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Sagot :
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].
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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