Question

Find remainder when p(x)/g(x) (by remainder theorem )
P(x)=x^4-3x^2+2x+1 g(x)=(x-1)

Answer 1

Answer:

• Remainder = 1 or p(1) = 1

Step-by-step explanation:

$\mapsto\sf{g(x) = (x - 1)}$

$\mapsto\sf{p(x) = x^4 - 3x^2 + 2x + 1}$

★ By using remainder theorem :-

→ g(x) = x - 1 = 0

= g(x) = x = 0 + 1

= g(x) = x = 1

→ p(x) = x⁴ - 3x² + 2x + 1

= p(1) = (1)⁴ - 3(1)² + 2(1) + 1

= p(1) = 1 - 3 + 2 + 1

= p(1) = -2 + 2 + 1

= p(1) = 1

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★ What is a remainder theorem?

→ Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x - a then the remainder is p(a).

★ One example :-

→ Find the remainder when x⁴ + x³ - 2x² + x + 2 is divided by (x - 1).

= g(x) = x - 1 = 0

= g(x) = x = 0 + 1 = 1

= p(x) = x⁴ + x³ - 2x² + x + 2

= p(x) = (1)⁴ + (1)³ - 2(1)² + (1) + 2

= p(x) = 1 + 1 - 2 + 1 + 2

= p(x) = 11

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Answer 2

Hey there !

Hey there ! Given :-

Hey there!

Given :-

g(x) = x-1

if g(x) = 0 then we can find out its zero

which Is x= 1

Now putting it into

p(x)

p(1) = 1 - 3 +2+1 = 1

Hope this was helpful :)