1. Which of the following is the greatest common factor in 5x^2+20x−30
A. 5x
B. 5
C. 10
D. X
2. Factor 4x^2−4x−8
A. 4(x+1)(x−2)
B. (x+1)(x−2)
C. (x−1)(x+2)
D. 4(x−1)(x+2)
3. Factor 6x^2−24x−30
A. 6(x−1)(x+5)
B. (6x+1)(x−30)
C. (6x−5)(x+6)
D. 6(x+1)(x−5)
4. Factor 4x^2+15x+9
A. 4(x+3)(x+3)
B. (x+3)(4x+3)
C. (x−3)(4x−3)
D. (2x+3)(2x+3)
5. The area of a rectangle is represented by the expression 2x^2+3x−14. Factor this expression to determine expressions that could represent the side lengths.
A. (x+4)(x−3)
B. (x+7)(x−2)
C. (2x+4)(x−3)
D. (2x+7)(x−2)
1. A. 5x
2. D. 4(x-1)(x+2)
3. A. 6(x-1)(x+5)
4. A. 4(x+3)(x+3)
5. B. (x+7)(x-2)
1. To find the greatest common factor (GCF), we need to factorize the expression 5x^2 + 20x - 30.
The common factor among all the terms is 5. Divide each term by 5:
5x^2 / 5 = x^2
20x / 5 = 4x
-30 / 5 = -6
The factored expression becomes:
5(x^2 + 4x - 6)
Now, we need to factorize the quadratic expression inside the parentheses.
2. To factor 4x^2 - 4x - 8:
The common factor among all the terms is 4. Divide each term by 4:
4x^2 / 4 = x^2
-4x / 4 = -x
-8 / 4 = -2
The factored expression becomes:
4(x^2 - x - 2)
3. To factor 6x^2 - 24x - 30:
The common factor among all the terms is 6. Divide each term by 6:
6x^2 / 6 = x^2
-24x / 6 = -4x
-30 / 6 = -5
The factored expression becomes:
6(x^2 - 4x - 5)
Now, we need to factorize the quadratic expression inside the parentheses.
4. To factor 4x^2 + 15x + 9:
This quadratic expression cannot be factored directly, so we can use the quadratic formula or complete the square. After applying the quadratic formula or completing the square, we'll find that the factored expression is:
(2x + 3)(2x + 3) or (2x + 3)^2
5. To factor 2x^2 + 3x - 14:
This quadratic expression cannot be factored directly either. We can use the quadratic formula or complete the square to find that the factored expression is:
(x + 7)(2x - 2) or (x + 7)(2(x - 1))
Therefore, the correct answer is option B: (x + 7)(x - 2) for question 5.