Question

Which value is needed in the expression below to create a perfect square trinomial?

Answer 1

Answer:

16

Step-by-step explanation:

i know because i did the test

Answer 2

Answer:

The value which is needed to be added to transform the quadratic expression $x^{2}+8x$ as a perfect square trinomial is 16.

Step-by-step explanation:

A quadratic expression is an expression in which the highest power of the variable is 2 or it can be said that the degree of the expression is 2.  

The identity for $(a+b)^{2}$ is given as follows:  

$(a+b)^{2}=a^{2}+b^{2}+2\times(a)\times(b)$

Step 1:  

Break down the given polynomial $x^{2}+2\times(x)\times(4)$.

Step 2:  

Now compare the polynomial with the above indentity.  

On comparing it is observed that the value of a is x and the value of b is 4.  

Step 3:  

In order to make the polynomial $x^{2}+8x+$ a perfect square, add $16$ to the broked down polynomial because on comparing the above polynomials the value of b is 4 and the square of 4 is 16.  

$x^{2}+2\times(x)\times4+16$  

Step 4:  

Now as per the identity $(a+b)^{2}=a^{2}+2\times(a)\times(b)+b^{2}$ the polynomial $x^{2}+2\times(x)\times4+16$ is written as follows:  

$(x+4)^{2}$.  

Therefore, the perfect square for the given polynomial is $(x+4)^{2}$ which is created by adding 16 to the given expression.  

Learn more:  

1. A problem to obtain the y-intercept of a quadratic function brainly.com/question/1332667  
2. A problem to obtain the binomial and trinomial brainly.com/question/1394854  

Answer details  

Grade: Middle school  

Subject: Mathematics  

Chapter: Quadratic expression  

Keywords: Quadratic, quadratic expression, polynomial, quadratic polynomial, perfect square, trinomial, degree, highest power, transform, identities, break down, perfect square, middle term split, x^2+8x,methamatics, algebra.