Factor completely

Question

Ex) 2x^2 + 5x -3: (2x -1) (x+3)
6) 2x^2 + x -10: ___ ____

Answer 1

To factor the quadratic expression $2x^2+x-10$, we can follow these steps:

1. Multiply the leading coefficient (2) by the constant term (-10): $$2\times -10=-20$$

2. Find two numbers that multiply to -20 and add up to the middle coefficient (1): The numbers that satisfy this are 5 and -4 because: $$5\times -4=-20\text{and}5+(-4)=1$$

3. Rewrite the middle term using these two numbers: $$2x^2+5x-4x-10$$

4. Group the terms: $$(2x^2+5x)+(-4x-10)$$

5. Factor out the common factors from each group: $$x(2x+5)-2(2x+5)$$

6. Notice that $2x+5$ is a common factor: $$(2x+5)(x-2)$$

Thus, the completely factored form of $2x^2+x-10$ is: $$(2x+5)(x-2)$$