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Title: Polynomial functions

Grade: 1400-a Lesson: S2-L2

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Consider the cubic function \$f(x) = x^3 + 2x^2 - 5x - 6\$. Let’s find the zero’s of this function.
2	Step	Given function	\$f(x) = x^3 + 2x^2 - 5x - 6\$
3	Step	Finding zero’s f(x) = 0	\$ x^3 + 2x^2 - 5x - 6 = 0 \$
4	Hint	Using synthetic division , we have \$x^2 + 4x + 3\$ is the other factor then after simplification	\$ (x - 2)( x^2 + 4x + 3) = 0 \$ \$ (x - 2)(x + 3)(x + 1) = 0 \$ \$ x = 2 ,x = - 3 ,x = - 1 \$
5	Step	Therefore, the zero’s of this function are \$ x = 2,x = - 3,x = - 1 \$.
6	Choice.A	This is incorrect. The zero’s of the function are -1, -3, and 2, not 0	x = - 1, -3, 0
7	Choice.B	This choice is wrong. The root 1 isn’t a solution to the function. The correct roots are -1, -3, and 2	x = 0, -3, 1
8	Choice.C	This option is correct and matches the zero’s of the cubic function \$ f(x) = x^3 + 2x^2 - 5x - 6 \$	x = -1, -3, 2
9	Choice.D	This is incorrect. There is a missing zero (-1) and an extraneous value (-5) included	x = 2, -5, 3
10	Answer	Option	C
11	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Consider the cubic function
\$f(x) = x^3 + 2x^2 - 5x - 6\$. Let’s find the zero’s of this function.

Step

Given function

\$f(x) = x^3 + 2x^2 - 5x - 6\$

Step

Finding zero’s f(x) = 0

\$ x^3 + 2x^2 - 5x - 6 = 0 \$

Hint

Using synthetic division , we have \$x^2 + 4x + 3\$ is the other factor then after simplification

\$ (x - 2)( x^2 + 4x + 3) = 0 \$

\$ (x - 2)(x + 3)(x + 1) = 0 \$

\$ x = 2 ,x = - 3 ,x = - 1 \$

Step

Therefore, the zero’s of this function are \$ x = 2,x = - 3,x = - 1 \$.

Choice.A

This is incorrect. The zero’s of the function are -1, -3, and 2, not 0

x = - 1, -3, 0

Choice.B

This choice is wrong. The root 1 isn’t a solution to the function. The correct roots are -1, -3, and 2

x = 0, -3, 1

Choice.C

This option is correct and matches the zero’s of the cubic function \$ f(x) = x^3 + 2x^2 - 5x - 6 \$

x = -1, -3, 2

Choice.D

This is incorrect. There is a missing zero (-1) and an extraneous value (-5) included

x = 2, -5, 3

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?