Verified Answer :
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 1 :Step 2 :Pulling out like terms :
2.1 Pull out like factors :
t2 - 8t = t • (t - 8)
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.
3.2 Solve : t = 0
Solution is t = 0
3.3 Solve : t-8 = 0
Add 8 to both sides of the equation :
t = 8
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 \(t(t+8).\)