Problem 3
Question
Factor out the greatest common factor. $$3 x^{2}+6 x$$
Step-by-Step Solution
Verified Answer
\The factored form of \(3x^2 + 6x\) is \(3x(x + 2)\)
1Step 1: Identify the Greatest Common Factor
First, identify the greatest common factor (GCF) among all the terms. In this case, the GCF is \(3x\) which is present in both \(3x^2\) and \(6x\).
2Step 2: Factor Out the GCF
Next, factor out the GCF from each term by dividing each term of the polynomial by the GCF. This gives us, \(3x(1x + 2)\).
3Step 3: Check the Answer
To ensure the answer is correct, distribute \(3x\) back into the parenthesis. If the result equals the original expression, the factored version is correct. \n Distribute: \(3x*x + 3x*2 => 3x^2 + 6x\) which is equal to original expression. Hence solution is correct.
Other exercises in this chapter
Problem 3
In Exercises 1–4, is the algebraic expression a polynomial? If it is, write the polynomial in standard form. $$ \frac{2 x+3}{x} $$
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Evaluate each expression indicate that the root is not a real number. $$ -\sqrt{36} $$
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Evaluate each exponential expression. $$ (-2)^{6} $$
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Evaluate each algebraic expression for the given value or values of the variable(s). $$6 x-y,\quad for\quad x=3\quad and\quad y=8$$
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