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| What is the Standard Form of a Polynomial Equation? |
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Definition
| Zero on one side, with the polynomial in descending powers of the variable on the other side. |
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Term
| What form must a polynomial be in for it to be factored? |
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Definition
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| What is the greatest common factor of a polynomial? |
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Definition
| The largest number that goes into both factors with the lowest degree of the two factors set in parenthesis next to the equation needed to form the original polynomial. |
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| The equation the greatest common factor of the polynomial can be multiplied by to form the original polynomial is what type of equation? |
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Definition
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Term
| When you factor the greatest common factor out of a polynomial you must also do what? |
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Definition
| Factor the Quadratic Equation that the greatest common factor can be multiplied by in order to form the original polynomial equation. |
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| What are the Steps to Factoring a Polynomial Equation? |
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Definition
1.)Find the greatest common factor of the polynomial.
2.)Factor the Quadratic Equation that the greatest common factor can be multiplied by to form the original polynomial.
3.)Set all factors equal to zero and solve for the variable.
4.)List your solutions in a solution set. |
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| How do you factor ((x^2)+a)? |
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Definition
In factored form it equals
(x+(factor of a))(x-(factor of a)) |
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Term
| What is the difference of cubes formula? |
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Definition
| (a^3)-(b^3)=(a-b)((a^2)+(ab)+(b^2)) |
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Term
| If you have a negative discriminant then there are no real what? |
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Definition
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| What is the discriminant? |
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Definition
| The Squareroot of (b^2)-4(a)(c) |
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| How do you find the real solutions of an equation of the form (x^4)=ax? |
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Definition
1.)Factor Out the x.
2.)Set the factors equal to zero
3.)Set "a" as an equivalent number cubed.
3.)Use the Difference of Cubes Formula
4.)Set factors equal to zero and solve, use quadratic formula if necessary.
5.)Place only the real solutions in a solution set. |
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What are the solutions to
x^4=1000? |
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Definition
{0,10}
The solutions are zero, and the cuberoot of 1000 in a solution set. |
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What are the solutions to
x^4=64 |
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Definition
{0,4}
The solutions are zero, and the cuberoot of 64 in a solution set. |
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What are the solutions to
x^4=216 |
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Definition
{0,6}
The solutions are zero, and the cuberoot of 216 in a solution set. |
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Term
How do you find the solution set to a problem in this form?
((x+a)/(bx-c))=((dx-e)/(bx+c)) |
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Definition
1.) Set as
(x+a)(bx+c)=(dx-e)(bx-c)
2.) Use the distributive property on both sides.
3.)Make one side of the equal sign equal zero.
4.)If the first term is negative, change the signs of each term. Factor the left side of the equal sign.
5.)Set your solutions in a solution set. |
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| How do you solve "a" problem in the form of Square root of x-"a" equals negative "b"? |
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Definition
| The answer is always no solution |
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Term
How do you find the solution to a problem of this form?
((ax-b)^2)+c(ax-b)-c=0 |
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Definition
1.) Substitute (ax-b) for a variable
2.) Factor
3.) Set each factor to equal zero and solve.
4.)Replace the variable you chose for (ax-b) and solve for "x".
5.)Place your solutions in a solution set. |
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How to solve an equation in this form?
(x^4)-ax^2+b=0 |
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Definition
1.)Set (x^2) as a variable.
2.)Factor
3.)Set each factor equal to zero and solve for the variable.
4.)Set the variable as x^2 and solve for x.
5.)Place your solutions for x in a solution set, there is a negative and positive form of each solution. |
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Term
How do you solve an equation in this form?
ay-b(squareroot of y)=-c |
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Definition
1.)Collect all terms to one side
2.)Set y to equal squareroot of y
3.)Factor
4.)Set each factor equal to zero and solve for y.
5.)Set "y" as square root of y, and solve for "y".
6.)Place your solutions in a solution set. |
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Term
How do you square a fraction in this form?
1/a |
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Definition
1.)Square the denominator
(1/(a^2) |
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Term
How do you solve an equation of this format?
x-(square root of ax+b)=-c |
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Definition
1.)Add (square root of ax+b) to both sides. Then add c to both sides.
x-(square root of ax+b)+(square root of ax+b)+c=-c+c+(square root of ax+b)
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2.)Square both sides of the equation
(ax+b)^2=(square root of ax+b)^2
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3.)Simplify both sides.
(ax+b)*(ax+b)=ax+b
Which Becomes This
(ax^2)+(2axb)+(b^2)=ax+b
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4.)Subtract ax+b from both sides.
((ax^2)+(2axb)+(b^2))-ax+b=ax+b-ax+b
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5.)Factor
((ax^2)+(2axb)+(b^2))-ax+b
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6.)Place your solutions in a solution set. |
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Term
How do you find the solution to a problem in this form?
(x/x-a)-(a/x+a)=(2a/(x^2))-(a^2) |
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Definition
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