Question

Express your answer as a polynomial in standard form.

a) (2x^2 - 3x + 1)(x^2 + x - 2)
b) (3x^3 - 2)(x^2 + 4x - 1)
c) (4x^4 + 2x^3 - x^2 + 3) + (x^4 - 2x^3 + 5x^2)
d) (5x^2 - 3)(2x^3 + x)

Answer 1

To multiply polynomials in standard form, use the distributive property and combine like terms. In these examples, we multiplied two polynomials using this method and simplified the expressions.

Step-by-step explanation:

a) To multiply polynomials, we use the distributive property. By multiplying each term in the first polynomial by each term in the second polynomial, we get:

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

b) Using the same method, we can multiply:

(3x^3 - 2)(x^2 + 4x - 1) = 3x^5 + 12x^4 - 3x^3 - 2x^2 - 8x + 2

c) We can combine like terms:

(4x^4 + 2x^3 - x^2 + 3) + (x^4 - 2x^3 + 5x^2) = 4x^4 + x^4 + 2x^3 - 2x^3 - x^2 + 5x^2 + 3 = 5x^4 + 4x^2 + 3

d) Finally, we can multiply:

(5x^2 - 3)(2x^3 + x) = 10x^5 + 5x^3 - 6x^3 - 3x = 10x^5 - x^3 - 3x