Question

using factor theorem show that g(x) is a factor of p(x) ,when
please answer these two questions!

Answer 1

Hey dear !!!

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Q.9) p(x) = 7x² - 4√2 x - 6 , g(x) = x -√2

==> Solution

( x - √2 ) = 0

∴ x = √2

[ By using factor theorem ]

∴ x = √2 taking in the given polynomial we get,

=> 7x² - 4√2 x - 6

=> 7(√2)² - 4√2(√2) - 6

=> 7*2 - 4*2 - 6

=> 14 - 8 - 6

=> 6 - 6

=> 0

Therefore, ( x - √2) is a factor of the given polynomial as remainder is zero .

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Q.10.) p(x) = 2√2 x² + 5x + √2 ,
g(x) = (x + √ 2)

==> Solution

( x + √2) = 0

∴ x = -√2

[ By using factor theorem ]

∴ x = -√2 taking in the given polynomial we get,

=> 2√2 x² + 5x + √2

=> 2√2(-√2)² + 5(-√2) + √2

=> 2√2* 2 - 5√2 + √2

=> 4√2 - 5√2 + √2

=> - √2 + √2

=> 0

Therefore, (x + √2) is a factor of the given polynomial as the remainder is zero .

Thanks !!!!

[ Be Brainly ]

Answer 2

Answer- By using factor theorem-
9. p(x)= 7x²-4√2x-6, g(x)= x-√2
g(x)= 0
x-√2=0
x=√2
Substituting values-
p(√2)= 7(√2)² -4√2(√2) -6
      = 7×2 -4×2 -6
      = 14-8-6
      = 14-14
      = 0
Therefore, g(x) is a factor of p(x).

10. p(x)= 2√2x²+5x+√2, g(x)= x+√2
g(x)= 0
x+√2= 0
x= -√2
Substituting values-
p(-√2)= 2√2(-√2)²+ 5(-√2)+ √2
          = 2√2×2+ (-5√2) +√2
          = 4√2 -5√2 +√2
          = 5√2 -5√2
          = 0
Therefore, g(x) is a factor of p(x).
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