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Answer :
Sure! Let's walk through how to multiply these two polynomials step by step:
We need to multiply [tex]\( (x^2 - 5x) \)[/tex] by [tex]\( (2x^2 + x - 3) \)[/tex].
1. Distribute Each Term: We first distribute each term from the first polynomial to each term in the second polynomial. Here's how it's done:
- Multiply [tex]\( x^2 \)[/tex] by each term in the second polynomial:
[tex]\[
x^2 \cdot 2x^2 = 2x^4
\][/tex]
[tex]\[
x^2 \cdot x = x^3
\][/tex]
[tex]\[
x^2 \cdot (-3) = -3x^2
\][/tex]
- Multiply [tex]\(-5x\)[/tex] by each term in the second polynomial:
[tex]\[
-5x \cdot 2x^2 = -10x^3
\][/tex]
[tex]\[
-5x \cdot x = -5x^2
\][/tex]
[tex]\[
-5x \cdot (-3) = 15x
\][/tex]
2. Combine Like Terms: Now, let's combine all the terms:
- For [tex]\( x^4 \)[/tex] terms:
[tex]\( 2x^4 \)[/tex]
- For [tex]\( x^3 \)[/tex] terms:
[tex]\( x^3 - 10x^3 = -9x^3 \)[/tex]
- For [tex]\( x^2 \)[/tex] terms:
[tex]\(-3x^2 - 5x^2 = -8x^2 \)[/tex]
- For [tex]\( x \)[/tex] terms:
[tex]\( 15x \)[/tex]
3. Write the Final Polynomial: Combine all of these results to get the final polynomial:
[tex]\[
2x^4 - 9x^3 - 8x^2 + 15x
\][/tex]
So the answer is A. [tex]\(2x^4 - 9x^3 - 8x^2 + 15x\)[/tex].
We need to multiply [tex]\( (x^2 - 5x) \)[/tex] by [tex]\( (2x^2 + x - 3) \)[/tex].
1. Distribute Each Term: We first distribute each term from the first polynomial to each term in the second polynomial. Here's how it's done:
- Multiply [tex]\( x^2 \)[/tex] by each term in the second polynomial:
[tex]\[
x^2 \cdot 2x^2 = 2x^4
\][/tex]
[tex]\[
x^2 \cdot x = x^3
\][/tex]
[tex]\[
x^2 \cdot (-3) = -3x^2
\][/tex]
- Multiply [tex]\(-5x\)[/tex] by each term in the second polynomial:
[tex]\[
-5x \cdot 2x^2 = -10x^3
\][/tex]
[tex]\[
-5x \cdot x = -5x^2
\][/tex]
[tex]\[
-5x \cdot (-3) = 15x
\][/tex]
2. Combine Like Terms: Now, let's combine all the terms:
- For [tex]\( x^4 \)[/tex] terms:
[tex]\( 2x^4 \)[/tex]
- For [tex]\( x^3 \)[/tex] terms:
[tex]\( x^3 - 10x^3 = -9x^3 \)[/tex]
- For [tex]\( x^2 \)[/tex] terms:
[tex]\(-3x^2 - 5x^2 = -8x^2 \)[/tex]
- For [tex]\( x \)[/tex] terms:
[tex]\( 15x \)[/tex]
3. Write the Final Polynomial: Combine all of these results to get the final polynomial:
[tex]\[
2x^4 - 9x^3 - 8x^2 + 15x
\][/tex]
So the answer is A. [tex]\(2x^4 - 9x^3 - 8x^2 + 15x\)[/tex].
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