How to do this? 20x³ + 40x² - 5x – 10

Question

20x³ + 40x² - 5x – 10

Answer 1

5(2x+1)(2x-1)(x+2)

= 5(4x^2-1)(x+2)

= 5(4x^3 +8x^2 -x -2)

= 20x^3 +40x^2 -5x -10

zeros, roots or x intercepts are: -1/2, -2 and 1/2

20x^3 +40x^2 -5x -10

factor by grouping

= 20x^2(x +2) -5(x+2)

= (20x^2 -5)(x+2)

=5(4x^2 -1)(x+2). use the formula (a^2-b^2)= (a-b)(a+b) with a=2x and b= 1

=5(2x-1)(2x+1)(x+2)

or use Descartes Rule to find one possible positive root and two possible negative roots

try easy intergers, such as x=0 and x=1

f(x) changes sign from x=0 to 1, so one postive root is between 0 and 1, try x=1/2, it works

(x-1/2) is one factor

or 2(x-1/2) = (2x-1)

divide into the cubic to get a more easily factorable quadratic