Math, asked by Yadavchild67890, 1 year ago

Use remainder theorem to factorize: 2x^3+3x^2-9x-10

Answers

Answered by MaheswariS
42

Answer:

\textsf{The factors are (x-2), (x+1) and (2x+5)}

Step-by-step explanation:

\text{Let}\bf\,P(x)=2x^3+3x^2-9x-10

\text{put x=2}

P(2)=2(2)^3+3(2)^2-9(2)-10

P(2)=16+12-18-10

P(2)=0

\therefore\textbf{(x-2) is a factor of P(x)}

\text{put x=-1}

P(-1)=2(-1)^3+3(-1)^2-9(-1)-10

P(-1)=-2+3+9-10

P(-1)=0

\therefore\textbf{(x+1) is a factor of P(x)}

\text{By synthetic division, we have}

\begin{array}{r|rrrr}2&2&3&-9&-10\\&&4&14&10\\\cline{2-5}\\-1&2&7&5&|\;0\\&&-2&-5&\\\cline{2-5}\\&2&5&|\;0&\end{array}

\therefore\textbf{The remaining factor is (2x+5)}

Answered by pithwaheer
27

Step-by-step explanation:

refer to the answer above

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