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Q: What value in place of the question mark makes the polynomial below a perfect square trinomial x2 plus 24x plus questionmark?

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38

Complete the square is the process of creating a "perfect square" polynomial. We call (x + a)^2 a perfect square, where a is a constant. Using simple distributivity of numbers, we get x^2 + 2ax + a^2 is a representation of a perfect square in simplified formed. so (x + a) ^2 = x^2 + 2ax + a^2. Given a degree polynomial in the form x^2 + nx, where m and n are constants, when we "complete the square", we are looking for values that will turn it into something like x^2 + 2ax + a^2. The entire idea is to find what "a" is. 2a is the coefficient for the degree one monomial "2ax" for what we want, also n is the coefficient for the degree one monomial "nx" for what we have. Then why don't we just say n = 2a for some a. To find a, it's obvious a = n/2. We have the degree 2 term (x^2), degree 1 term (nx = 2 . n/2 .x). We need the constant of a^2. a^2 = (n/2)^2 = n^2 / 4. In this case, n = 13.

the three numbers that are less than 1000 and are perfect squares and perfect cubes are:1, 64, 7291 = 1 x 1 = 1 x 1 x 164 = 8 x 8 = 4 x 4 x 4729 = 27 x 27 = 9 x 9 x 9

4x4 = 16 is a perfect square.

Related questions

48

What value, in place of the question mark, makes the polynomial below a perfect square trinomial?x2 + 12x+ ?

64

16 does that.

64

-12

TrUE

(b/2)^2= 64

-26

True

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

No, it isn't. It would be, if that "36" in the middle were "24" instead.

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