What is coefficient ?
The value that appears in front of the variable is coefficient.
For example,
6x^{2} + 3x
The coefficient of x^{2 }is 6.
Identify the numerical coefficients of terms (other than constants) in the following expressions :
Problem 1 :
5 – 3t^{2}
Solution :
5 – 3t^{2}
Numerical coefficient of t^{2} is -3.
5 is a constant term.
Problem 2 :
1 + t + t^{2} + t^{3}
Solution :
1 + t + t^{2} + t^{3}
Numerical coefficient of t is1.
Numerical coefficient of t^{2} is1.
Numerical coefficient of t^{3} is1.
1 is a constant term.
Problem 3 :
x + 2xy + 3y
Solution :
x + 2xy + 3y
Numerical coefficient of x is1.
Numerical coefficient of xy is 2.
Numerical coefficient of y is 3.
0 is a constant term.
Problem 4 :
100m + 1000n
Solution :
100m + 1000n
Numerical coefficient of m is100.
Numerical coefficient of n is1000.
0 is a constant term.
Problem 5 :
-p^{2}q^{2} + 7pq
Solution :
-p^{2}q^{2} + 7pq
Numerical coefficient of p^{2}q^{2 }is -1.
Numerical coefficient of pq is 7.
0 is a constant term.
Problem 6 :
1.2 a + 0.8 b
Solution :
1.2 a + 0.8 b
Numerical coefficient of a is1.2.
Numerical coefficient of b is 0.8.
0 is a constant term.
Problem 7 :
3.14 r^{2}
Solution :
3.14 r^{2}
Numerical coefficient of r^{2} is 3.14.
0 is a constant term.
Problem 8 :
2(l + b)
Solution :
= 2(l + b)
= 2l + 2b
Numerical coefficient of l is 2.
Numerical coefficient of b is 2.
0 is a constant term.
Problem 9 :
0.1 y + 0.01 y^{2}
Solution :
0.1 y + 0.01 y^{2}
Numerical coefficient of y is 0.1.
Numerical coefficient of y^{2} is 0.01.
0 is a constant term.
Identify terms which contain x and give the coefficients of x.
Problem 1 :
y^{2}x + y
Solution :
y^{2}x + y
y^{2}x is the term containing x.
Coefficient of x is y^{2}.
Problem 2 :
13y^{2} – 8yx
Solution :
13y^{2} – 8yx
-8yx is that term containing x.
Coefficient of x is -8y.
Problem 3 :
x + y + 2
Solution :
x + y + 2
x is that term containing x.
Coefficient of x is 1.
Problem 4 :
5 + z + zx
Solution :
Given, 5 + z + zx
zx is that term containing x.
Coefficient of x is z.
Problem 5 :
1 + x + xy
Solution :
1 + x + xy
x is that term containing x.
xy is that term containing x.
Coefficient of x is 1.
Coefficient of x is y.
Problem 6 :
12xy^{2} + 25
Solution :
12xy^{2} + 25
12xy^{2} is that term containing x.
Coefficient of x is12y^{2}.
Problem 7 :
7x + xy^{2}
Solution :
7x + xy^{2}
7x is that term containing x.
xy^{2} is that term containing x.
Coefficient of x is 7.
Coefficient of x is y^{2}.
Identify terms which contain y^{2} and give the coefficients of y^{2}.
Problem 1 :
8 – xy^{2}
Solution :
Given, 8 – xy^{2}
-xy^{2} is that term containing y^{2}.
Coefficient of y^{2} is -x.
Problem 2 :
5y^{2} + 7x
Solution :
Given, 5y^{2} + 7x
5y^{2} is that term containing y^{2}.
Coefficient of y^{2} is 5.
Problem 3 :
2x^{2}y – 15xy^{2} + 7y^{2}
Solution :
Given, 2x^{2}y – 15xy^{2} + 7y^{2}
– 15xy^{2} is that term containing y^{2}.
7y^{2} is that term containing y^{2}.
Coefficient of y^{2} is -15x.
Coefficient of y^{2} is 7.
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