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Lesson Example Discussion Quiz: Class Homework

Step-2

Title: Multiplication of Polynomials

Grade: 8-a Lesson: S1-L2

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

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	If \$4y^3 +10y^2 - 5y + 4\$ is multiplied by 3.5y - 5, what is the coefficient of \$y^2\$ in the resulting polynomial?
2	Step	The given polynomials expressions are	\$4y^3 +10y^2 - 5y + 4\$ is multiplied by 3.5y - 5
3	Step	First, let’s multiply \$4y^3+10y^2−5y + 4\$ by 3.5y	\$3.5y (4y^3 +10y^2 - 5y + 4)\$ \$= 14y^4 + 35y^3 - 17.5y^2 +14y\$
4	Step	Next multiply \$4y^3+10y^2−5y + 4\$ by -5	\$-5 (4y^3+10y^2−5y + 4)\$ \$= - 20y^3 - 50y^2 + 25y - 20\$
5	Step	Then, now sum up all the results:	\$14y^4 + 35y^3 - 17.5y^2 +14y - 20y^3 - 50y^2 + 25y - 20\$
6	Step	After simplification	\$14y^4 +15y^3 - 67.5y^2 +39y - 20\$
7	Step	Now, find the coefficient of \$y^2\$	\$y^2 = - 67.5\$
8	Step	Therefore, the coefficient of \$y^2\$ in the resulting polynomial is − 67.5.
9	Choice.A	Incorrect because the coefficient of \$y^2\$ in the resulting polynomial is actually − 67.5, not 67.5	67.5
10	Choice.B	This is not correct because it has a positive coefficient (76.5), while the correct coefficient is negative (- 67.5)	76.5
11	Choice.C	Correct: The polynomial is accurate due to its coefficient of \$y^2\$, which is precisely - 67.5 as specified	-67.5
12	Choice.D	Wrong, as it doesn’t represent the coefficient of \$y^2\$ in the resulting polynomial; it’s - 67.5	-76.5
13	Answer	Option	C
14	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

If \$4y^3 +10y^2 - 5y + 4\$ is multiplied by 3.5y - 5, what is the coefficient of \$y^2\$ in the resulting polynomial?

Step

The given polynomials expressions are

\$4y^3 +10y^2 - 5y + 4\$ is multiplied by 3.5y - 5

Step

First, let’s multiply \$4y^3+10y^2−5y + 4\$ by 3.5y

\$3.5y (4y^3 +10y^2 - 5y + 4)\$

\$= 14y^4 + 35y^3 - 17.5y^2 +14y\$

Step

Next multiply \$4y^3+10y^2−5y + 4\$ by -5

\$-5 (4y^3+10y^2−5y + 4)\$

\$= - 20y^3 - 50y^2 + 25y - 20\$

Step

Then, now sum up all the results:

\$14y^4 + 35y^3 - 17.5y^2 +14y - 20y^3 - 50y^2 + 25y - 20\$

Step

After simplification

\$14y^4 +15y^3 - 67.5y^2 +39y - 20\$

Step

Now, find the coefficient of \$y^2\$

\$y^2 = - 67.5\$

Step

Therefore, the coefficient of \$y^2\$ in the resulting polynomial is − 67.5.

Choice.A

Incorrect because the coefficient of \$y^2\$ in the resulting polynomial is actually − 67.5, not 67.5

67.5

Choice.B

This is not correct because it has a positive coefficient (76.5), while the correct coefficient is negative (- 67.5)

76.5

Choice.C

Correct: The polynomial is accurate due to its coefficient of \$y^2\$, which is precisely - 67.5 as specified

-67.5

Choice.D

Wrong, as it doesn’t represent the coefficient of \$y^2\$ in the resulting polynomial; it’s - 67.5

-76.5

Answer

Option

Sumup

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