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Square root of a square polynomial

Find the square root of a square quadratic

This math skill teaches how to find the root of a square quadratic by factoring. It involves identifying two numbers that add to the coefficient of the linear term and multiply to the constant term, splitting the quadratic into binomials, and then simplifying by extracting common factors.

Learn square root of a square polynomial

Teaching Transcript

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Let's find the root of this square polynomial.

Notice that it's a quadratic. The trick to factoring quadratic equations is to split the 'X' variables. We need to find two values that will add to our 'X' coefficient of negative 8, and multiply to our constant of 16.

Negative 4 and negative 4 meet that criteria, so those are the pair that we can split the negative 8 'X' into.

Let's rewrite our quadratic with the 'X' term split out

Now let's group into two binomials. Pay close attention to the sign on the second binomial. Since we're subtracting the entire bracket, and we started with a positive 16, we need that to be negative inside the brackets, because subtracting negative 16 is the same as positive 16.

We can remove a common factor of 'X' from the first bracket, and a factor of 4 from the second bracket

We now have the entire term in brackets, 'X' minus 4, as a common factor, so we can remove that.

The brackets we are left with are the same, so we can express them as a square. So the root of our polynomial is 'X' minus 4

Skill Practice

Find the square root of a square quadratic

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