please anwer these:
1) how can i multiply and divide polynomials containing radicals?
2) how can i solve radical equations?
3) how can i solve qudratic equations by factoring ?
4) how can i solve quadratic equations graphically ?
thank you !!!!!
Surely your text has sections on these topics. I expect that the accompanying graphs and sample problems there will be at least as good as any impromptu explanations here.
Do a google on any of the above topics for many discussions.
After that, if there's some kind of problem that vexes you, post an example, and we can help you work through it.
1) To multiply and divide polynomials containing radicals, you can follow these steps:
For multiplication:
1. Multiply the coefficients of the radicals.
2. Multiply the radicands (the expressions inside the radicals) using the usual rules of multiplication.
3. Simplify the resulting expression, combining like terms if necessary.
For division:
1. Multiply both the numerator and denominator by the conjugate of the denominator. The conjugate is found by changing the sign between the two terms containing radicals.
2. Use the distributive property to multiply the binomials in the numerator and denominator.
3. Simplify and combine like terms if needed.
Remember to simplify the radicals whenever possible by finding perfect square factors.
2) To solve radical equations:
1. Isolate the radical term on one side of the equation.
2. Raise both sides of the equation to the power that eliminates the radical (e.g., square both sides to eliminate a square root).
3. Solve the resulting equation.
4. Check your solution(s) by substituting them back into the original equation. Sometimes extraneous solutions may arise, so it's essential to verify.
3) To solve quadratic equations by factoring:
1. Set the quadratic equation equal to zero.
2. Factorize the quadratic trinomial expression.
3. Set each factor equal to zero and solve the resulting linear equations.
4. Check your solutions by substituting them back into the original equation.
4) To solve quadratic equations graphically:
1. Plot the quadratic equation on a coordinate plane.
2. Identify the x-intercepts of the graph, which are the solutions to the equation.
3. If necessary, use the quadratic formula to find the exact solutions.
Note: The graph of a quadratic equation is a parabola, and the x-intercepts are the points where the parabola intersects the x-axis.