Algebraic Expressions & Algebraic Formulas Flashcards
what is a term?
number part x variable part
6x
what is a polynomial?
polynomials are series of terms joined together by adding or subtracting.
what is the leading coefficient?
The leading coefficient of a polynomial is the coefficient of the term with the highest degree or exponent.
P(x) = 3x⁴ - 2x² + 5x +1, the leading coefficient is 3. It corresponds to the term with the highest degree, which is x⁴.
P(x) = 2x⁴ - 4x² + 5x +1 where is the leading coefficient?
the leading coefficient is 2 it has the highest degree which is x⁴
8
what degree term is it?
zero degree term or constant term
3x4
what degree term is it?
4th degree term
P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + … + a₂x² + a₁x + a₀
what is n here?
non-negative integer called the degree.
P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + … + a₂x² + a₁x + a₀
what is aₙ here?
real number
what is rational expression?
the quotient p(x)/q(x) of two polynomials , where q (x) is a non-zero polynomial, is called a rational expression.
additive inverse of p(x)/q(x) _______
-p(x)/q(x)
multiplicative inverse of p(x)/q(x)
q(x)/p(x)
reciprocal
when is a rational expression p(x)/q(x) in lowest form?
integral coefficients
no common factor
how to know if a rational expression is in its lowest form or not?
find HCF
HCF= 1 is in lowest form
(a+b+c)2 involves how many expressions?
3
(a+b+c)
(a2+b2+c2)
2(ab+bc+ac)
(a+b)2 + (a-b)2=
2(a2+b2)
(a+b)2 - (a-b)2=
4ab
(a+b)3=
(a-b)3=
what is a surd?
an irrational radical with a rational radicand.
√3
what should be irrational and rational for a surd?
3=rational
answer=irrational
which is non-terminating (goes on forever) & non- recurring (not follow any pattern)
n√a n√b = ?
n√ab
n√a/n√b=?
n√a/b
what is conjugate?
sign of the middle should be changed
what are surds?
the irrational radical of a rational radicand.
every surd is a ________ number.
irrational
how to simplify surds?
take LCM.
multiply it by perfect square.
perfect square = 4, 9, 16, 25, 36, 49, 64
example: √180 = take LCM or √36X5= 6√5
while simplifying surd in perfect square method make sure to choose perfect square that is the greatest.
example: √180 = √36X5= 6√5
√180 = √45X4= 2√45
the prefect square 36 is greater and hence the answer is more simplified
what is rationalization of surd?
process of multiplying a surd by its rationalizing factor to get a rational number.
rationalizing factor: product of 2 surds resulting in a rational number.
