Question

Please help! Simply the polonomials! ​

Answer 1

Answer:

1) 11x^3 - 6x - 3

2) 3x^3 + 4x^2 - 2x - 1

3) 9x^2 - 4

4) -4x^4 + 2x^3 - x^2

5) x^3 - 38x - 12

Step-by-step explanation:

1) (3x^4 + 5x^3 - 7x + 2) - (3x^4 - 6x^3 - x + 5)

Step 1: 3x^4 + 5x^3 - 7x + 2 - 3x^4 + 6x^3 + x - 5 (multiply the terms in the parenthesis by the constants, which are 1 and -1)

Step 2: 3x^4 - 3x^4 + 5x^3 + 6x^3 - 7x + x + 2 - 5 (reorganize the polynomial by exponential values (ex: x^4 before x^3 before x^1))

Step 3: 11x^3 - 6x - 3 (add like terms)

2) (3x^3 + 8x - 3) + (4x^2 - 10x + 2)

Step 1: 3x^3 + 8x - 3 + 4x^2 - 10x + 2 (multiply the terms in the parenthesis by the constants)

Step 2: 3x^3 + 4x^2 + 8x - 10x - 3 + 2 (reorganize the polynomial)

Step 3: 3x^3 + 4x^2 - 2x - 1 (add like terms)

3) (3x + 2)(3x - 2)

Step 1: 9x^2 - 6x + 6x - 4 (Use FOIL to multiply binomials, or multiply the first terms, outside terms, inside terms, then last terms)

Step 2: 9x^2 - 4 (add like terms)

4) -x^2(4x^2 - 2x + 1)

Step 1: (-x^2*4x^2) + (-x^2*(-2x)) + (-x^2*1) (multiply -x^2 by each term)

Step 2: -4x^4 + 2x^3 - x^2 (simplify; remember x^2 is the same as -1*x^2)

5) (x + 6)(x^2 - 6x - 2)

Step 1: ((x*x^2) + (x*(-6x)) + (x*(-2))) + ((6*x^2) + (6*(-6x)) + (6*(-2))) (multiply the first term in the binomial by each term in the trinomial, and do the same with the second term)

Step 2: x^3 - 6x^2 + 6x^2 - 2x - 36x - 12 (simplify and reorganize)

Step 3: x^3 - 38x - 12 (add like terms again)