Question

check whether 7+3x is a factor of 3x cube +7x​

Answer 1

Answer:

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Answer 2

Answer

By division algorithm:-

p(x)=g(x)q(x)+r(x)

where, g(x) is the dividend,q(x) is the quotient, and r(x) is the remainder. Let r(x) here be denoted by k(any constant).

Here,

p(x)=3x³+7x=(7+3x)q(x)+k

=>p(-7/3)=-(343/9) - (49/3)={7+(-7)}q(x)+k

=>p(-7/3)= -490/9 = 0*q(x)+k

=>p(-7/3)= -490/9 =k

An expression can be the factor of a polynomial only if, on dividing that polynomial by the expression, the remainder (here, k) is equal to 0.

As k= -490/9 and k≠0

Hence, (7+3x) is not a factor of 3x³+7