Question

1. Factor x²+5x-24 2. Factor 2n²-5n-3

Answer 1

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.

• Equate to zero;

            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).