Period:
Polynomials
Across
Down
1. 4x-2y-3 has three terms, also known as a
2. When given 6x-2, x is referred to as the
. When looking at a polynomial, re-ordering the terms from highest to3. When looking at Zy, 2 is known as the _
west degree is known as_
-form
4. 3x is one term, known as a
. When you're multiplying numbers together, it's known as
7. A phrase that has variables and numbers, then is connected by
. (2x(3))/2-3x, x-
operators is known as an_
9. 3x/4-2x-5, x
12. Zy+4y are known as
terms
14. 11x/2=10x-9, x=_
15. 4x/2-3x-11, x=_
10. A_Is an algebraic expression that consists of adding or
subtracting terms
1. The
of 3xy is two
13. 12x-3 has two terms, also known as a
16. 7x- 3y are known as_
_ terms
7. 3x+4-5x-2, x=_
19. This has no variables
23. 2x-11=x+62, x=_
4. (3x-8)/4-x-6, x_
18. 3x+4=5x-2, this is known as an
20. 3x-7-4X-17, x
21. A number, variable or even the product of an equation are known
as
22. 4x-6-2x+8, x-_
Answers
So, the polynomial a2 is a quadratic polynomial.
(vi)
The degree of the polynomial 3r3 is 3.
So, the polynomial 3r3 is a cubic polynomial.
(i) y + 1y (ii) 2 − 5 x−−√ (iii) x2 + 7x + 9 (iv) 2m−2 + 7m − 5 (v) 10
ANSWER:
In an algebraic expression, if the powers of the variables are whole numbers then the algebraic expression is a polynomial.
(i)
y+1y=y+y−1
Here, one of the powers of y is −1, which is not a whole number. So, y + 1y is not a polynomial.
(ii)
2 − 5 x−−√=2−5x12
Here, the power of x is 12, which is not a whole number. So, 2 − 5 x−−√ is not a polynomial.
(iii)
x2 + 7x + 9
Here, the powers of the variable x are 2, 1 and 0, which are whole numbers. So, x2 + 7x + 9 is a polynomial.
(iv)
2m−2 + 7m − 5
Here, one of the powers of m is −2, which is not a whole number. So, 2m−2 + 7m − 5 is not a polynomial.
(v)
10 = 10 × 1 = 10x0
Here, the power of x is 0, which is a whole numbers. So, 10 is a polynomial (or constant polynomial).
Page No 39:
Question 2:
Write the coefficient of m3 in each of the given polynomial.
(i) m3 (ii) −3 2 + m − 3–√m3 (iii) −23m3 − 5m2 + 7m − 1
ANSWER:
(i)
Coefficient of m3 = 1
(ii)
−3 2 + m − 3–√m3
Coefficient of m3 = −3–√
(iii)
−23m3 − 5m2 + 7m − 1
Coefficient of m3 = −23
Page No 39:
Question 3:
Write the polynomial in x using the given information.
(i) Monomial with degree 7
(ii) Binomial with degree 35
(iii) Trinomial with degree 8
ANSWER:
(i) A polynomial having only one term is called a monomial. Also, the highest power of the variable in a polynomial is called the degree of the polynomial.
3x7 is a monomial in x with degree 7.
(ii) A polynomial having only two terms is called a binomial. Also, the highest power of the variable in a polynomial is called the degree of the polynomial.
2x35 + 1 is a binomial in x with degree 35.
(iii) A polynomial having only three terms is called a trinomial. Also, the highest power of the variable in a polynomial is called the degree of the polynomial.
5x8 + 6x4 + 7x is a trinomial in x with degree 8.
Page No 40:
Question 4:
Write the degree of the given polynomials.
(i) 5–√ (ii)x∘ (iii) x2 (iv) 2–√ m10 − 7 (v) 2p − 7–√ (vi) 7y − y3 + y5 (vii) xyz +xy − z (viii) m3n7 − 3m5n + mn
ANSWER:
The highest power of the variable in a polynomial of one variable is called the degreee of the polynomial. Also, the highest sum of the powers of the variables in each term of the polynomial in more than one variable is the degree of the polynomial.
(i)
5–√=5–√×1=5–√x0
The degree of the polynomial 5–√ is 0.
(ii)
The degree of the polynomial x0 is 0.
(iii)
The degree of the polynomial x2 is 2.
(iv)
The degree of the polynomial 2–√m10−7 is 10.
(v)
The degree of the polynomial 2p−7–√ is 1.
(vi)
The degree of the polynomial 7y−y3+y5 is 5.
(vii)
The sum of the powers of the variables in the polynomial xyz+xy−z are 1 + 1 + 1 = 3 and 1 + 1 = 2.
The degree of the polynomial xyz+xy−z is 3.
(viii)
The sum of the powers of the variables in the polynomial m3n7−3m5n+mn are 3 + 7 = 10, 5 + 1 = 6 and 1 + 1 = 2.
The degree of the polynomial m3n7−3m5n+mn is 10.
Page No 40:
Question 5:
Classify the following polynomials as linear, quadratic and cubic polynomial.
(i) 2x2 + 3 x + 1 (ii) 5p (iii) 2–√y − 12 (iv) m3 + 7m2 + 52m − 7–√ (v) a2 (vi) 3r3
ANSWER:
(i)
The degree of the polynomial 2x2 + 3x + 1 is 2.
So, the polynomial 2x2 + 3x + 1 is a quadratic polynomial.
(ii)
The degree of the polynomial 5p is 1.
So, the polynomial 5p is a linear polynomial.
(iii)
The degree of the polynomial 2–√y−12 is 1.
So, the polynomial 2–√y−12 is a linear polynomial.
(iv)
The degree of the polynomial m3+7m2+52m−7–√ is 3.
So, the polynomial m3+7m2+52m−7–√ is a cubic polynomial.
(v)
The degree of the polynomial a2 is 2. Page No 40:
Question 6:
Write the following polynomials in standard form.
(i) m3 + 3 + 5m (ii) −7y + y5 + 3y3 − 12 + 2y4 − y2
ANSWER:
A polynomial written in either descending or ascending powers of its variable is called the standard form of the polynomial.
(i)
The given polynomial is m3 + 3 + 5m.
The standard form of the polynomial is 3 + 5m + m3 or m3 + 5m + 3.
(ii)
The given polynomial is −7y+y5+3y3−12+2y4−y2.
The standard form of the polynomial is y5+2y4+3y3−y2−7y−12 or −12−7y−y2+3y3+2y4+y5.
(i) x3 − 2 (ii) 5y (iii) 2m4 − 3m2 + 7 (iv) −23
ANSWER:
(i)
x3−2=x3+0x2+0x−2
The coefficient form of the polynomial is (1, 0, 0, −2).
(ii)
5y = 5y + 0
The coefficient form of the polynomial is (5, 0).
(iii)
2m4−3m2+7=2m4+0m3−3m2+0m+7
The coefficient form of the polynomial is (2, 0, −3, 0, 7).
(iv)
The coefficient form of the polynomial −23 is (−23).