Check whether 7 + 3x is a factor of 3x3 + 7x.

Answer:

A polynomial is an algebraic expression in which the exponent on any variable is a whole number. Polynomial’s degree is the highest or the greatest power of a variable in a polynomial equation.

Factor Theorem

A polynomial P(x) divided by Q(x) results in R(x) with zero remainders if and only if Q(x) is a factor of P(x).

Given

  • Dividend is 3x3+7x
  • Divisor is 7+3x

Let us put divisor is equal to zero.

7 + 3x = 0

3x = -7

x = -7/3

Let us consider

p(x) = 3x3+7x

put x = -7/3 in the above equation

p(x) = 3(-7/3)3 + 7(-7/3)

p(x) = 3(-343/27) – 49/3

p(x) = -1029/27 – 49/3

p(x) = -343/9 – 49/3

p(x) = (-343 – 87)/9

p(x) = (-343-147)/9

p(x) = -490/9 ≠ 0

∴7 + 3x is not a factor of 3x3+7x.

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