Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Subtract. Your answer should be a polynomial in standard form.

[tex]\[
\left(3x^3 + 4x^2\right) - \left(2x^3 + 3x^2 - x\right) = \square
\][/tex]

Sagot :

GinnyAnswer
Sure, let's solve the given question step by step.

Given polynomials:

[tex]\[ P(x) = 3x^3 + 4x^2 \][/tex]
[tex]\[ Q(x) = 2x^3 + 3x^2 - x \][/tex]

We need to subtract [tex]\( Q(x) \)[/tex] from [tex]\( P(x) \)[/tex]:

[tex]\[ P(x) - Q(x) = (3x^3 + 4x^2) - (2x^3 + 3x^2 - x) \][/tex]

Step 1: Distribute the subtraction sign through the second polynomial:

[tex]\[ = 3x^3 + 4x^2 - 2x^3 - 3x^2 + x \][/tex]

Step 2: Combine like terms:

- For [tex]\( x^3 \)[/tex] terms: [tex]\( 3x^3 - 2x^3 = x^3 \)[/tex]
- For [tex]\( x^2 \)[/tex] terms: [tex]\( 4x^2 - 3x^2 = x^2 \)[/tex]
- For [tex]\( x \)[/tex] terms: [tex]\( 0 + x = x \)[/tex]

Putting it all together, we have:

[tex]\[ P(x) - Q(x) = x^3 + x^2 + x \][/tex]

This polynomial can be represented in a standard form:

[tex]\[ P(x) - Q(x) = x(x^2 + x + 1) \][/tex]

So, the result of subtracting the given polynomials is:

[tex]\[ x^3 + x^2 + x \][/tex]
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.