find the indicated sum.

\
\begin{array}{r}
8x^3 + 7x^2 \quad\quad + 19 \\
4x^3 - 2x^2 - 9x - 7 \\
\hline
\end{array}
\

Question

find the indicated sum.

\
\begin{array}{r}
8x^3 + 7x^2 \quad\quad + 19 \\
4x^3 - 2x^2 - 9x - 7 \\
\hline
\end{array}
\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Polynomial Addition" ], "current_concepts": [ "Polynomial Addition", "Polynomial Simplification" ] } ## Align like terms vertically $$ \begin{array}{rrcrcrcr} & 8x^3 & + & 7x^2 & & & + & 19 \ +& 4x^3 & - & 2x^2 & - & 9x & - & 7 \ \hline \end{array} $$ ## Add coefficients of like terms $$ \begin{aligned} (8 + 4)x^3 &= 12x^3 \ (7 - 2)x^2 &= 5x^2 \ 0x - 9x &= -9x \ 19 - 7 &= 12 \end{aligned} $$ ## Combine terms into final polynomial $$ 12x^3 + 5x^2 - 9x + 12 $$ Find the indicated sum. $$ \begin{array}{rrcrcrcr} & 8x^3 & + & 7x^2 & & & + & 19 \ & 4x^3 & - & 2x^2 & - & 9x & - & 7 \ \hline \end{array} $$ Answer: $12x^3 + 5x^2 - 9x + 12$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Addition" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Align like terms vertically

Add coefficients of like terms

Combine terms into final polynomial

Answer: