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

4

Step

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

\$(x \times (-1) = -x )\$

5

Step

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

\$(2 \times 3x) = 6x\$

6

Step

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

\$(2 \times (-1) = -2 )\$

7

Step

Combine the results from above steps:

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

8

Solution

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

9

Sumup

Please Summarize Problem, Hint, Clue, Formula and Steps

Choices

10

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

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

11

Choice-B

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

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

12

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

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

13

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

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

14

Step

option

C

15

Sumup

Please Summarize Choices