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SOLUTIONS SENT BY STUDENTS FOR CORRECTIONS/VALIDATIONS
SOLUTIONS SENT BY STUDENTS FOR CORRECTIONS/VALIDATIONS
Q. Classify the following polynomial based on the number of terms present: a²
Q. Classify the following polynomial based on the number of terms present: a²
What is a term?
It is separated from other terms in an algebraic expression using + or − sign.
Any + or − sign here?
No.
⇒ Only 1 term
⇒ Monomial
(mono means single/one)
Student sample
Student sample
Q. Classify a² − b² using the number of terms present.
Q. Classify a² − b² using the number of terms present.
Q.
Terms are separated by '+' or '−' sign.
E.g. □ + □ − □
∴ There are 2 terms here,
"a²" and "−b²"
∴ It is a binomial
(∵ bi means two)
Student sample
Student sample
Q. Classify the following polynomial based on the number of terms present: x³ + y³ − z³
Q. Classify the following polynomial based on the number of terms present: x³ + y³ − z³
Q.
A term is separated by a '+' or '−' sign.
There are 3 terms here:
x³, +y³, −z³
∴ It is a trinomial
(Tri means three)
Student sample
Student sample
Q. Classify based on the number of terms present in this polynomial: x³ + y³ + z³ + 3xyz
Q. Classify based on the number of terms present in this polynomial: x³ + y³ + z³ + 3xyz
Q.
Terms are separated by + or − sign.
∴ There are 4 terms:
x³, y³, z³, 3xyz
(We have not mentioned +x³, +y³, +z³, +3xyz as the + is understood)
⇒ Quadrinomial or a polynomial
(polynomial ⇒ any with more than 3 terms)
Student sample
Student sample
Q. Classify the following based on the number of terms present: 7 + 5
Q. Classify the following based on the number of terms present: 7 + 5
Q.
A term is separated from another term by a '+' or '−' sign.
But 7 & 5 are constants i.e. like terms.
So, we can add them
⇒ 7 + 5
⇒ 12
So, only one term i.e. Monomial
(∵ Mono means 1)
Student sample
Student sample
Q. abc + 1 is the given polynomial. Classify it based on the number of terms present.
Q. abc + 1 is the given polynomial. Classify it based on the number of terms present.
Q.
A term is separated from another term by a '+' or '−' sign.
___ + ___
So, there are 2 terms: abc, 1
∴ It is a binomial
(∵ bi means two, like in bicycle)
Student sample
Student sample
Q. Classify 3x − 2 + 5 based on the number of terms present.
Q. Classify 3x − 2 + 5 based on the number of terms present.
Q.
Two terms are separated by a + or a − sign.
But, −2 and +5 are like terms (constant numeric values). So, they can be combined/added.
−2 + 5 = +3
⇒ 3x + 3
⇒ There are 2 terms, not 3.
⇒ It is a binomial (not trinomial)
(bi means two, like in bicycle)
Student sample
Student sample
Q. Classify 2x − 3y + 4
Q. Classify 2x − 3y + 4
Q.
#1. Polynomial as all powers of variables when present in numerator are non-negative & whole.
2x¹y⁰ − 3y¹x⁰ + 4x⁰y⁰ ✓
#2. Linear polynomial as the degree or highest power of both variables is 1. In each term the total power of variables is 1. So, degree is 1.
#3. Linear polynomial in 2 variables namely x & y.
#4. Trinomial as there are 3 unlike terms:
2x, −3y and 4
Student sample
Student sample
Q. Classify xy + yz + zx
Q. Classify xy + yz + zx
Q.
It is a quadratic polynomial in 3 variables.
Degree of variables x, y & z individually are 1 i.e. the highest power of each variable is 1 ⇒ But in each term the total power is 1+1=2 E.g. x¹y¹, y¹z¹, z¹x¹. So, the degree is 2. So, quadratic polynomial.
There are 3 variables x, y and z.
It is a polynomial ∵ powers of all variables in numerator are whole & non-negative.
x¹y¹z⁰ + y¹z¹x⁰ + z¹x¹y⁰
Also, there are 3 unlike terms i.e. trinomial.
(tri means 3, like in tricycle)
Student sample
Student sample
Q. Classify ax³ + bx² + cx + d in all ways possible.
Q. Classify ax³ + bx² + cx + d in all ways possible.
Q.
This algebraic expression is a polynomial as the powers of all variables when present in the numerator are non-negative and whole.
ax³ + bx² + cx¹ + dx⁰
It is a polynomial in 1 variable, the variable being x.
It is a cubic polynomial in 1 variable, as the highest power of variable is 3 (x³), i.e. degree is 3.
There are 4 unlike terms:
ax³, bx², cx, d
⇒ It is a quadrinomial or polynomial
(∵ quadri means 4)
(poly means more than 3)
Student sample
Student sample
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