Algebraic Expressions & Algebraic Formulas

Question 1

what is a term?

Answer 1

number part x variable part
6x

Question 2

what is a polynomial?

Answer 2

polynomials are series of terms joined together by adding or subtracting.

Question 3

what is the leading coefficient?

Answer 3

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.

Question 4

P(x) = 2x⁴ - 4x² + 5x +1 where is the leading coefficient?

Answer 4

the leading coefficient is 2 it has the highest degree which is x⁴

Question 5

8
what degree term is it?

Answer 5

zero degree term or constant term

Question 6

3x4
what degree term is it?

Answer 6

4th degree term

Question 7

P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + … + a₂x² + a₁x + a₀
what is n here?

Answer 7

non-negative integer called the degree.

Question 8

P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + … + a₂x² + a₁x + a₀

what is aₙ here?

Answer 8

real number

Question 9

what is rational expression?

Answer 9

the quotient p(x)/q(x) of two polynomials , where q (x) is a non-zero polynomial, is called a rational expression.

Question 10

additive inverse of p(x)/q(x) _______

Answer 10

-p(x)/q(x)

Question 11

multiplicative inverse of p(x)/q(x)

Answer 11

q(x)/p(x)
reciprocal

Question 12

when is a rational expression p(x)/q(x) in lowest form?

Answer 12

integral coefficients
no common factor

Question 13

how to know if a rational expression is in its lowest form or not?

Answer 13

find HCF
HCF= 1 is in lowest form

Question 14

(a+b+c)2 involves how many expressions?

Answer 14

3
(a+b+c)
(a2+b2+c2)
2(ab+bc+ac)

Question 15

(a+b)2 + (a-b)2=

Answer 15

2(a2+b2)

Question 16

(a+b)2 - (a-b)2=

Answer 16

4ab

Question 17

(a+b)3=

Question 18

(a-b)3=

Question 19

what is a surd?

Answer 19

an irrational radical with a rational radicand.

Question 20

√3
what should be irrational and rational for a surd?

Answer 20

3=rational
answer=irrational
which is non-terminating (goes on forever) & non- recurring (not follow any pattern)

Question 21

n√a n√b = ?

Answer 21

n√ab

Question 22

n√a/n√b=?

Answer 22

n√a/b

Question 23

what is conjugate?

Answer 23

sign of the middle should be changed

Question 24

what are surds?

Answer 24

the irrational radical of a rational radicand.

Question 25

every surd is a ________ number.

Answer 25

irrational

Question 26

how to simplify surds?

Answer 26

take LCM.
multiply it by perfect square.

perfect square = 4, 9, 16, 25, 36, 49, 64

example: √180 = take LCM or √36X5= 6√5

Question 27

while simplifying surd in perfect square method make sure to choose perfect square that is the greatest.

Answer 27

example: √180 = √36X5= 6√5
√180 = √45X4= 2√45

the prefect square 36 is greater and hence the answer is more simplified

Question 28

what is rationalization of surd?

Answer 28

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.