Quadratic trinomial which is not a perfect square

Recognizing the pattern to perfect squares isn't a make-or-break issue — these are quadratics that you can factor in the usual way — but noticing the pattern can be a time-saver occasionally, which can be helpful on timed tests. The trick to seeing this pattern is really quite simple: If the first and third terms are squares, figure out what they're squares of. Multiply those things, multiply that product by 2 , and then compare your result with the original quadratic's middle term.

If you've got a match ignoring the sign , then you've got a perfect-square trinomial. And the original binomial that they'd squared was the sum or difference of the square roots of the first and third terms, together with the sign that was on the middle term of the trinomial. Well, the first term, x 2 , is the square of x. The third term, 25 , is the square of 5.

Multiplying these two, I get 5 x. Multiplying this expression by 2 , I get 10 x. This is what I'm needing to match, in order for the quadratic to fit the pattern of a perfect-square trinomial.

Looking at the original quadratic they gave me, I see that the middle term is 10 x , which is what I needed. So this is indeed a perfect-square trinomial:. I know that the first term in the original binomial will be the first square root I found, which was x. The second term will be the second square root I found, which was 5.

Negatives What if the squared binomial is a — b a — b? Figure 2: An example when the middle term is negative. You might also like. Math Review of Factoring Quadratic Trinomials. Math Review of Triangle Inequality. Share : Email Facebook Twitter Linkedin. Enter your text here. Login to Free Homework Help. What if the Binomial Has a Minus Sign?

You might also like. Math Review of Special Products of Binomials. Math Review of Factoring Quadratic Trinomials. Share : Email Facebook Twitter Linkedin.

Enter your text here. In fact, a trinomial is a perfect square if and only if it has only one zero. Joonas Ilmavirta Joonas Ilmavirta See my answer. I added a note. I made an implicit assumption explicit now. But it seemed to me that the OP was only interested in second order polynomials that happen to be perfect squares, so I confined myself to those.

I should have made the remark in the first version, though. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.

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