what is the factored form of the polynomial (27x^{2}y - 43xy^{2})?\n(xy(27x - 43y))\n(x^{2}y^{2}(27…

what is the factored form of the polynomial (27x^{2}y - 43xy^{2})?\n(xy(27x - 43y))\n(x^{2}y^{2}(27 - 43))\n(3xy(9x - 17y))\n(3x^{2}y(9 - 14y))

what is the factored form of the polynomial (27x^{2}y - 43xy^{2})?\n(xy(27x - 43y))\n(x^{2}y^{2}(27 - 43))\n(3xy(9x - 17y))\n(3x^{2}y(9 - 14y))

Answer

Explanation:

Step1: Find the greatest common factor (GCF)

For the terms (27x^{2}y) and (43xy^{2}), the GCF of the coefficients (27) and (43) is (1). For the variables, the GCF of (x^{2}y) and (xy^{2}) is (xy).

Step2: Factor out the GCF

Factor out (xy) from (27x^{2}y - 43xy^{2}): [ \begin{align*} 27x^{2}y-43xy^{2}&=xy(27x - 43y) \end{align*} ] Let's check other options:

  • For (x^{2}y^{2}(27 - 43)), when we expand (x^{2}y^{2}(27 - 43)=27x^{2}y^{2}-43x^{2}y^{2}\neq27x^{2}y - 43xy^{2})
  • For (3xy(9x - 17y)), (3xy\times9x=27x^{2}y) and (3xy\times(- 17y)=-51xy^{2}\neq - 43xy^{2})
  • For (3x^{2}y(9 - 14y)), (3x^{2}y\times9 = 27x^{2}y) and (3x^{2}y\times(-14y)=-42x^{2}y^{2}\neq-43xy^{2})

Answer:

A. (xy(27x - 43y))