Question

lucia finds that $(3x^{2}+3x+5)+(7x^{2}-9x+8)=10x^{2}-12x+13$. what error did lucia make?
she found the difference instead of the sum.
she combined the terms $3x^{2}$ and $7x^{2}$ incorrectly.
she combined the terms $3x$ and $-9x$ incorrectly.
she did not combine all like terms.

Explanation:

Step1: Combine $x^2$ terms

$3x^2 + 7x^2 = 10x^2$

Step2: Combine $x$ terms

$3x + (-9x) = -6x$

Step3: Combine constant terms

$5 + 8 = 13$

Step4: Compare to Lucia's result

Correct sum: $10x^2 -6x +13$; Lucia's result: $10x^2 -12x +13$

Answer:

She combined the terms $3x$ and $-9x$ incorrectly.