write the following polynomial in standard form. -7y+y^5+3y^4-10+2y^4-y^2
Answers
Step-by-step explanation:
y^5+5y^4-y^2-7y-10
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Answer:
Aggarwal 2019 Solutions for class Class 9 Math are prepared by experts and are 100% accurate.
Page No 74:
Question 1:
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
(i) x5-2x3+x+
√
3
(ii) y3+
√
3
y
(iii) t2-
2
5
t+
√
5
(iv) x100-1
(v)
1
√
2
x2-
√
2
x+2
(vi) x-2+2x-1+3
(vii) 1
(viii)
-3
5
(ix)
x2
2
-
2
x2
(x) 3
√
2
x2-8
(xi)
1
2x2
(xii)
1
√
5
x
1
2
+1
(xiii)
3
5
x2-
7
3
x+9
(xiv) x4-x
3
2
+x-3
(xv) 2x3+3x2+
√
x
-1
ANSWER:
(i) x5-2x3+x+
√
3
is an expression having only non-negative integral powers of x. So, it is a polynomial. Also, the highest power of x is 5, so, it is a polynomial of degree 5.
(ii) y3+
√
3
y is an expression having only non-negative integral powers of y. So, it is a polynomial. Also, the highest power of y is 3, so, it is a polynomial of degree 3.
(iii) t2-
2
5
t+
√
5
is an expression having only non-negative integral powers of t. So, it is a polynomial. Also, the highest power of t is 2, so, it is a polynomial of degree 2.
(iv) x100-1 is an expression having only non-negative integral power of x. So, it is a polynomial. Also, the highest power of x is 100, so, it is a polynomial of degree 100.
(v)
1
√
2
x2-
√
2
x+2 is an expression having only non-negative integral powers of x. So, it is a polynomial. Also, the highest power of x is 2, so, it is a polynomial of degree 2.
(vi) x-2+2x-1+3 is an expression having negative integral powers of x. So, it is not a polynomial.
(vii) Clearly, 1 is a constant polynomial of degree 0.
(viii) Clearly, -
3
5
is a constant polynomial of degree 0.
(ix)
x2
2
-
2
x2
=
x2
2
-2x-2
This is an expression having negative integral power of x i.e. −2. So, it is not a polynomial.
(x) 3
√
2
x2-8 is an expression having only non-negative integral power of x. So, it is a polynomial. Also, the highest power of x is 2, so, it is a polynomial of degree 2.
(xi)
1
2x2
=
1
2
x-2 is an expression having negative integral power of x. So, it is not a polynomial.
(xii)
1
√
5
x
1
2
+1
In this expression, the power of x is
1
2
which is a fraction. Since it is an expression having fractional power of x, so, it is not a polynomial.
(xiii)
3
5
x2-
7
3
x+9 is an expression having only non-negative integral powers of x. So, it is a polynomial. Also, the highest power of x is 2, so, it is a polynomial of degree 2.
(xiv) x4-x
3
2
+x-3
In this expression, one of the powers of x is
3
2
which is a fraction. Since it is an expression having fractional power of x, so, it is not a polynomial.
(xv) 2x3+3x2+
√
x
-1=2x3+3x2+x
1
2
-1
In this expression, one of the powers of x is
1
2
which is a fraction. Since it is an expression having fractional power of x, so, it is not a polynomial.
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