factorise fully:xsquared-11x+18

which two factors of 18 add to 11?

4 nd 10

No.

4 + 10 = 14

11+7

To factorize the expression xsquared-11x+18, we need to find two binomial expressions whose product results in the given expression.

First, we need to find two numbers whose product is equal to the coefficient of the x^2 term (which is 1) multiplied by the constant term (which is 18). In this case, the numbers are -2 and -9 because (-2) * (-9) = 18.

Next, we need to determine the sum of these two numbers, which gives us the coefficient of the x term (which is -11 in this case). So -2 + (-9) = -11.

Now, we can rewrite the expression xsquared-11x+18 as follows, using the two numbers we found:
x^2 - 2x - 9x + 18

Notice that we have split the -11x term into -2x and -9x.

Then, we group the terms and factor by grouping:
(x^2 - 2x) + (-9x + 18)

Now, we can factor out the greatest common factor from each group:
x(x - 2) - 9(x - 2)

Finally, we can see that we have a common factor of (x - 2), so we can factor that out:
(x - 2)(x - 9)

Therefore, the fully factorized expression for xsquared-11x+18 is (x - 2)(x - 9).