4.7 Steps for Solving Polynomial Equations but harder

Question 1

step one

Answer 1

Simplify each side completely

Question 2

step two

Answer 2

Put equation in standard form

Question 3

step three

Answer 3

Factor one side completely. First, use distributive property to factor out the gcf. Second, look for factoring patterns including difference of squares, trinomial squares, sum of cubes, and difference of cubes. Third, replace factorable trinomial with binomial factors.

Question 4

step four

Answer 4

Set each variable factor equal to zero and solve.

Question 5

step five

Answer 5

Write the answer in set notation.

Question 6

difference of squares

Answer 6

a^2 - b^2 = (a-b)(a+b)

Question 7

trinomial squares

Answer 7

a^2 - 2ab + b^2 = (a-b)(a-b)

Question 8

sum of cubes

Answer 8

a^3+b^3 = (a+b)(a^2 - ab + b^2)

Question 9

difference of cubes

Answer 9

a^3 - b^3 = (a - b)(a^2+ab+b^2)