Question

In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not: a. b. C. f(x) = 4x ^ 3 - 12x ^ 2 + 14x - 3, g(x) = 2x - 1 f(x) = x ^ 3 - 6x ^ 2 + 2x - 4, g(x) = 1 - 2x f(x) = 9x ^ 3 - 3x ^ 2 + x - 5 , g(x) = x - 2/3​

Answer 1

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According to remainder theorem, We know if f(x) is divided by ( x - a) , then remainder = f(a) ,

If f(x) is divided by (x-a) we have taken it (x -a) = 0 .So, Remainder would be f(a) .

Now, p(x) = 4x³ -12x²+14x - 3 .

If p(x) is divided by 2x-1 , then (2x-1) = 0 , x = 1/2 .So when p(x) is divided by (2x-1) , it leaves a remainder p(1/2)

p(1/2)

= 4(1/2)³ -12(1/2)²+14(1/2)-3

= 4(⅛)-12(1/4)+7-3

= 1/2 -3 + 7 - 3

= 1/2 +1

= 3/2

The remainder when 4x³-12x²+14x-3 divided by 2x-1 is 3/2

Answer 2

theorem, We know if f(x) is divided by ( x - a) , then remainder = f(a) ,

If f(x) is divided by (x-a) we have taken it (x -a) = 0 .So, Remainder would be f(a) .

Now, p(x) = 4x³ -12x²+14x - 3 .

If p(x) is divided by 2x-1 , then (2x-1) = 0 , x = 1/2 .So when p(x) is divided by (2x-1) , it leaves a remainder p(1/2)

p(1/2)

= 4(1/2)³ -12(1/2)²+14(1/2)-3

= 4(⅛)-12(1/4)+7-3