Question

divide the following in full answer x²-7x18 by x-9​

Answer 1

Step-by-step explanation:

Explanation:

Step 1:

Look for two numbers(a and b) whose product is -18 and whose sum is -7.

That is, axxb = -18 and a+b = -2

To find those numbers write down the factors of -18 which are: {-1,1,-2,2,-3,3,-6,6,-9,9,-18,18}

Now you will need some intuition to see that -9xx2 = -18

and -9+2 = -7

So the two numbers are -9 and 2.

Step 2:

Write down the second term of the expression(7x) as a sum of two terms whose coeficients are the two numbers we have found above.

x^2-7x-18 rarr x^2+2x-9x-18

Step 3:

Write down the factor out the first two terms and the two other terms.

x^2+2x-9x-18 rarr x(x+2)-9(x+2)

Step 4:

You remain with two terms(x(x+2) and -9(x+2))

which can further be factored, like this

x(x+2)-9(x+2) rarr color(blue)((x+2)(x-9))

Which cannot be further factored.