Simplifying and Factoring Quadratic Expression: x^2 – 11x + 18

x^2 – 11x + 18

To understand this math expression, let’s break it down

To understand this math expression, let’s break it down.

The expression x^2 – 11x + 18 is a quadratic expression. Quadratic expressions have the form ax^2 + bx + c, where a, b, and c are constants.

In our case, a = 1, b = -11, and c = 18.

To simplify this expression, we can factor it.

Step 1: Multiply the coefficient of x^2 (which is 1) by the constant term (which is 18). In this case, 1 * 18 = 18.

Step 2: Find two numbers that multiply to give 18 and add up to the coefficient of x (which is -11). In this case, the numbers are -2 and -9 because (-2) * (-9) = 18 and (-2) + (-9) = -11.

Step 3: Rewrite the expression using the two numbers we found in Step 2. We can split the middle term -11x into -2x and -9x.

So, x^2 – 11x + 18 can be rewritten as x^2 – 2x – 9x + 18.

Step 4: Factor by grouping. We can group the first two and last two terms together.

(x^2 – 2x) – (9x – 18)

Step 5: Factor out the greatest common factor from each group.

x(x – 2) – 9(x – 2)

Step 6: Notice that (x – 2) is a common factor in both terms. Factor it out.

(x – 2)(x – 9)

So, x^2 – 11x + 18 can be factored as (x – 2)(x – 9).

This gives us the two solutions for the expression, x = 2 and x = 9.

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