Question
Subtract. Express your answers as a polynomial in standard form. (1 point)
(4x5+3x3+7x)−(3x4−8x3+4x2)=
(4x5+3x3+7x)−(3x4−8x3+4x2)=
Answers
GPT-4o mini
To subtract the polynomials \((4x^5 + 3x^3 + 7x) - (3x^4 - 8x^3 + 4x^2)\), we'll first distribute the negative sign to the second polynomial:
\[
4x^5 + 3x^3 + 7x - 3x^4 + 8x^3 - 4x^2
\]
Now, we can combine like terms:
1. The term with \(x^5\): \(4x^5\)
2. The term with \(x^4\): \(-3x^4\)
3. The terms with \(x^3\): \(3x^3 + 8x^3 = 11x^3\)
4. The term with \(x^2\): \(-4x^2\)
5. The term with \(x\): \(7x\)
Putting it all together, we have:
\[
4x^5 - 3x^4 + 11x^3 - 4x^2 + 7x
\]
Thus, the result in standard form is:
\[
\boxed{4x^5 - 3x^4 + 11x^3 - 4x^2 + 7x}
\]
\[
4x^5 + 3x^3 + 7x - 3x^4 + 8x^3 - 4x^2
\]
Now, we can combine like terms:
1. The term with \(x^5\): \(4x^5\)
2. The term with \(x^4\): \(-3x^4\)
3. The terms with \(x^3\): \(3x^3 + 8x^3 = 11x^3\)
4. The term with \(x^2\): \(-4x^2\)
5. The term with \(x\): \(7x\)
Putting it all together, we have:
\[
4x^5 - 3x^4 + 11x^3 - 4x^2 + 7x
\]
Thus, the result in standard form is:
\[
\boxed{4x^5 - 3x^4 + 11x^3 - 4x^2 + 7x}
\]