144
48
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 future perfect tense is will have given.
Present Perfect Continuous Tense:I/you/we/they have been coming.He/she/it has been coming.Past Perfect Continuous Tense:Had been coming.Future Perfect Continuous Tense:Will have been coming.
48
What value, in place of the question mark, makes the polynomial below a perfect square trinomial?x2 + 12x+ ?
64
To make the polynomial ( x^2 - 28x + ? ) a perfect square trinomial, we need to find the value that completes the square. The formula for a perfect square trinomial is ( (x - a)^2 = x^2 - 2ax + a^2 ). Here, ( a ) is half of the coefficient of ( x ), which is ( -28 ). Thus, ( a = 14 ), and we need ( a^2 = 196 ). Therefore, the value in place of the question mark is ( 196 ).
64
To form a perfect square trinomial from the expression (x^2 + 26x + ?), we need to find the constant that completes the square. The formula for a perfect square trinomial is ((x + a)^2 = x^2 + 2ax + a^2). Here, (2a = 26) gives (a = 13), so (a^2 = 169). Therefore, the value that replaces the question mark is (169).
-12
TrUE
True
(b/2)^2= 64
-26
There are infinitely many possible answers: c = ±4x + 33