Use the correct form of factoring in order to find the x intercepts.
9r^2-5r-10
That doesn't factor
That polynomial can't be factored.
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It can't be factored.
To find the x-intercepts of the expression 9r^2 - 5r - 10, we need to factorize it by applying the correct form of factoring.
Step 1: Look for any common factors among the coefficients of the expression. In this case, there are no common factors other than 1.
Step 2: Multiply the coefficient of the quadratic term (9) with the constant term (-10), which gives us -90.
Step 3: Find two numbers that multiply to -90 and add up to the coefficient of the linear term (-5). These numbers are -10 and 9, since -10*9 = -90 and -10+9 = -1.
Step 4: Rewrite the linear term (-5r) using the two numbers from step 3. This will break down the expression into two terms:
9r^2 - 10r + 9r - 10
Step 5: Group the terms and factor by grouping:
(9r^2 - 10r) + (9r - 10)
Step 6: Factor out the greatest common factors from each group:
r(9r - 10) + 1(9r - 10)
Step 7: Notice that we have a common binomial factor, (9r - 10), which can be factored out:
(9r - 10)(r + 1)
Step 8: Set each factor equal to zero and solve for r to find the x-intercepts:
9r - 10 = 0 ---> r = 10/9
r + 1 = 0 ---> r = -1
Therefore, the x-intercepts of the expression 9r^2 - 5r - 10 are r = -1 and r = 10/9.