Find the HCF of x⁴+x²+1 and x⁴-x
Answers
Answer:
x2+x+1
Step-by-step explanation:
x
x 3
x 3 −1=x
x 3 −1=x 3
x 3 −1=x 3 −1
x 3 −1=x 3 −1 3
x 3 −1=x 3 −1 3
x 3 −1=x 3 −1 3 =(x−1)(x
x 3 −1=x 3 −1 3 =(x−1)(x 2
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1)
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x)
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x 2
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x 2 +1−x)
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x 2 +1−x)=(x
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x 2 +1−x)=(x 2
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x 2 +1−x)=(x 2 +x+1)(x
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x 2 +1−x)=(x 2 +x+1)(x 2
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x 2 +1−x)=(x 2 +x+1)(x 2 −x+1)
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x 2 +1−x)=(x 2 +x+1)(x 2 −x+1)Hence, H.C.F. of x
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x 2 +1−x)=(x 2 +x+1)(x 2 −x+1)Hence, H.C.F. of x 3
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x 2 +1−x)=(x 2 +x+1)(x 2 −x+1)Hence, H.C.F. of x 3 −1 and x
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x 2 +1−x)=(x 2 +x+1)(x 2 −x+1)Hence, H.C.F. of x 3 −1 and x 4
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x 2 +1−x)=(x 2 +x+1)(x 2 −x+1)Hence, H.C.F. of x 3 −1 and x 4 +x
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x 2 +1−x)=(x 2 +x+1)(x 2 −x+1)Hence, H.C.F. of x 3 −1 and x 4 +x 2
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x 2 +1−x)=(x 2 +x+1)(x 2 −x+1)Hence, H.C.F. of x 3 −1 and x 4 +x 2 +1 is x
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x 2 +1−x)=(x 2 +x+1)(x 2 −x+1)Hence, H.C.F. of x 3 −1 and x 4 +x 2 +1 is x 2
x 3 −1=x 3 −1 3 =(x−1)(x 2 +x+1)x 4 +x 2 +1=(x 4 +2x 2 +1)−x 2 =(x 2 +1) 2 −(x) 2 =(x 2 +1+x)(x 2 +1−x)=(x 2 +x+1)(x 2 −x+1)Hence, H.C.F. of x 3 −1 and x 4 +x 2 +1 is x 2 +x+1.
Step-by-step explanation:
Step-by-step explanation:x^4-1=(x^2-1)x^2+1
Step-by-step explanation:x^4-1=(x^2-1)x^2+1x^2-1=x^2-1¹1
Step-by-step explanation:x^4-1=(x^2-1)x^2+1x^2-1=x^2-1¹1hcf=x^2-1
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