Question

check whether the polynomial p(x)=x-3is a factor of Q(x)=2x⁴+3x³-2x²-9x-4 without doing division processes ​

Answer 1

$\huge\underline\mathfrak\red{AnSwEr}$

First we will find the zero of x-3 that will be-

$x - 3 = 0$

$x = 0 + 3$

$x = 3$

_____________________________________

Now ATQ:-

$Q(x)=2x⁴+3x³-2x²-9x-4$

$Q(3)=2(3)⁴+3(3)³-2(3)²-9(3)-4$

$= > 162 + 81 - 18 - 27 - 4$

$= > 194 \: ans$

_____________________________________

$\therefore$ x-3 is not a factor.

Answer 2

Answer:

First we will find the zero of x-3 that will be-

x - 3 = 0x−3=0

x = 0 + 3x=0+3

x = 3x=3

_____________________________________

Now ATQ:-

Q(x)=2x⁴+3x³-2x²-9x-4Q(x)=2x⁴+3x³−2x²−9x−4

Q(3)=2(3)⁴+3(3)³-2(3)²-9(3)-4Q(3)=2(3)⁴+3(3)³−2(3)²−9(3)−4

= > 162 + 81 - 18 - 27 - 4=>162+81−18−27−4

= > 194 \: ans=>194ans

_____________________________________

\therefore∴ x-3 is not a factor.