Math, asked by however30, 1 year ago

check whether (-2x-5) is a factor of the polynomial p(x)=3x^4+5x^3-2x^2-4 or not


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Answers

Answered by Anonymous
13

Answer:

(-2x-5) \ is \ not \ a \ factor \ of \ the \ polynomial \ p(x)=3x^4+5x^3-2x^2-4

Step-by-step explanation:

\large \text{Given $p(x)=3x^4+5x^3-2x^2-4 \ and \ g(x)=-2x-5$}\\\\\\\\large \text{zeroes of g(x)=-2x-5=0}\\\\\\\\\large \text{$x=\dfrac{-5}{2}$}\\\\\\\large \text{putting g(x) value in p(x)}\\\\\\\\\\\large \text{$p(\dfrac{-5}{2})=3(\dfrac{-5}{2})^4+5(\dfrac{-5}{2})^3-2(\dfrac{-5}{2})^2-4 $}\\\\\\\\\\\large \text{$p(\dfrac{-5}{2})=3(\dfrac{625}{16})+5(\dfrac{-125}{8})-2(\dfrac{25}{4})-4 $}\\\\\\\\\\\\\large \text{$p(\dfrac{-5}{2})=(\dfrac{1875}{16})-(\dfrac{625}{8})-(\dfrac{50}{4})-4 $}\\\\\\\\\\\large \text{$p(\dfrac{-5}{2})=(\dfrac{1875-1250-200-64}{16})$}\\\\\\\\\\\large \text{$p(\dfrac{-5}{2})=\dfrac{1875-1514}{16}$}\\\\\\\\\\\large \text{$p(\dfrac{-5}{2})=\dfrac{361}{16}$}\\\\\\\\\\\large \text{Since remainder does not come 0 }\\\\\\\\\\\large \text{Therefore g(x) is not a factor of (p)x}


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