Given problems;
1. Factor; x²+5x-24
To factor this equation, we must understand that this is a quadratic equation.
A quadratic equation usually has two roots.
x²+5x-24 = 0
- Then find two numbers whose product is -24 and their sum is +5
the numbers are +8 and -3
then replace 5x with the number;
x² + 8x - 3x - 24 = 0
Now factorize;
x(x +8) - 3(x + 8) = 0
(x-3)(x+8) = 0
Factoring gives (x-3)(x+8)
2. Factor 2n² - 5n -3;
Equate to zero;
2n² - 5n -3 = 0
Find the number whose sum is -5 and the product gives -6( 2 x -3);
the number is -6 and +1;
2n² - 6n + n -3 = 0
2n(n-3) + 1(n-3) = 0
(2n + 1)(n-3) = 0
The factor of the equation is (2n + 1)(n-3).