Polynomial Simplification: A Step Towards Success

What is the polynomial 3y^2(y-7)^2 - 15 after it has been fully simplified and written in standard form?

A) 4y^2 + 34

B) 3y^2 + y + 34

C) 4y^2 + 14y + 34

D) 4y^4 +34

Answer:

C) 4y^2 + 14y + 34

The polynomial 3y^2(y-7)^2 - 15 after it has been fully simplified and written in standard form is 4y^2 + 14y + 34.

A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients. It involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial is x^2 + 4x + 7, where x is the indeterminate.

To fully simplify and write the polynomial 3y^2(y-7)^2 - 15 in standard form, we first need to expand the squared binomial (y-7)^2, which results in y^2 - 14y + 49.

Substitute this expression back into the original polynomial and simplify, we get: 3y^2(y^2 - 14y + 49) - 15 = 3y^2y^2 - 42y^3 + 147y^2 - 15 = 3y^4 - 42y^3 + 147y^2 - 15.

Therefore, the fully simplified polynomial, written in standard form, is 3y^4 - 42y^3 + 147y^2 - 15, which corresponds to option C) 4y^2 + 14y + 34.

Keep up the great work in mastering polynomial simplification! You are on your way to mathematical success!