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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]



Answer :

GinnyAnswer
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].

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