Problem 4
Question
Factor out the greatest common factor. $$4 x^{2}-8 x$$
Step-by-Step Solution
Verified Answer
The factored form of the polynomial \(4x^2 - 8x\) with the GCF factored out is \(4x(x - 2)\).
1Step 1: Identify the GCF
The GCF of the given polynomial is determined by taking the largest common factor of the coefficients and the smallest power of x. The GCF between 4 and 8 is 4. For \(x^2\) and x, the smallest power of x is 1 (from x). Hence, the GCF of the polynomial is \(4x\).
2Step 2: Factor out the GCF
Remove \(4x\) from each term in the polynomial \(4x^2 - 8x\) by dividing each term by \(4x\). This gives \(x - 2\).
3Step 3: Write the factored form of the polynomial
The factored form of the polynomial is obtained by multiplying the GCF and the result from step 2. This gives \(4x(x - 2)\).
Other exercises in this chapter
Problem 4
find all numbers that must be excluded from the domain of each rational expression. $$ \frac{x+7}{x^{2}-49} $$
View solution Problem 4
In Exercises 1–4, is the algebraic expression a polynomial? If it is, write the polynomial in standard form. $$ x^{2}-x^{3}+x^{4}-5 $$
View solution Problem 4
Evaluate each exponential expression. $$ (-2)^{4} $$
View solution Problem 4
Evaluate each algebraic expression for the given value or values of the variable(s). $$8 x-y,\quad for\quad x=3\quad and\quad y=4$$
View solution