x + 1)(x - 4).

Live Worksheet

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