All Common Core: High School - Algebra Resources
Example Questions
Example Question #211 : High School: Algebra
What is the remainder when is divided by
In order to solve this problem, we need to perform synthetic division. We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.
The first step is to bring the coefficient of the term down.
Now we multiply the zero by the term we just put down, and place it under the term coefficient.
Now we add the column up to get.
Now we multiply the number we got by the zero, and place it under the constant term.
Now we add the column together to get.
The last number is the remainder, so our final answer is .
Example Question #212 : High School: Algebra
What is the remainder when is divided by
In order to solve this problem, we need to perform synthetic division. We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.
The first step is to bring the coefficient of the term down.
Now we multiply the zero by the term we just put down, and place it under the term coefficient.
Now we add the column up to get.
Now we multiply the number we got by the zero, and place it under the constant term.
Now we add the column together to get.
The last number is the remainder, so our final answer is .
Example Question #141 : Arithmetic With Polynomials & Rational Expressions
What is the remainder when is divided by
In order to solve this problem, we need to perform synthetic division. We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.
The first step is to bring the coefficient of the term down.
Now we multiply the zero by the term we just put down, and place it under the term coefficient.
Now we add the column up to get.
Now we multiply the number we got by the zero, and place it under the constant term.
Now we add the column together to get.
The last number is the remainder, so our final answer is .
Example Question #142 : Arithmetic With Polynomials & Rational Expressions
What is the remainder when is divided by
In order to solve this problem, we need to perform synthetic division. We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.
The first step is to bring the coefficient of the term down.
Now we multiply the zero by the term we just put down, and place it under the term coefficient.
Now we add the column up to get.
Now we multiply the number we got by the zero, and place it under the constant term.
Now we add the column together to get.
The last number is the remainder, so our final answer is .
Example Question #143 : Arithmetic With Polynomials & Rational Expressions
What is the remainder when is divided by x
In order to solve this problem, we need to perform synthetic division. We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.
The first step is to bring the coefficient of the term down.
Now we multiply the zero by the term we just put down, and place it under the term coefficient.
Now we add the column up to get.
Now we multiply the number we got by the zero, and place it under the constant term.
Now we add the column together to get.
The last number is the remainder, so our final answer is .
Example Question #144 : Arithmetic With Polynomials & Rational Expressions
What is the remainder when is divided by
In order to solve this problem, we need to perform synthetic division. We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.
The first step is to bring the coefficient of the term down.
Now we multiply the zero by the term we just put down, and place it under the term coefficient.
Now we add the column up to get.
Now we multiply the number we got by the zero, and place it under the constant term.
Now we add the column together to get.
The last number is the remainder, so our final answer is .
Example Question #145 : Arithmetic With Polynomials & Rational Expressions
What are the -intercept(s) of the function?
To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a value equal to zero.
One technique that can be used is factorization. In general form,
where,
and are factors of and when added together results in .
For the given function,
the coefficients are,
therefore the factors of that have a sum of are,
Now find the -intercepts of the function by setting each binomial equal to zero and solving for .
To verify, graph the function.
The graph crosses the -axis at -2 and 3, thus verifying the results found by factorization.
Example Question #146 : Arithmetic With Polynomials & Rational Expressions
What are the -intercept(s) of the function?
To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a value equal to zero.
One technique that can be used is factorization. In general form,
where,
and are factors of and when added together results in .
For the given function,
the coefficients are,
therefore the factors of that have a sum of are,
Now find the -intercepts of the function by setting each binomial equal to zero and solving for .
To verify, graph the function.
The graph crosses the -axis at 3 and 4, thus verifying the results found by factorization.
Example Question #3 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3
What are the -intercept(s) of the function?
To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a value equal to zero.
One technique that can be used is factorization. In general form,
where,
and are factors of and when added together results in .
For the given function,
the coefficients are,
therefore the factors of that have a sum of are,
Now find the -intercepts of the function by setting each binomial equal to zero and solving for .
To verify, graph the function.
The graph crosses the -axis at -3 and -6, thus verifying the results found by factorization.
Example Question #4 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3
What are the -intercept(s) of the function?
To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a value equal to zero.
One technique that can be used is factorization. In general form,
where,
and are factors of and when added together results in .
For the given function,
the coefficients are,
therefore the factors of that have a sum of are,
Now find the -intercepts of the function by setting each binomial equal to zero and solving for .
To verify, graph the function.
The graph crosses the -axis at -4 and 2, thus verifying the results found by factorization.