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Lesson Example Discussion Quiz: Class Homework

Step-4

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 \$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 . 2x = 6x^3 \$
4	Step	Multiply the second term of the first polynomial by the first term of the second polynomial	\$ −7x . 2x = − 14x^2 \$
5	Step	Multiply the third term of the first polynomial by the first term of the second polynomial	\$ (4 . 2x) = 8x \$
6	Step	Multiply the first term of the first polynomial by the second term of the second polynomial	\$ 3x^2 . (−5) = − 15x^2 \$
7	Step	Multiply the second term of the first polynomial by the second term of the second polynomial	\$−7x . (−5) = 35x \$
8	Step	Multiply the third term of the first polynomial by the second term of the second polynomial	\$4 . (- 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	Step	Therefore, the coefficient of x in the resulting polynomial is 43.
13	Choice.A	This option doesn’t match the coefficient of x in the resulting polynomial 43. Therefore, option A is incorrect	56
14	Choice.B	This option perfectly matches the coefficient of x in the resulting polynomial 43. Therefore, option B is correct	43
15	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	25
16	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	34
17	Answer	Option	B
18	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

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

Step

Given polynomials

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

Step

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

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

Step

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

\$ −7x . 2x = − 14x^2 \$

Step

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

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

Step

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

\$ 3x^2 . (−5) = − 15x^2 \$

Step

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

\$−7x . (−5) = 35x \$

Step

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

\$4 . (- 5) = - 20\$

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\$

Step

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

Step

Identify the coefficient of x, which is

Step

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

Choice.A

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

Choice.B

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

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

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

Answer

Option

Sumup

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