Lorie made a mistake in the subtraction and combination of constants during polynomial long division, which is a critical step in the overall division process.
- In reviewing the division of polynomials provided by Lorie, the mistake that was made appears to be related to the incorrect subtraction and combination of constants in the last step.
- When performing polynomial long division, it's important to correctly subtract polynomial expressions and combine like terms.
- Lorie should have subtracted the entire polynomial expression after multiplying by the term found in the quotient.
- This process is akin to dividing exponentials, where the division of terms is performed by subtracting the exponents of exponential terms.
- To ensure the correct result, every step of the polynomial long division must be done with meticulous care to avoid mistakes in subtraction or overlooking terms that should be combined.
Question:
Lorie is using long division to find the quotient of x^3+6x^2+5 and x^2+x-1 , as shown. x+5- 4x/x^2+x-1 x^2+x-1overline )x^3+6x^2+0x+5 - ((x^3+x^2-x))/5x^2+x +5 - ((5x^2+5x-5))/-4x+0 What mistake did Lorie make?
A. The second term in the quotient should be 7
B. She combined the constants incorrectly in the last step..
C. She added an extra term to the dividend.
D. The last term in the quotient has an incorrect denominator.