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]
