Graded Assignment Unit Test, Part 2: Polynomials

1. What is the product of 1/2x-1/4 and 5x^2-2x+6? Write your answer in standard form. 2. (b) Is the product of 1/2x_1/4 and 5x^2-2x+6 equal to the product of 1/4-1/2 and 5x^2-2x+6? Explain your answer.

Step-by-step explanation:

In multiplying, we would apply the distributive property by multiplying each term in one bracket by each term in the other bracket.

1) the product of

(x/2 - 1/4) (5x²-2x + 6)

= (x/2*5x²) - (2x * x/2) + (6 * x/2) - (1/4*5x²) + (2x * 1/4) - (1/4 * 6)

= 5x²/2 - 2x²/2 + 3x - 5x²/4 + x/2 - 3/2

= 5x²/2 - 2x²/2 - 5x²/4 + 3x + x/2 - 3/2

= (10x² - 4x² - 5x²) / 4 + (6x + x) / 2 - 3/2

= x²/4 + 7x/2 - 3/2

2) the product of

(1/4 - 1/2) (5x²-2x + 6)

= - 1/4 (5x²-2x + 6)

= ( - 1/4 * 5x²) + (1/4 * 2x) - (1/4 * 6)

= - 5x²/4 + x/2 - 3/2

The products are not the same.

1.) 5x^3 - 7x^2/2 + 7x/2 - 3/2

2.) No. The product of 1/2x_1/4 and 5x^2-2x + 6 = 5x^3/2 - 9x^2/4 + 7x/2 - 3/2. The product of 1/4-1/2 and 5x^2 - 2x + 6 = - 5x^2/4 + x/2 - 3/2.