poopey
Answered

Marcus finds that [tex]$\left(3 x^2-2 y^2+5 x\right)+\left(4 x^2+12 y^2-7 x\right)=7 x^2-10 y^2-2 x$[/tex]. What error did Marcus make?

A. He combined the terms [tex]$5 x$[/tex] and [tex]$-7 x$[/tex] incorrectly.
B. He combined the terms [tex]$3 x^2$[/tex] and [tex]$4 x^2$[/tex] incorrectly.
C. He combined the terms [tex]$-2 y^2$[/tex] and [tex]$12 y^2$[/tex] incorrectly.
D. He subtracted the polynomials instead of adding.



Answer :

Let's carefully analyze Marcus's polynomial addition step by step to determine the error he made.

Given expressions:
1. \( 3x^2 - 2y^2 + 5x \)
2. \( 4x^2 + 12y^2 - 7x \)

To find the combined expression, we should add the corresponding terms from each polynomial.

1. Combine the \( x^2 \) terms:
[tex]\[ (3x^2) + (4x^2) = 7x^2 \][/tex]

2. Combine the \( y^2 \) terms:
[tex]\[ (-2y^2) + (12y^2) = 10y^2 \][/tex]

3. Combine the \( x \) terms:
[tex]\[ 5x + (-7x) = -2x \][/tex]

Thus, the correctly combined expression should be:
[tex]\[ 7x^2 + 10y^2 - 2x \][/tex]

However, Marcus stated that:
[tex]\[ (3x^2 - 2y^2 + 5x) + (4x^2 + 12y^2 - 7x) = 7x^2 - 10y^2 - 2x \][/tex]

Comparing the correct combined expression \( 7x^2 + 10y^2 - 2x \) with Marcus's result \( 7x^2 - 10y^2 - 2x \), we can see that Marcus combined the \(-2y^2\) and \(12y^2\) terms incorrectly. He ended up with \(-10y^2\) instead of the correct \(10y^2\).

Therefore, the error Marcus made is:

He combined the terms [tex]\(-2 y^2\)[/tex] and [tex]\(12 y^2\)[/tex] incorrectly.