Question

Using factor theorem, show that (x -2) is a factor of 2x+ 5x-4x-3.​

Answer 1

Answer:

let g (x)=(x-2) then

g (0)= x-2=0

x=2

now

p (2)=2×2-4×2-3

4-8-3

=-7

Answer 2

Step-by-step explanation:

The factor theorem states that if a polynomial P(x) has a factor x - c, then P(c) = 0. In other words, if a polynomial evaluates to 0 at a particular value c, then x - c must be a factor of the polynomial.

Using this theorem, we can show that (x - 2) is a factor of$2x + 5x - 4x - 3$by evaluating the polynomial $2x + 5x - 4x - 3$ at $x = 2.$ If the evaluation results in 0, then $x - 2$must be a factor of the polynomial.

Evaluating the polynomial 2x + 5x - 4x - 3 at x = 2, we get:

$2x + 5x - 4x - 3 = 2 * 2 + 5 * 2 - 4 * 2 - 3 = 7 - 4 - 3 = 0$

Since the evaluation of the polynomial results in 0, x - 2 must be a factor of the polynomial $2x + 5x - 4x - 3.$ Therefore, using the factor theorem, we can conclude that (x - 2) is a factor of$2x + 5x - 4x - 3.$

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