Extract the common factor:
Extract the common factor:
\( 4x^3+8x^4= \)
Solve the following by removing a common factor:
\( 6x^6-9x^4=0 \)
\( x^4-8x=0 \)
\( x^3-7x^2+6x=0 \)
\( x^3-x^2-4x+4=0 \)
Extract the common factor:
First, we use the power law to multiply terms with identical bases:
It is necessary to keep in mind that:
Next, we return to the problem and extract the greatest common factor for the numbers separately and for the letters separately,
For the numbers, the greatest common factor is
and for the letters it is:
and therefore for the extraction
outside the parenthesis
We obtain the expression:
To determine what the expression inside the parentheses is, we use the power law, our knowledge of the multiplication table, and the answer to the question: "How many times do we multiply the common factor that we took out of the parenthesis to obtain each of the terms of the original expression that we factored?
Therefore, the correct answer is: a.
It is always recommended to review again and check that you get each and every one of the terms of the expression that is factored when opening the parentheses (through the distributive property), this can be done in the margin, on a piece of scrap paper, or by marking the factor we removed and each and every one of the terms inside the parenthesis, etc.
Solve the following by removing a common factor:
First, we take out the smallest power
If possible, we reduce the numbers by a common factor
Finally, we will compare the two sections with:
We divide by:
To solve the equation , we'll follow these steps:
Now, let's work through each step:
Step 1: The equation given is . Both terms on the left contain as a factor. We can factor out to rewrite the equation as:
Step 2: To find the solutions, set each factor to zero.
If , then one solution is:
Next, solve for in the equation :
Add 8 to both sides:
Take the cube root of both sides:
Therefore, the solutions to the equation are and .
Thus, the correct answer is: .
To solve the given cubic equation , follow these steps:
There is an common in all terms:
Look for two numbers that multiply to (the constant term) and add up to (the coefficient of the linear term). The numbers are and . Thus:
Now that the equation is fully factored as , apply the zero product property:
, (so ), (so )
Thus, the solutions to the equation are , , and .
To solve this problem, we need to factor the cubic polynomial equation . We'll begin by applying the Rational Root Theorem, which suggests that possible rational roots are factors of the constant term (4) divided by factors of the leading coefficient (1). This gives us potential roots: .
Let's test these possible roots by substituting them into the polynomial:
From these calculations, we identified , , and as roots of the polynomial.
The polynomial can be factored as . Solving each factor for zero, we obtain the roots , , and .
Therefore, the correct answer from the given choices is Answers a and c, which correspond to the roots and .
Answers a and c
\( x^3+x^2-12x=0 \)
To solve the equation , follow these steps:
Therefore, the solutions to the equation are , , and .
Thus, the complete solution set for is .