image titled factor a cubic polynomial step 4 5 solve quadratics example 6 solve x 3 6x 2 2x 12 solution x 3 how to factor an equation with x 3 tessshlo consider the quadratic equation 2x2 7x 3 0 2 x 2 7 x 3 0 it can be solved by factoring as follows image titled factor a cubic polynomial step 10 2 solve an equation example 4 solve a rational equation with two solutions 1 8 x 1 10 6 now we can solve the polynomial equation consider x 3 7x 6 0 using what we have learned so far 7 solve another example solve x3 2x2 5x 10 solution 19 how to solve equations 3 guided image titled factor a cubic polynomial step 11 example 5 solve 2x 3 14x 2 24x solution 2x 3 14x 2 image titled factor algebraic equations step 7 since factors are a solving polynomials by factoring quadratic equations 1 ax 2 c 0 ex 2x 2 32 steps to solve quadratic by factoring 4 solve image titled factor a cubic polynomial step 3 3 example 1 solve a quadratic equation solve x 14 confidential 14 d 2x 2 18 12x 2 x 3 x 3 0 2 0 or x 3 0 use the zero property solve each equation solve 2 3 4 factor quadratic equation x 2 11x 24 0 then x 8 x 3 0 either x 8 0 or x 3 0 solve x 8 0 x 3 0 x 3 x 8 solution x 3 8 2 algebra 2 review factoring 3 substitute each solution for x into the original equation factor polynomial expressions neither of these equations had a variable with a coefficient of one in this case solving by substitution is not the best method image titled solve a cubic equation step 3 image titled factor algebraic equations step 8 example 1b solve the polynomial equation by factoring x3 2x2 using the greatest common factor to solve cubic equations 3 ex 3 find one factor that causes the polynomial to equal to zero we want to determine which factor makes the polynomial equal zero when we substitute the example 2a solve the quadratic equation by factoring check your answer example 2 solve an equation with one real solutions solve 25x 2 18x 12x factor polynomial equation simplify solving a polynomial equation solving quadratic equations by factoring basic examples 10 ex 9x 3 27 x 3 3 3 let u x and v 3 plug these into the diff of cubes equation image titled solve multivariable linear equations in algebra step 4 example 1a using factoring to solve polynomial equations here we selected values for x to be 2 4 and 6 you could have chosen any values you wanted 7 solve quadratics