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 $(x-1)$?
- 3 (correct)
- 1
- 7
- 5
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?
- Determining the leading coefficient
- Finding $P(a)$ and checking if it equals zero (correct)
- Calculating the roots of the polynomial
- Examining the degree of the polynomial
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{?} \
- (1, 0)
- (4, 3)
- (2, 1) (correct)
- (3, 2)
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 \ $
What solution satisfies the system $egin{cases} 3x + y = 1 \ xy = -2 \ $?
What solution satisfies the system $egin{cases} 3x + y = 1 \ xy = -2 \ $?
Flashcards
Divisibility of Polynomials
Divisibility of Polynomials
A polynomial P(x) is divisible by (x-a) if substituting x=a into P(x) results in 0.
Remainder Theorem
Remainder Theorem
When a polynomial P(x) is divided by (x-a), the remainder is P(a).
System of Equations
System of Equations
A set of two or more equations with the same variables that need to be solved simultaneously.
Consistent System (Example a)
Consistent System (Example a)
Signup and view all the flashcards
Inconsistent System (Example a)
Inconsistent System (Example a)
Signup and view all the flashcards
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.
