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.

Question

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.

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4 months 2021-10-12T01:56:06+00:00 2 Answers 0 views 0

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.

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.