Problem 6
Question
Factor out the greatest common factor. $$6 x^{4}-18 x^{3}+12 x^{2}$$
Step-by-Step Solution
Verified Answer
The factorized form of the polynomial \(6 x^{4}-18 x^{3}+12 x^{2}\) is \(6x^2(x^2 - 3x + 2)\).
1Step 1: Identifying the GCF
For \(6 x^{4}\), \(18 x^{3}\), and \(12 x^{2}\), the GCF is \(6x^2\). You can find this by examining each term: Both 6 and 18 are divisible by 6, and all three terms have at least two factors of x.
2Step 2: Factorization
Factor out \(6x^2\) from each term. The process follows the rule \(A(B + C) = AB + AC\).
3Step 3: Simplifying each term
\(6x^2(1*x^2 - 3*x + 2)\). Simplify each term by dividing by the GCF. This gives us \(x^2 - 3x + 2\) after factorization.
Other exercises in this chapter
Problem 6
find all numbers that must be excluded from the domain of each rational expression. $$ \frac{x-3}{x^{2}+4 x-45} $$
View solution Problem 6
In Exercises 5–8, find the degree of the polynomial. $$ -4 x^{3}+7 x^{2}-11 $$
View solution Problem 6
Evaluate each expression indicate that the root is not a real number. $$ \sqrt{-25} $$
View solution Problem 6
Evaluate each exponential expression. $$ -2^{4} $$
View solution