Question

Q3. If p(x) = x – 5x² + 4x – 3 and g(x) = x - 2, show that p(x) is not a
multiple of g(x).​

Answer 1

g(x)=x-2

so equate gx with 0

x-2=0

x=0+2=2

x=2

Now put the value of x in p(x)

p(2)= 2-5(2)^2+ 4(2) -3

2 - 5(4)+ 8 - 3

2-20+8-3

-18+5

-13

This the solution is not zero so we can say that g(x) is not the factor of p(x).

Hope it helps.....

Answer 2

Step-by-step explanation:

$g(x) = x-2,\\or, x-2 =0\\or,x=0+2\\or, x=2$

Then,

$p(x)= x^{3}-5x^{2} +4x-3\\or, p(2) = 2^{3} -5(2^{2}) +4(2) -3\\=8-5(4)+8-3\\=-20-3\\=-23$

Since the remainder is not zero so p(x) is not a multiple of g(x).