Question

Factor the polynomial t2+8t

Answer 1

Two solutions were found : t = 8 t = 0Reformatting 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).`