Question

Factor completely.
2u^2 –9u+10

Answer 1

To factor the quadratic expression \(2u^2 - 9u + 10\), we can use the method of factoring by grouping.

First, we multiply the coefficient of \(u^2\) (which is 2) by the constant term (which is 10):
\[
2 \times 10 = 20
\]
Next, we look for two numbers that multiply to 20 and add to -9. The numbers that meet these criteria are -4 and -5, since:
\[
-4 \times -5 = 20 \quad \text{and} \quad -4 + -5 = -9
\]
Now, we can rewrite the middle term \(-9u\) using -4 and -5:
\[
2u^2 - 4u - 5u + 10
\]
Next, we group the terms:
\[
(2u^2 - 4u) + (-5u + 10)
\]
Now we factor out the common factors from each group:
\[
2u(u - 2) - 5(u - 2)
\]
Now we can factor out the common binomial factor \((u - 2)\):
\[
(2u - 5)(u - 2)
\]

So, the completely factored form of the expression \(2u^2 - 9u + 10\) is:
\[
(2u - 5)(u - 2)
\]