Question

Factor the polynomial t2+8t

Answer 1

Two solutions were found : t = 8 t = 0

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "t2"   was replaced by   "t^2". 

Step by step solution :Skip Ad
Step  1  :Step  2  :Pulling out like terms :

 2.1     Pull out like factors :

   t2 - 8t  =   t • (t - 8) 

Equation at the end of step  2  : t • (t - 8) = 0 Step  3  :Theory - Roots of a product :

 3.1    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 :

 3.2      Solve  :    t = 0 

  Solution is  t = 0 

Solving a Single Variable Equation :

 3.3      Solve  :    t-8 = 0 

 Add  8  to both sides of the equation : 
                      t = 8 

Two solutions were found : t = 8 t = 0

Answer 2

Answer:  The required factored form of the given polynomial is $t(t+8).$

Step-by-step explanation:  We are given to factorize the following quadratic polynomial :

$P=t^2+8t~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following property :

$ab+ac=a(b+c).$

From expression (i), we get

$P\\\\=t^2+8t\\\\=t(t+8).$

Thus, the required factored form of the given polynomial is $t(t+8).$