Question

Check whether g(x) is a factor of p(x) or not where p(x)= 8x^3-6x^2-4x+3 and g(x)=x/3-1/4

Answer 1

Solution :

Given p(x)=8x³-6x²-4x+3

and

g(x) = x/3 - 1/4

The zero of g(x) is 3/4

[ since , To find zero of g(x)

we must take g(x) = 0

x/3 - 1/4 = 0

=> x/3 = 1/4

=> x = 3/4 ]

Then

Find p(3/4) :

p(3/4) =8(3/4)³-6(3/4)²-4(3/4)+3

= 8(3³/4³)-6(3²/4²)-3+3

= (8×27)/64 - (6×9)/16

= 27/8 - 27/8

= 0

Therefore,

p(3/4) = 0

_______________________

By factor theorem:

" If (x-a) is a factor of a polynomial p(x) then p(a) = 0"

________________________

Therefore,

g(x) is a factor of p(x)

•••••

Answer 2

Answer:

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