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Lesson Example Discussion Quiz: Class Homework

Step-3

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	Consider the polynomials (x + 2) and (3x - 1). What is the product of these two expressions?
2	Step	Given polynomials	(x + 2), (3x - 1)
3	Step	Multiply the first term of the first polynomial by each term of the second polynomial	\$(x . 3x) = 3x^2 \$
4	Step	Multiply the first term of the first polynomial by second term of the second polynomial	(x . (- 1) = - x )
5	Step	Multiply the second term of the first polynomial by the first term of the second polynomial	(2 . 3x) = 6x
6	Step	Multiply the second term of the first polynomial by the second term of the second polynomial	(2 . (- 1) = - 2 )
7	Step	Combine the results from steps 1, 2, 3, and 4:	(x + 2)(3x - 1) = \$ 3x^2 - x + 6x - 2 \$
8	Step	So, the product of (x + 2) and (3x - 1) is \$ 3x^2 + 5x - 2 \$.
9	Choice.A	This option doesn’t match our result \$ 3x^2 + 5x − 2 \$ because it has a different coefficient for the term involving x. Therefore, option A is incorrect	\$3x^2 + 4x - 1\$
10	Choice.B	This option doesn’t match our result \$ 3x^2 + 5x − 2 \$ because it has different terms altogether. Therefore, option B is incorrect	\$4x^2 - 5x - 2\$
11	Choice.C	This option perfectly matches our result \$ 3x^2 + 5x − 2 \$ Each term has the correct coefficient and power of x. Therefore, option C is correct	\$3x^2 + 5x - 2\$
12	Choice.D	This option has a term involving \$x^3\$, which is not present in our result \$ 3x^2 + 5x − 2 \$. Therefore, option D is incorrect	\$4x^3 - 4x - 1\$
13	Answer	Option	C
14	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Consider the polynomials (x + 2) and (3x - 1). What is the product of these two expressions?

Step

Given polynomials

(x + 2), (3x - 1)

Step

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

\$(x . 3x) = 3x^2 \$

Step

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

(x . (- 1) = - x )

Step

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

(2 . 3x) = 6x

Step

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

(2 . (- 1) = - 2 )

Step

Combine the results from steps 1, 2, 3, and 4:

(x + 2)(3x - 1) = \$ 3x^2 - x + 6x - 2 \$

Step

So, the product of (x + 2) and (3x - 1) is \$ 3x^2 + 5x - 2 \$.

Choice.A

This option doesn’t match our result \$ 3x^2 + 5x − 2 \$ because it has a different coefficient for the term involving x. Therefore, option A is incorrect

\$3x^2 + 4x - 1\$

Choice.B

This option doesn’t match our result \$ 3x^2 + 5x − 2 \$ because it has different terms altogether. Therefore, option B is incorrect

\$4x^2 - 5x - 2\$

Choice.C

This option perfectly matches our result \$ 3x^2 + 5x − 2 \$ Each term has the correct coefficient and power of x. Therefore, option C is correct

\$3x^2 + 5x - 2\$

Choice.D

This option has a term involving \$x^3\$, which is not present in our result \$ 3x^2 + 5x − 2 \$. Therefore, option D is incorrect

\$4x^3 - 4x - 1\$

Answer

Option

Sumup

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