Question

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The questions are in the image. Answer only if you know how to solve them.

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Answer 1

hello my friend !

1)see that gx. x -2. (finding the value of x from gx)

hence x=2

putting in px

p(2). = 2^3-8
p(2)= 0 hence gx is factor of of by factor theorem

2) gx = x-3 (finding value of x)

x=3

putting in px
p(3) = 54 +63-72-45=0
by factor theorem if p(k) = 0 then x-k is factor of p(x) hence gx here is factor of px

3)gx = x-1
x= 1
putting in px

p(1) = 2+9+6-11-6=0
again by factor theorem gx is factor of pc

Answer 2

(1)

f(x) = x^3-  8

g(x) = x - 2.

Apply remainder theorem, we get

x - 2 = 0

x = 2.

plug x = 2 in f(x), we get

= > 2^3 - 8

= > 8 - 8

= > 0.

Remainder is 0, therefore g(x) is a factor of f(x).



(2)

p(x) = 2x^3 + 7x^2 - 24x - 45

g(x) = x - 3.

Apply remainder theorem, we get

x - 3 = 0

x = 3.

Plug x = 3 in f(x), we get

= > 2(3)^3 + 7(3)^2 - 24(3) - 45

= > 54 + 63 - 72 - 45

= > 0.

Remainder is 0, Therefore g(x) is  factor of f(x).



(3)

Given :

p(x) = 2x^4 + 9x^3 + 6x^2 - 11x - 6.

g(x) = x - 1.

Apply remainder theorem, we get

 x - 1 = 0

x = 1.

plug x = 1 in f(x), we get

= > 2(1)^4 + 9(1)^3 + 6(1)^2 - 11(1) - 6

= > 2 + 9 + 6 - 11 - 6

= > 17 - 11 - 6

= > 6- 6

= > 0.

Remainder is 0, therefore g(x) is a factor of f(x).


Hope this helps!