Podcast
Questions and Answers
What must be the value of $m$ in the polynomial $P(x) = 4x^{3} - 2x^{2} + mx - 2$ for it to leave a remainder of 1 when divided by $(x-1)$?
What must be the value of $m$ in the polynomial $P(x) = 4x^{3} - 2x^{2} + mx - 2$ for it to leave a remainder of 1 when divided by $(x-1)$?
Which stated procedure can tell if a polynomial $P(x)$ is divisible by $(x-a)$ without division?
Which stated procedure can tell if a polynomial $P(x)$ is divisible by $(x-a)$ without division?
What is the solution for $x$ and $y$ in the system $egin{cases} x - y = 1 \ 2x - 2y = 4 ext{?} \
What is the solution for $x$ and $y$ in the system $egin{cases} x - y = 1 \ 2x - 2y = 4 ext{?} \
For the system of equations $egin{cases} logx - logy = 1 \ x + y = 22 \ $
For the system of equations $egin{cases} logx - logy = 1 \ x + y = 22 \ $
Signup and view all the answers
What solution satisfies the system $egin{cases} 3x + y = 1 \ xy = -2 \ $?
What solution satisfies the system $egin{cases} 3x + y = 1 \ xy = -2 \ $?
Signup and view all the answers
Study Notes
Polynomial Divisibility
-
To determine if a polynomial P(x) is divisible by another polynomial (x-a) without division, evaluate P(a). If the result is zero, (x-a) is a factor.
-
For polynomial P(x) = 4x³ - 2x² + mx - 2, if division by (x-1) leaves a remainder of 1, then P(1) = 1.
Systems of Equations
-
Problem a: Solving the system x - y = 1, 2x - 2y = 4. This system has no unique solution.
-
Problem b: Solving the system logx - logy = 1, x + y = 22. This involves logarithmic rules and substitution.
-
Problem c: Solving the system 3x + y = 1, xy = -2. This system involves substitution and possible quadratic equations.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers topics in algebra focusing on polynomial divisibility and systems of equations. You will explore concepts such as checking the divisibility of polynomials through evaluation and solving various types of equation systems, including linear and logarithmic. Test your understanding and problem-solving skills in these fundamental algebraic concepts.
