Question

show that (x-1) is factor of x^4+5x^2=5x+1

Answer 1

Answer:

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Step-by-step explanation:

x+5 hence factories x3−5x2−x+5.

Medium

Answer

Given, 

f(x)=x3−5x2−x+5

Let us assume, x−1=0⇒x=1

Now, substitute the value of x=1 in f(x),

f(1)=13−(5×12)−1+5

=1−5−1+5

=−6+6

=0

∴ by factor theorem, 

(x−1) is a factor of f(x)

Now dividing f(x) by (x−1), we get

x3−5x2−x+5=(x−1)(x2−4x−5)

=(x−1)(x2−5x+x−5)

=(x−1){x(x−5)+1(x−5)}

=(x−1)(x+1)(x−5)