Question

The factors of

p2 - 16 are:​

Answer 1

Answer:

Step-by-step explanation:

STEP

1

:

Trying to factor as a Difference of Squares:

1.1      Factoring:  p2-16  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 16 is the square of 4

Check :  p2  is the square of  p1  

Factorization is :       (p + 4)  •  (p - 4)  

Equation at the end of step

1

:

 (p + 4) • (p - 4)  = 0  

STEP

2

:

Theory - Roots of a product

2.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2      Solve  :    p+4 = 0  

Subtract  4  from both sides of the equation :  

                     p = -4

Solving a Single Variable Equation:

2.3      Solve  :    p-4 = 0  

Add  4  to both sides of the equation :  

                     p = 4

Two solutions were found :

p = 4

p = -4

Answer 2

p² - 16

(p)² - (4)²

(p+4) (p-4)

[Using identity a²-b² = (a+b)(a-b)]

Therefore, (p+4) and (p-4) are the factors of the given polynomial