Factor: can't get these two!!?

Question

a) 2x^3 + 7x^2 + 2x - 3

b) 10x^3 + 33x^2 + 23x - 6


show steps please :) thanks

Answer 1

Use synthetic division:-

Question a)
-1 |2____7____2____-3
__|____-2____-5____3
__|2____5____-3____0

R = 0 shows that x + 1 is a factor

( x + 1 )( 2 x ² + 5 x - 3 )
( x + 1 )( 2 x - 1 )( x + 3 )

Question b)
-2 |10___33___23___-6
__|____-20___-26___6
__|10___13___-3____0

(x + 2)(10 x ² + 13 x - 3)

Answer 2

Go with como (answerer 2), but he did not see that his last factor (10 x² + 13 x - 3) is equal to (2 x + 3)(5 x - 1).

To get that, you need either trial and error, or use the quadratic formula to solve 10 x ² + 13 x - 3 = 0. That gives the solutions x = -3/2, x = 1/5 and you can transpose these into the factors.

Answer 3

Sometimes trial and error is the best method. By guessing, find a number b that makes the expression zero (factor definition). Then your first factor is x-b. Divide the expression by x-b and then factor the quotient.