What is the factored form of 4x2 + 12x + 5?
(1 point)
Responses
(2x + 4)(2x + 3)
(2 x + 4)(2 x + 3)
(4x + 5)(x + 1)
(4 x + 5)( x + 1)
(2x + 1)(2x + 5)
(2 x + 1)(2 x + 5)
(4x + 1)(x + 5)
The factored form of 4x2 + 12x + 5 is (2x + 1)(2x + 5).
What is the factored form of 2x2 + x – 3?
(1 point)
Responses
(2x + 3)(x – 1)
(2 x + 3)( x – 1)
(2x + 1)(x – 3)
(2 x + 1)( x – 3)
(2x – 3)(x + 1)
(2 x – 3)( x + 1)
(2x – 1)(x + 3)
(2 x – 1 )(x + 3 )
The factored form of 2x2 + x - 3 is (2x + 3)(x - 1).
The area of a rectangular swimming pool is 10x2 – 19x – 15. The length of the pool is 5x + 3. What is the width of the pool?
(1 point)
Responses
2x – 18
2 x – 18
2x – 5
2 x – 5
5x – 5
5 x – 5
5x – 22
To find the width of the pool, we can divide the area by the length:
10x^2 - 19x - 15 / (5x + 3)
By performing polynomial division or simplification, we determine that the width of the pool is:
2x - 5
Therefore, the width of the pool is 2x - 5.
What is the factored form of 16x2 – 16x – 12?
(1 point)
Responses
4(2x – 2)(2x + 2)
4(2 x – 2)(2 x + 2)
4(4x – 6)(x + 2)
4(4 x – 6)( x + 2)
4(2x – 2)(2x + 3)
4(2 x – 2)(2 x + 3)
4(2x – 3)(2x + 1)
4(2 x – 3)(2 x + 1)
To factor the quadratic expression 16x^2 - 16x - 12, we can first factor out the greatest common factor, which is 4:
4(4x^2 - 4x - 3)
Now, we need to factor the quadratic within the parenthesis:
4(2x - 3)(2x + 1)
Therefore, the factored form of 16x^2 - 16x - 12 is 4(2x - 3)(2x + 1).
What is the factored form of 3x2 + 21x – 24?
(1 point)
Responses
3(x + 8)(x – 1)
3( x + 8)( x – 1)
3(x + 6)(x – 3)
3( x + 6)( x – 3)
3(x + 5)(x – 3)
3( x + 5)( x – 3)
3(x + 7)(x – 3)
To factor the quadratic expression 3x^2 + 21x - 24, we can first factor out the greatest common factor, which is 3:
3(x^2 + 7x - 8)
Next, we factor the quadratic within the parentheses:
3(x + 8)(x - 1)
Therefore, the factored form of 3x^2 + 21x - 24 is 3(x + 8)(x - 1).