Articles

Bit by Bit guide for Multiplying a Polynomial and a Monomial

• Whenever you multiply monomials, you must utilize the product rule for exponents.
• Whenever you multiply a monomial by a polynomial, you must utilize the distributive ...

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To use the quadratic formula, we must change the quadratic equation we are solving into "standard form". If we don't do this, none of the following steps will work. The goal is to change the quadratic equation so that the quadratic expression is on one side of the equation and only the number zero, \(0\), is on the other.
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Step1: Isolate the radical on one side of the equation.
Step2: Square both sides of the equation, to remove the radical
Step3: Solve the equation for the variable
Step4: Plugin the answer into the original equation to avoid extraneous values.
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Adding and Subtracting Radical Expressions Course

Only numbers that have the same radical part can be added or subtracted.
Remember, combining "unlike" radical terms is not possible.
For number with the same radical part, just add or subtract factors outside the radicals.
Example:\(4\sqrt{2}+6\sqrt{2}=10\sqrt{2}\)
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To multiply two square roots, radicands should be multiplied together and then write the result under a single radical. Sometimes it could be necessary to further simplify the radical expression. This procedure always stays the same, regardless of the index's value.
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Radical expressions are simplified by taking them down to their simplest form and, if feasible, altogether deleting the radical. When a radical expression appears in the denominator of an algebraic expression, the radical expression is simplified by multiplying the numerator and denominator by the appropriate radical expression.
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To solve logarithmic equations, we must use the rules of logarithms to rewrite the expressions in a way that is easier to understand. After rewriting the logarithmic expressions, we usually get one of two types of logarithmic equations. Depending on the equation type, we can get the answer by comparing the logarithms' arguments or by writing the logarithm in its exponential form.
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This article will focus on solving exponential equations that require using logarithms, which are more challenging to answer without them. This is because we can't change the exponential equation to that both sides of the equation have the same base.
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The natural logarithm of a number is its logarithm to the base, \(e\).
The \(e\) constant also called Euler's number, \(e \ = \ 2.71828183\)
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A matrix equation has the form \(AX \ = \ B\), where \(A\) is the coefficient matrix, X is the column matrix of variables, and \(B\) is the column matrix of constants on the right side of the equations in a system.
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