2x^3 +x^2-18x=9

Question

Solving higher order polynomials by factoring. 

Answer 1

Subtract 9 on both sides of the equation.

 

2x³ + x²- 18x - 9 = 0

 

 

Factor by grouping.  This means we group all the terms that have common factors.  As it is, the first two are grouped together and the last two are grouped together.

 

x²(2x + 1) - 9(2x + 1) = 0

 

 

Notice the (2x+1) is a common factor on the left side?  This is the GCF.

 

(2x + 1)(x² - 9) = 0

 

 

Then, we can factor the difference of perfect square term (x² - 9).

 

(2x + 1)(x - 3)(x + 3) = 0

 

 

Do you know what comes next?

Answer 2

2x³ + x² - 18x = 9

2x³ + x² - 18x - 9 = 0

x²(2x + 1) - 9(2x + 1) = 0

(x² - 9)(2x + 1) = 0

 

Can you solve for x?