Question

Factor the following:

1) 9x + 6
2) 8x - 1
3) 4x^2 + 6x - 8
4) 15x^2 - 10x
5) 8x^3 + 24x^2 - 32x
6) 14x^5 - 21x^2
7) 2x^2 + 3x + 4

Answer 1

To factor the given expressions, we can look for common factors and use factoring techniques such as grouping and factoring quadratic trinomials.

Step-by-step explanation:

1) To factor 9x + 6, we can look for the greatest common factor. In this case, the greatest common factor is 3, so we can rewrite the expression as 3(3x + 2).

2) To factor 8x - 1, we can rearrange the terms and rewrite it as 8x + (-1). There is no common factor, so it cannot be factored any further.

3) To factor 4x^2 + 6x - 8, we can look for two numbers that multiply to give -8 and add up to 6. The numbers are 4 and -2, so we can rewrite the expression as (2x + 4)(2x - 2).

4) To factor 15x^2 - 10x, we can take out the greatest common factor, which is 5x. We then have 5x(3x - 2).

5) To factor 8x^3 + 24x^2 - 32x, we can take out the greatest common factor, which is 8x. We then have 8x(x^2 + 3x - 4).

6) To factor 14x^5 - 21x^2, we can take out the greatest common factor, which is 7x^2. We then have 7x^2(2x^3 - 3).

7) To factor 2x^2 + 3x + 4, we cannot factor it any further.