Find the difference of the polynomials. x 4 + 7 x 3 + 5 x − 7 − ( − 3 x 3 + 2 x + 7 ) \begin{array} { l } x ^ { 4 } + 7 x ^ { 3 } + 5 x - 7 \- \left( - 3 x ^ { 3 } + 2 x + 7 ight) \\hline\end{array} x 4 + 7 x 3 + 5 x − 7 − ( − 3 x 3 + 2 x + 7 ) A) x 4 + 10 x 3 + 3 x − 14 x ^ { 4 } + 10 x ^ { 3 } + 3 x - 14 x 4 + 10 x 3 + 3 x − 14 B) x 4 + 10 x 3 + 7 x − 14 x ^ { 4 } + 10 x ^ { 3 } + 7 x - 14 x 4 + 10 x 3 + 7 x − 14 C) x 4 + 10 x 3 + 3 x + 14 x ^ { 4 } + 10 x ^ { 3 } + 3 x + 14 x 4 + 10 x 3 + 3 x + 14 D) x 4 + 4 x 3 + 3 x + 14 x ^ { 4 } + 4 x ^ { 3 } + 3 x + 14 x 4 + 4 x 3 + 3 x + 14 E) x 4 + 4 x 3 + 7 x + 14 x ^ { 4 } + 4 x ^ { 3 } + 7 x + 14 x 4 + 4 x 3 + 7 x + 14

Question

Find the difference of the polynomials.   x 4 + 7 x 3 + 5 x − 7 − ( − 3 x 3 + 2 x + 7 )  \begin{array} { l } x ^ { 4 } + 7 x ^ { 3 } + 5 x - 7 \- \left( - 3 x ^ { 3 } + 2 x + 7 ight) \\hline\end{array} x 4 + 7 x 3 + 5 x − 7 − ( − 3 x 3 + 2 x + 7 )  ​ ​ A)    x 4 + 10 x 3 + 3 x − 14 x ^ { 4 } + 10 x ^ { 3 } + 3 x - 14 x 4 + 10 x 3 + 3 x − 14 B)    x 4 + 10 x 3 + 7 x − 14 x ^ { 4 } + 10 x ^ { 3 } + 7 x - 14 x 4 + 10 x 3 + 7 x − 14 C)    x 4 + 10 x 3 + 3 x + 14 x ^ { 4 } + 10 x ^ { 3 } + 3 x + 14 x 4 + 10 x 3 + 3 x + 14 D)    x 4 + 4 x 3 + 3 x + 14 x ^ { 4 } + 4 x ^ { 3 } + 3 x + 14 x 4 + 4 x 3 + 3 x + 14 E)    x 4 + 4 x 3 + 7 x + 14 x ^ { 4 } + 4 x ^ { 3 } + 7 x + 14 x 4 + 4 x 3 + 7 x + 14

Khaled Yasen · Accepted Answer

Final Answer : A, Explanation :   Subtracting the second polynomial from the first involves changing the signs of the terms in the second polynomial and then adding them to the first. This results in   x 4 + 7 x 3 + 5 x − 7 + 3 x 3 − 2 x − 7 x^4 + 7x^3 + 5x - 7 + 3x^3 - 2x - 7 x 4 + 7 x 3 + 5 x − 7 + 3 x 3 − 2 x − 7  , which simplifies to   x 4 + 10 x 3 + 3 x − 14 x^4 + 10x^3 + 3x - 14 x 4 + 10 x 3 + 3 x − 14  .

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