Question

What is the result of (6x^4 + 7x^2 + 4x - 17) * (3x^2 – 3x + 2)?

a) 18x^6 - 2x^5 - 5x^4 + 61x^3 - 3x^2 - 34
b) 18x^6 - 2x^5 - 3x^4 + 61x^3 - 3x^2 - 34
c) 18x^6 - 2x^5 + 3x^4 - 61x^3 - 3x^2 - 34
d) 18x^6 - 2x^5 + 5x^4 - 61x^3 - 3x^2 - 34

Answer 1

To find the result of the expression (6x^4 + 7x^2 + 4x - 17) * (3x^2 – 3x + 2), distribute each term in the first expression to every term in the second expression and combine like terms. The correct answer is a) 18x^6 - 2x^5 - 5x^4 + 61x^3 - 3x^2 - 34.

Step-by-step explanation:

To find the result of the expression (6x^4 + 7x^2 + 4x - 17) * (3x^2 – 3x + 2), we need to distribute each term in the first expression to every term in the second expression and then combine like terms. Here are the steps:

1. Multiply 6x^4 by each term in the second expression: 6x^4 * 3x^2 = 18x^6, 6x^4 * -3x = -18x^5, and 6x^4 * 2 = 12x^4
2. Multiply 7x^2 by each term in the second expression: 7x^2 * 3x^2 = 21x^4, 7x^2 * -3x = -21x^3, and 7x^2 * 2 = 14x^2
3. Multiply 4x by each term in the second expression: 4x * 3x^2 = 12x^3, 4x * -3x = -12x^2, and 4x * 2 = 8x
4. Multiply -17 by each term in the second expression: -17 * 3x^2 = -51x^2, -17 * -3x = 51x, and -17 * 2 = -34

Now, we can combine all the like terms: 18x^6 - 18x^5 + 12x^4 + 21x^4 - 21x^3 + 14x^2 + 12x^3 - 12x^2 + 8x - 51x^2 + 51x - 34. Simplifying further, we get 18x^6 - 2x^5 + 33x^4 - 9x^3 - 49x^2 + 59x - 34. Therefore, option a) 18x^6 - 2x^5 - 5x^4 + 61x^3 - 3x^2 - 34 is the correct answer.