Question

Could you factor 2u^2+u-10

Answer 1

The quadratic expression 2u^2+u-10 can be factored into (u - 2)(2u + 5) by finding numbers that multiply to -20 and add up to 1 and then grouping and factoring by grouping.

Step-by-step explanation:

To factor the quadratic expression 2u^2+u-10, we can use the factoring method to rewrite it as a product of two binomials.

First, we need to find two numbers that multiply to give -20 (which is the product of the coefficient of u^2 that is 2, and the constant term -10) and add up to 1 (the coefficient of u).

These two numbers are 5 and -4.

The expression can then be decomposed as:

• 2u^2 + 5u - 4u - 10

Next, we can group the terms to factor by grouping:

• (2u^2 + 5u) + (-4u - 10)

Factor out the greatest common factor from each group:

• u(2u + 5) - 2(2u + 5)

Now, we see that (2u + 5) is a common factor, and we can rewrite the entire expression as:

• (u - 2)(2u + 5)

In this form, the quadratic is completely factored.