Question

7. Find if (-2x – 5) is a factor of the polynomial p(x)=3x4 + 5x3 – 2x2 – 4 or not.

Answer 1

it is so difficult question

Answer 2

Answer: (-2x-5) is  not a factor of $p(x)=3x^4+5x^3-2x^2-4$, then by factor theorem $\frac{-5}{2}$ must be a zero of p(x)

Step-by-step explanation:

Let $g(x)=-2x-5$

Put $g(x)=0$, we get

$-2x-5=0\\\Rightarrow\ x=\frac{-5}{2}$

If g(x) is a factor of $p(x)=3x^4+5x^3-2x^2-4$, then by factor theorem $\frac{-5}{2}$ must be a zero of p(x).

$f(\frac{-5}{2})=3(\frac{-5}{2})^4+5(\frac{-5}{2})^3-2(\frac{-5}{2})^2-4\\=3(39.0625)+5(-15.625)-2(6.25)-4\\=117.1875-78.125-12.5-4=22.5625\neq0$

Hence, g(x) is not a factor of $p(x)=3x^4+5x^3-2x^2-4$, then by factor theorem $\frac{-5}{2}$ must be a zero of p(x).