Examples of sign in the following topics:
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- We can see that the negative signs cancel out for any even power.
- This function has one sign change between the second and third terms.
- We know that the number of roots of either sign is the number of sign changes, or a multiple of two less than that.
- To find the positive roots we count the sign changes.
- Since there are no sign changes, there are no positive roots $(p=0)$.
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- The cofactor of an entry $(i,j)$ of a matrix $A$ is the signed minor of that matrix.
- Specifically the cofactor of the $(i,j)$ entry of a matrix, also known as the $(i,j)$ cofactor of that matrix, is the signed minor of that entry.
- To know what the signed minor is, we need to know what the minor of a matrix is.
- The determinant of any matrix can be found using its signed minors.
- The determinant is the sum of the signed minors of any row or column of the matrix scaled by the elements in that row or column.
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- Roots are written using a radical sign, and a number denoting which root to solve for.
- Roots are written using a radical sign.
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- Multiplication of radicals simply requires that we multiply the variable under the radical signs.
- the value under the radical sign can be written as an exponent,
- Then, the fraction under the radical sign can be addressed, and the radical in the numerator can again be simplified.
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- Subtract the product just obtained from the appropriate terms of the original dividend (remember that subtracting something having a minus sign is equivalent to adding something having a plus sign): $(x^3 − 12x^2) − (x^3 − 3x^2) = −12x^2 + 3x^2 = −9x^2$.
- Subtract the product just obtained from the appropriate terms of the original dividend (being careful that subtracting something having a minus sign is equivalent to adding something having a plus sign): $(x^3 − 12x^2) − (x^3 − 3x^2) = −12x^2 + 3x^2 = −9x^2$.
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- A linear inequality looks exactly like a linear equation, with the inequality sign replacing the equality sign.
- A linear inequality looks like a linear equation, with the inequality sign replacing the equal sign.
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- Set up two separate equations: For the first, keep the new equation you found in step 1, but remove the absolute value signs; for the second, keep the equation you found in step 1, remove the absolute value signs, and multiply one side by -1.
- The first is the equation we found in Step 1, but with the absolute value signs removed:
- The second equation is the one we found in Step 1, with the absolute value signs removed, and with the other side multiplied by -1:
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- Functions of even degree will go to positive or negative infinity (depending on the sign of the coefficient of the highest-degree term) if $x$ goes to infinity.
- Every time we cross a zero of odd multiplicity (if the number of zeros equals the degree of the polynomial, all zeros have multiplicity one and thus odd multiplicity) we change sign.
- So in our example, we start with a negative sign until we reach $x = -4$, when our graph rises above the $x$-axis.
- With this procedure, we can draw a reasonable sketch of our graph, by only looking at the sign of the function and drawing a smooth line with the same sign!
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- When multiplying positive and negative numbers, the sign of the product is determined by the following rules:
- The sign rules for division are the same as for multiplication.
- If the dividend and the divisor have the same sign, that is to say, the result is always positive.
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- First, look for a perfect square under the square root sign, and remove it: