Answered

Find answers to your most challenging questions with the help of IDNLearn.com's experts. Whether it's a simple query or a complex problem, our community has the answers you need.

Match the multiplication problem on the left with the simplified polynomial on the right.

[tex]\[
\begin{array}{ll}
1. \quad 5x\left(3x^2 + 2x - 3\right) & A. \quad 15x^2 + 10x + 2 \\
2. \quad (3x + 5)(5x - 3) & B. \quad 15x^2 + 16x - 15 \\
3. \quad 3x\left(5x^2\right) & C. \quad 15x^3 \\
4. \quad (3x - 2)\left(5x^2 + 6x - 5\right) & D. \quad 15x^3 - x^2 - 3x + 10 \\
& E. \quad 15x^3 + 8x^2 - 27x + 10 \\
& F. \quad 15x^3 + 10x^2 - 15x
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
Let's carefully match each multiplication problem on the left with its corresponding simplified polynomial on the right.

1. Problem: [tex]\( 5x(3x^2 + 2x - 3) \)[/tex]

- Let's consider the polynomial:
- [tex]\( 15x^2 + 10x + 2 \)[/tex]
- [tex]\( 15x^2 + 16x - 15 \)[/tex]
- [tex]\( 15x^3 \)[/tex]
- [tex]\( 15x^3 - x^2 - 3x + 10 \)[/tex]
- [tex]\( 15x^3 + 8x^2 - 27x + 10 \)[/tex]
- [tex]\( 15x^3 + 10x^2 - 15x \)[/tex]

- The correct match here is [tex]\( 15x^3 + 10x^2 - 15x \)[/tex].

2. Problem: [tex]\( (3x + 5)(5x - 3) \)[/tex]

- Let's consider the remaining polynomials:
- [tex]\( 15x^2 + 10x + 2 \)[/tex]
- [tex]\( 15x^2 + 16x - 15 \)[/tex]
- [tex]\( 15x^3 \)[/tex]
- [tex]\( 15x^3 - x^2 - 3x + 10 \)[/tex]
- [tex]\( 15x^3 + 8x^2 - 27x + 10 \)[/tex]

- The correct match is: [tex]\( 15x^2 + 16x - 15 \)[/tex].

3. Problem: [tex]\( 3x(5x^2) \)[/tex]

- Let's consider the remaining polynomials:
- [tex]\( 15x^2 + 10x + 2 \)[/tex]
- [tex]\( 15x^3 - x^2 - 3x + 10 \)[/tex]
- [tex]\( 15x^3 \)[/tex]
- [tex]\( 15x^3 + 8x^2 - 27x + 10 \)[/tex]

- The correct match is: [tex]\( 15x^3 \)[/tex].

4. Problem: [tex]\( (3x - 2)(5x^2 + 6x - 5) \)[/tex]

- Let's consider the remaining polynomials:
- [tex]\( 15x^2 + 10x + 2 \)[/tex]
- [tex]\( 15x^3 - x^2 - 3x + 10 \)[/tex]
- [tex]\( 15x^3 + 8x^2 - 27x + 10 \)[/tex]

- The correct match here is [tex]\( 15x^3 + 8x^2 - 27x + 10 \)[/tex].

Thus, the correct pairs are:

- [tex]\( 5x(3x^2 + 2x - 3) \)[/tex] matches with [tex]\( 15x^3 + 10x^2 - 15x \)[/tex].
- [tex]\( (3x + 5)(5x - 3) \)[/tex] matches with [tex]\( 15x^2 + 16x - 15 \)[/tex].
- [tex]\( 3x(5x^2) \)[/tex] matches with [tex]\( 15x^3 \)[/tex].
- [tex]\( (3x - 2)(5x^2 + 6x - 5) \)[/tex] matches with [tex]\( 15x^3 + 8x^2 - 27x + 10 \)[/tex].
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.