Multiple Choice
Write the polynomial in factored form.
4x3 + 8x2 – 96x
(1 point)
Responses
6x(x + 4)(x – 4)
6 x ( x + 4)( x – 4)
4x(x – 4)(x + 6)
4 x ( x – 4)( x + 6)
4x(x + 6)(x + 4)
4 x ( x + 6)( x + 4)
–4x(x + 6)(x + 4)
–4 x ( x + 6)( x + 4)
4x(x – 4)(x + 6)
To determine the factored form of the given polynomial 4x^3 + 8x^2 – 96x, we need to look for common factors among the terms. In this case, the common factor is 4x.
So, we can factor out 4x from each term: 4x(x^2 + 2x - 24).
Now, we need to factor the quadratic expression inside the parentheses, x^2 + 2x - 24.
To factorize the quadratic expression, we need to find two numbers whose product is -24 and whose sum is 2. These numbers are 6 and -4.
Now we can rewrite the expression as: 4x(x + 6)(x - 4).
Therefore, the correct factored form of the polynomial 4x^3 + 8x^2 – 96x is 4x(x + 6)(x - 4).
So, the answer is: 4x(x + 6)(x - 4).
The polynomial in factored form is:
4x(x - 4)(x + 6)
Response:
4 x ( x - 4)( x + 6)
What are the zeroes of the function? Graph the function.
y = x(x + 2)(x + 5)
(1 point)
Responses
–2, –5
assessment question 2 answer b
–2, –5 Image with alt text: assessment question 2 answer b
0, 2, 5
assessment question 2 answer aAs x increases, the function first increases, then decreases, and then increases. The function passes through the points left-parenthesis 0 comma 0 right-parenthesis, left-parenthesis 2 comma 0 right-parenthesis, and left-parenthesis 5 comma 0 right-parenthesis.
0, 2, 5 Image with alt text: assessment question 2 answer a As x increases, the function first increases, then decreases, and then increases. The function passes through the points left-parenthesis 0 comma 0 right-parenthesis, left-parenthesis 2 comma 0 right-parenthesis, and left-parenthesis 5 comma 0 right-parenthesis.
0, –2, –5
assessment question 2 answer dAs x increases, the function first increases, then decreases, and then increases. The graph of the function passes through the points left-parenthesis negative 5 comma 0 right-parenthesis, left-parenthesis negative 2 comma 0 right-parenthesis, and left-parenthesis 0 comma 0 right-parenthesis.0, –2, –5 Image with alt text: assessment question 2 answer d As x increases, the function first increases, then decreases, and then increases. The graph of the function passes through the points left-parenthesis negative 5 comma 0 right-parenthesis, left-parenthesis negative 2 comma 0 right-parenthesis, and left-parenthesis 0 comma 0 right-parenthesis.
–2, –5, 2
assessment question 2 answer c
The zeroes of the function y = x(x + 2)(x + 5) are 0, -2, and -5.
To graph the function, plot the points (0,0), (-2,0), and (-5,0) on a coordinate system. The function will intersect the x-axis at these points. Since the degree of the function is odd and the leading coefficient is positive, the graph will start in the bottom left quadrant, pass through the x-axis at -5, then pass through the x-axis at -2, and finally pass through the x-axis at 0 before going back up to the top right quadrant.
Here is a rough sketch of the graph:
```
^
|
|
| x x
| xx x
| x x x
| x x x
| x x x
| x x x
| x x x
| x x x
| x xx x
| x xx x
| x xx x
| x xx
-----------------------------x----------->
```
Please note that this is a rough sketch and not to scale. It is always best to graph using a graphing calculator or software for accurate results.