Question

# Match the polynomials with their respective factors.x−1x−3x−5x−7

Solution

## The correct option is According to the factor theorem, if (x−a) is a factor of a polynomial f(x), then f(a) = 0. For  f(x)=x2−3x+2 f(1)=12−3× 1+2=0. Hence, (x−1) is the factor of  x2−3x+2. For  f(x)=x2−7x+12 f(3)=32−7× 3+12=0. Hence, (x−3) is the factor of  x2−7x+12. For  f(x)=x2−11x+30  f(5)=52−11× 5+30=0. Hence, (x−5) is the factor of  x2−11x+30. For  f(x)=x2−15x+56 f(7)=72−15× 7+56=0. Hence, (x−7) is the factor of  x2−15x+56.

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