Question

What is the product of 3x – 4 and 5x^2–2x+6. Write your answer in standard form.

Part a: SHOW WORK
Part b: Is the product of 3x – 4 and 5x^2–2x+6 equal to the product of 4 – 3x and 5x^2 – 2x + 6? EXPLAIN.

50 points, please show work. Thanks.

Answer 1

Part a:
To find the product of (3x - 4) and (5x^2 - 2x + 6), we can use the distributive property of multiplication:
(3x - 4) × (5x^2 - 2x + 6)
= 3x × (5x^2 - 2x + 6) - 4 × (5x^2 - 2x + 6)
= 15x^3 - 6x^2 + 18x - 20x^2 + 8x - 24
= 15x^3 - 26x^2 + 26x - 24

Therefore, the product of (3x - 4) and (5x^2 - 2x + 6) is 15x^3 - 26x^2 + 26x - 24, in standard form.

Part b:
No, the product of (3x - 4) and (5x^2 - 2x + 6) is not equal to the product of (4 - 3x) and (5x^2 - 2x + 6). This is because when we expand the product (4 - 3x) and (5x^2 - 2x + 6), we get:
(4 - 3x) × (5x^2 - 2x + 6)
= 20x^2 - 8x + 24 - 15x^3 + 6x^2 - 18x
= -15x^3 + 26x^2 - 26x + 24

As we can see, the product of (4 - 3x) and (5x^2 - 2x + 6) is not the same as the product of (3x - 4) and (5x^2 - 2x + 6). This is because the order of the factors matters when we multiply polynomials.