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A perfect square is a binomial squared, like (x+3)^2. You would calculate this by remembering: Square the first, twice the product, square the last. So x^2 (square the first), plus 6x (twice the product), plus 9 (square the last), so we get x^2+6x+9. We can factor this in reverse to see that this is a perfect square. With this simple trick, you can solve for perfect squares.

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Q: What is a requirement for a trinomial to be factored as a perfect square?

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If you mean: n2+20n+100 then yes it is because (n+10)(n+10) when factored

If you mean: x2-25x+100 then it is (x-5)(x-20) when factored

The binomial usually has an x2 term and an x term, so we complete the square by adding a constant term. If the coefficient of x2 is not 1, we divide the binomial by that coefficient first (we can multiply the trinomial by it later). Then we divide the coefficient of x by 2 and square that. That is the constant that we need to add to get the perfect square trinomial. Then just multiply that trinomial by the original coefficient of x2.

If you mean: 9x2-36x+16 then it is not a perfect square because its discriminant is greater than zero

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Related questions

A trinomial is perfect square if it can be factored into the form

It can be factored as the SQUARE OF A BINOMIAL

A trinomial of the form ax2 + bx + c is a perfect square if (and only if) b2-4ac = 0 and, in that case, it is factored into a*(x + b/2a)2

A trinomial is perfect square if it can be factored into the form (a+b)2 So a2 +2ab+b2 would work.

The given quadratic expression can not be factored as a perfect square.

Yes; the factored form would be (9c+4)(9c+4) or just (9c+4)2 Since the two factors are the same, the beginning trinomial 81c2+72c+16 is a perfect square trinomial

4x2-42x+110 = (2x-10)(2x-11) when factored

No.

If you mean: n2+20n+100 then yes it is because (n+10)(n+10) when factored

Yes because 25x2-70x+49 = (5x-7)(5x-7) when factored

x2-18x+81 = (x-9)(x-9) when factored

Yes because if x2-14x+49 then it is (x-7)(x-7) when factored

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