How to Factor the Quadratic Expression x^2 – 11x + 18

x^2 – 11x + 18

To begin, let’s factor the quadratic expression x^2 – 11x + 18

To begin, let’s factor the quadratic expression x^2 – 11x + 18.

We are looking for two numbers whose product is 18 and whose sum is -11, since the quadratic expression is in the form ax^2 + bx + c.

To determine these numbers, we can list out the factor pairs of 18:

1 * 18 = 18
2 * 9 = 18
3 * 6 = 18

Next, we need to determine which of these pairs sums up to -11. We can see that 2 and 9 meet this condition, as 2 + 9 = 11. However, since the -11 coefficient is negative in the original expression, we need to choose -2 and -9.

Now we can rewrite the expression as follows:

x^2 – 2x – 9x + 18

We can rearrange it by grouping the terms:

(x^2 – 2x) + (-9x + 18)

Taking out a common factor from each pair:

x(x – 2) – 9(x – 2)

Notice that both terms have a common factor of (x – 2), so we can factor that out:

(x – 9)(x – 2)

Therefore, the factored form of the quadratic expression x^2 – 11x + 18 is (x – 9)(x – 2).

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