The HCF of polynomials (x – 2x + 1) (x + 4) and (x + 3x – 4) (x + 1) is?
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The HCF of polynomials (x – 2x + 1) (x + 4) and (x + 3x – 4) (x + 1) is?
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Answer:
HCF is (x-1)(x+4) = x²+3x-4.
Step-by-step explanation:
Let us split these expressions into factors by the method of 'splitting middle terms'
x²+3x - 4 = x² -x + 4x - 4 = x(x-1) +4 (x-1) = (x-1)(x+4)
=> (x²+3x-4) can be written as (x-1)*(x+4)
Now, consider (x²-2x+1)
x²-2x+1 = (x)²-2(x)(1)+(1)² = (x-1)²
=> x²-2x+1 can be written as (x-1)² = (x-1)*(x-1)
So now, (x²+3x-4) (x+1) can be written as (x-1)(x+4)(x+1)
and, (x²-2x+1) can be written as (x-1)(x-1)(x+4).
Now, as you can clearly see, in both of these expressions, we have two terms in common,
they are, (x-1)*(x+4)
So we can say that H.C.F (highest common factor) of these two expressions is (x-1)(x+4) = x²+3x-4.
Hope it helps..!
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