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 polynomial expression 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

Solution

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

9

Sumup

Please Summarize Problem, Hint, Clue, Formula and Steps

Choices

10

Choice-A

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

Wrong 67.5

11

Choice-B

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

Wrong 76.5

12

Choice-C

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

Correct -67.5

13

Choice-D

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

Wrong -76.5

14

Step

Option

C

15

Sumup

Please Summarize Choices