Question

Using the distributive property to find the product (yâÂ’4x)(y2 4y 16) results in a polynomial of the form y3 4y2 ayâÂ’4xy2âÂ’axyâÂ’64x. What is the value of a in the polynomial? 4 8 16 32.

Answer 1

Option C: 16 is the correct option, presenting the value of the arbitrary constant a.

Given polynomial product is:

$(y-4x)(y^2 + 4y + 16)\\= y^3 + 4y^2 + 16y -4xy^2 -16xy - 64x$

and the given second form is:

$= y^3 + 4y^2 + ay -4xy^2 -16xy - 64x$

Thus the value of a after comparing both the polynomial expressions can be deduced as 16 since coefficient comparison can be done in polynomial if the variable expression in both of the polynomials are same.

Thus answer is 16, given by option C.

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