You have been invited to a fancy dinner party celebrating your hard work in Algebra 2 so far. The distinguished guests come from various aspects of math disciplines like professors, engineers, and financial analysts.
1. A mysterious box is delivered to the dinner party you are attending. The label on the box says that the volume of a box is the function f(x) = x3 + 3x2 – 10x – 24. To open the box, you need to identify the correct factors of f(x). Partygoers offer up solutions, and it is your job to find the right ones.
Their suggestions are:
• (x – 1)
• (x + 2)
• (x – 3)
• (x + 4)
• (x + 6)
• (x – 12)
List the correct factors. Then justify your selections with complete sentences.
I have concluded that the correct factors are (x+2)(x-3)(x+4). I arrived at this decision by factoring, grouping and employing synthetic division on the equation f(x): …show more content…
In a polynomial equation, if a number # if (x-#) is a factor of g(x), then # is a zero/root of the polynomial. If the group of three wants to prove that the binomial (x+2) is a factor of the g(x) equation, one option they could explore is using long division with the binomial in the divisor position.
Essentially, no one was wrong. Prof. McCory and Ms. Guerra were in the green.
3. Dr. Collier summons you over to his table. He wants to demonstrate the graph of a fourth-degree polynomial function, but the batteries in his graphing calculator have run out of juice. Explain to Dr. Collier how to create a rough sketch of a graph of a fourth-degree polynomial function.
1. It is critical to find the x-intercepts.
2. Find the y-intercept. This is done by substituting x with zero and solving for y.
3. To determine if it opens up or down, you must evaluate if the function is positive or negative. Negative: opens down. Positive: opens up.
4. Plot points and draw.
1. A mysterious box is delivered to the dinner party you are attending. The label on the box says that the volume of a box is the function f(x) = x3 + 3x2 – 10x – 24. To open the box, you need to identify the correct factors of f(x). Partygoers offer up solutions, and it is your job to find the right ones.
Their suggestions are:
• (x – 1)
• (x + 2)
• (x – 3)
• (x + 4)
• (x + 6)
• (x – 12)
List the correct factors. Then justify your selections with complete sentences.
I have concluded that the correct factors are (x+2)(x-3)(x+4). I arrived at this decision by factoring, grouping and employing synthetic division on the equation f(x): …show more content…
In a polynomial equation, if a number # if (x-#) is a factor of g(x), then # is a zero/root of the polynomial. If the group of three wants to prove that the binomial (x+2) is a factor of the g(x) equation, one option they could explore is using long division with the binomial in the divisor position.
Essentially, no one was wrong. Prof. McCory and Ms. Guerra were in the green.
3. Dr. Collier summons you over to his table. He wants to demonstrate the graph of a fourth-degree polynomial function, but the batteries in his graphing calculator have run out of juice. Explain to Dr. Collier how to create a rough sketch of a graph of a fourth-degree polynomial function.
1. It is critical to find the x-intercepts.
2. Find the y-intercept. This is done by substituting x with zero and solving for y.
3. To determine if it opens up or down, you must evaluate if the function is positive or negative. Negative: opens down. Positive: opens up.
4. Plot points and draw.