This math topic focuses on practicing how to make polynomials into perfect squares by completing the square. Students are given quadratic expressions and asked to identify the constant term that will transform each quadratic into a perfect square trinomial. This skill involves understanding the structure of a quadratic expression and applying algebraic manipulation to achieve a specific form. Each question is presented with two potential answers. The problems are part of an introductory unit on completing the square specifically for polynomials.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Polynomials - Complete the Square (to Polynomial) Worksheet

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Polynomials - Complete the Square (to Polynomial)
1
A LaTex expression showing t to the power of 2 - 18t + ?
Which constant value makes this polynomial a perfect square?
a A LaTex expression showing t to the power of 2 - 18t + 81
b A LaTex expression showing t to the power of 2 - 18t + 79
2
A LaTex expression showing x to the power of 2 - 8x + ?
Which constant value makes this polynomial a perfect square?
a A LaTex expression showing x to the power of 2 - 8x + 16
b A LaTex expression showing x to the power of 2 - 8x + 18
3
A LaTex expression showing y to the power of 2 + 16y + ?
Which constant value makes this polynomial a perfect square?
a A LaTex expression showing y to the power of 2 + 16y + 63
b A LaTex expression showing y to the power of 2 + 16y + 64
4
A LaTex expression showing r to the power of 2 + 2r + ?
Which constant value makes this polynomial a perfect square?
a A LaTex expression showing r to the power of 2 + 2r + 0
b A LaTex expression showing r to the power of 2 + 2r + 1
5
A LaTex expression showing n to the power of 2 + 2n + ?
Which constant value makes this polynomial a perfect square?
a A LaTex expression showing n to the power of 2 + 2n + 3
b A LaTex expression showing n to the power of 2 + 2n + 1
6
A LaTex expression showing t to the power of 2 - 12t + ?
Which constant value makes this polynomial a perfect square?
a A LaTex expression showing t to the power of 2 - 12t - 36
b A LaTex expression showing t to the power of 2 - 12t + 36
7
A LaTex expression showing z to the power of 2 + 18z + ?
Which constant value makes this polynomial a perfect square?
a A LaTex expression showing z to the power of 2 + 18z + 81
b A LaTex expression showing z to the power of 2 + 18z + 80
8
A LaTex expression showing m to the power of 2 - 16m + ?
Which constant value makes this polynomial a perfect square?
a A LaTex expression showing m to the power of 2 - 16m + 62
b A LaTex expression showing m to the power of 2 - 16m + 64