# HOW TO FIND THE LAST TERM OF A PERFECT SQUARE TRINOMIAL

## About "How to find the last term of a perfect square trinomial"

How to find the last term of a perfect square trinomial :

To make any quadratic expression a perfect square, a method called completing the square may be used.

To complete the square for a quadratic expression of the form x2 + bx + missing value (or) x2 - bx + missing value, we can follow the steps below.

Step 1 : Try to split the middle term that is coefficient of x as the multiple of 2. If it is not an even number, we should multiply and divide it by 2 to represent it as 2ab.(Here "a" and "b" are first and last terms respectively.)

Step 2 : The middle term represents the product of 2, first term and the last term.

Step 3 : The square of the last term is the missing value.

Let us look into some example problems to understand the above concept.

## How to find the last term of a perfect square trinomial - Examples

Example 1 :

Find the value of c that makes each trinomial a perfect square.

a2 - 12a + c

Solution :

=  a2 - 12a + c

=  a2 - 2  a  6 + c

Instead of "c" if we write 62, the given polynomial will become a perfect square.

=  a2 - 2  a  6 + 62

Since the above polynomial is in the form a2 - 2ab + b2, we can write it as (a + b)2

=  (a + 6)2

Hence the value of c is 62, that is 36.

Example 2 :

Find the value of c that makes each trinomial a perfect square.

x2 - 16x + c

Solution :

=  x2 - 16x + c

=  x2 - 2  x  8 + c

Instead of "c" if we write 82, the given polynomial will become a perfect square.

=  x2 - 2  x  8 + 82

Since the above polynomial is in the form a2 - 2ab + b2, we can write it as (a - b)2

=  (x - 8)2

Hence the value of c is 82, that is 64.

Example 3 :

Find the value of c that makes each trinomial a perfect square.

x2 - 10x + c

Solution :

=  x2 - 10x + c

=  x2 - 2  x  5 + c

Instead of "c" if we write 52, the given polynomial will become a perfect square.

=  x2 - 2  x  5 + 52

Since the above polynomial is in the form a2 - 2ab + b2, we can write it as (a - b)2

=  (x - 5)2

Hence the value of c is 52, that is 25.

Example 4 :

Find the value of c that makes each trinomial a perfect square.

x2 - 7x + c

Solution :

=  x2 - 7x + c

=  x2 - (2/2)  7 ⋅ x + c

=  x2 - 2⋅ x ⋅ (7/2) + c

Instead of "c" if we write (7/2)2, the given polynomial will become a perfect square.

=  x2 - 2⋅ x ⋅ (7/2) + (7/2)2

Since the above polynomial is in the form a2 - 2ab + b2, we can write it as (a - b)2

=  (x - (7/2))2

Hence the value of c is (7/2)2, that is 49/4.

Example 5 :

Find the value of c that makes each trinomial a perfect square.

x2 + 11x + c

Solution :

=  x2 + 11x + c

=  x2 - (2/2)  11 ⋅ x + c

=  x2 - 2⋅ x ⋅ (11/2) + c

Instead of "c" if we write (11/2)2, the given polynomial will become a perfect square.

=  x2 - 2⋅ x ⋅ (11/2) + (11/2)2

Since the above polynomial is in the form a2 - 2ab + b2, we can write it as (a - b)2

=  (x - (11/2))2

Hence the value of c is (11/2)2, that is 121/4.

We hope that the students would have understood the stuff and example problems explained on "How to find the last term of a perfect square trinomial".

Apart from the stuff and example problems explained above, if you want to know more about "How to find the last term of a perfect square trinomial", please click here

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