Answer:
Certainly! To factor the quadratic expression x^2 - 3x - 10 as (x + p)(x + q we need to find the values of p and q.
Here's how you can do it using the table:
Step 1: Write down the coefficients of the quadratic expression in standard form: x^2 - 3x - 10.
Step 2: Look at the coefficient of x^2 which is 1. Write it in the upper-left cell of the table.
| p | q
--------------
1 | |
Step 3: Look at the constant term which is -10. Write it in the bottom-right cell of the table.
| p | q
--------------
1 | | -10
Step 4: Find two numbers that multiply to give -10 and add up to -3 (the coefficient of x). Write these numbers in the remaining cells of the table.
| | q
--------------
1 | 5 | -10
Step 5: The values of p and q are 5 and -2 respectively.
Therefore the factored form of x^2 - 3x - 10 is (x + 5)(x - 2).
I hope this helps! Let me know if you have any further questions.