1

Problem

If \$3x^2 - 7x + 4\$ is multiplied by 2x - 5, what is the coefficient of x in the resulting polynomial?

2

Step

Given polynomials:

\$3x^2 - 7x + 4\$ and (2x - 5)

3

Step

Multiply the first term of the first polynomial by the first term of the second polynomial

\$ 3x^2 \times 2x = 6x^3 \$

4

Step

Multiply the second term of the first polynomial by the first term of the second polynomial

\$ −7x \times 2x = −14x^2 \$

5

Step

Multiply the third term of the first polynomial by the first term of the second polynomial

\$(4 \times 2x) = 8x\$

6

Step

Multiply the first term of the first polynomial by the second term of the second polynomial

\$ 3x^2 \times (−5) = −15x^2 \$

7

Step

Multiply the second term of the first polynomial by the second term of the second polynomial

\$−7x \times (−5) = 35x \$

8

Step

Multiply the third term of the first polynomial by the second term of the second polynomial

\$4 \times -5 = -20\$

9

Step

Combine all the terms obtained and Combine like terms

\$6x^3 − 14x^2 + 8x − 15x^2 + 35x − 20\$
\$6x^3 − 29x^2 + 43x − 20\$

10

Step

So, the resulting polynomial after multiplication is \$6x^3 − 29x^2 + 43x − 20\$.

11

Step

Identify the coefficient of x, which is

43

12

Solution

Therefore, the coefficient of x in the resulting polynomial is 43.

13

Sumup

Please Summarize Problem, Hint, Clue, Formula and Steps

Choices

14

Choice-A

This option doesn’t match the coefficient of x in the resulting polynomial 43. Therefore, option A is incorrect

Wrong 56

15

Choice-B

This option perfectly matches the coefficient of x in the resulting polynomial 43. Therefore, option B is correct

Correct 43

16

Choice-C

Option C suggests that the coefficient of x in the resulting polynomial is 25. However, this value does not match the result we obtained from the multiplication, which was 43. Therefore, option C is incorrect

Wrong 25

17

Choice-D

This option proposes that the coefficient of x in the resulting polynomial is 34. However, our calculation showed that the coefficient of x is 43. Therefore, option D is incorrect

Wrong 34

18

Step

option

B

19

Sumup

Please Summarize Choices