Your classmate wonders how we get the constant of x^2 + 10x to make it a perfect square trinomial. What is the correct response? A. Divide 10 by 2. B. Square the quotient of 10 and 2. C. Half the quotient of 10 and 2. D. Twice the quotient of 10 and 2.
Answer (1)
To make the expression x 2 + 10 x a perfect square trinomial, we need to add a specific constant to it. Here is a step-by-step explanation of how to determine that constant:
Find Half of the Coefficient of x :
The coefficient of x in the expression x 2 + 10 x is 10.
Divide 10 by 2, which gives 5.
Square the Result:
Take the result from step 1, which is 5, and square it: 5 2 = 25
Add the Result to the Expression:
The constant that should be added to make x 2 + 10 x a perfect square trinomial is 25.
Therefore, the expression x 2 + 10 x + 25 is a perfect square trinomial, which can be written as ( x + 5 ) 2 .
Therefore, the correct multiple-choice option is B. Square the quotient of 10 and 2.
By following these steps, you ensure that the expression becomes a perfect square trinomial, which is useful in solving certain types of algebraic problems efficiently.
