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Q: Is the perfect square trinomial a product of the square of a binomial?

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It can be factored as the SQUARE OF A BINOMIAL

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.

Each has two binomial factors.

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A factor of a perfect square trinomial is eithera number that is a factor of each term of the trinomial,a binomial that is a factor of the trinomial, ora product of the above two.For example, consider 4x2 + 8x + 4It has the factors2 or 4,(x + 1) or2x+2 = 2*(x+1) or 4x+4 = 4*(x+1)

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

No.

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

It is not possible for a perfect square to have just 2 terms.

This is related to the fact that the square of both a positive and a negative number is always positive. The last term is simply the square of the second term, in the original binomial.

perfect trinomial square?? it has the form: a2 + 2ab + b2

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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