-x^2- Chapter 2.5 Review Factor completely. If the polynomial is not factorable, write prime. 31. x^2+10x-39 32. x^2-16 33. 8x^3+27 34. 18x^3+3x^2-3x (x+8)(x+8) 36. 9x^2-30x+16 37. 25x^2+36 39. 4x^2+13x-12

## Step 1: Factoring ### We look for two numbers that multiply to -39 and add up to 10. These numbers are 13 and -3. Thus, the factored form is .## Step 2: Factoring ### This is a difference of squares, . The factored form is .## Step 3: Factoring ### This is a sum of cubes, . The factored form is .## Step 4: Factoring ### First, factor out the greatest common factor, : . Then, factor the quadratic: .## Step 5: Factoring ### We are looking for two numbers that multiply to and add up to -30. These numbers are -24 and -6. Rewrite the middle term and factor by grouping: . Alternatively, recognize this as a perfect square trinomial close to . Expanding that gives . Since we have instead of , it is not a perfect square trinomial.## Step 6: Factoring ### This is a sum of squares and cannot be factored further using real numbers. Thus, it is prime.## Step 7: Factoring ### We look for two numbers that multiply to and add up to 13. These numbers are 16 and -3. Rewrite the middle term and factor by grouping: .