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Complete the square for a polynomial

Find a constant that makes the quadratic a perfect square

This math skill teaches how to find a constant that turns a quadratic expression into a perfect square trinomial. It involves identifying a constant that, when combined with given terms, allows the quadratic to be factored as the square of a binomial.

Learn complete the square for a polynomial

Teaching Transcript

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Let's find the constant that would make this a perfect square polynomial.

Remembering how we factor quadratics, we know that we need two numbers that add to 10, but multiply to our constant. Since it's a square, we know that the two numbers are the same.

So the numbers must be 5 and 5.

If we multiply them together we see that the constant we need is 25. To verify that this is correct, we can complete the factoring and we see that the root is 'X' plus 5, all squared.

Skill Practice

Find a constant that makes the quadratic a perfect square

Test your understanding of complete the square for a polynomial by practicing it! Work through the below exercises to use it in practice.