FIND THE NUMERICAL COEFFICIENT OF THE TERMS

Identify the numerical coefficients of terms (other than constants) in the following expressions :

Problem 1 :

5 – 3t²

Solution :

5 – 3t²

Numerical coefficient of t² is -3.

5 is a constant term.

Problem 2 :

1 + t + t² + t³

Solution :

1 + t + t² + t³

Numerical coefficient of t is1.

Numerical coefficient of t² is1.

Numerical coefficient of t³ 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 :

-p²q² + 7pq

Solution :

-p²q² + 7pq

Numerical coefficient of p²q² 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 r²

Solution :

3.14 r²

Numerical coefficient of r² 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 y²

Solution :

0.1 y + 0.01 y²

Numerical coefficient of y is 0.1.

Numerical coefficient of y² is 0.01.

0 is a constant term.

Identify terms which contain x and give the coefficients of x.

Problem 1 :

y²x + y

Solution :

y²x + y

y²x is the term containing x.

Coefficient of x is y².

Problem 2 :

13y² – 8yx

Solution :

13y² – 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 :

12xy² + 25

Solution :

12xy² + 25

12xy² is that term containing x.

Coefficient of x is12y².

Problem 7 :

7x + xy²

Solution :

7x + xy²

7x is that term containing x.

xy² is that term containing x.

Coefficient of x is 7.

Coefficient of x is y².

Identify terms which contain y² and give the coefficients of y².

Problem 1 :

8 – xy²

Solution :

Given, 8 – xy²

-xy² is that term containing y².

Coefficient of y² is -x.

Problem 2 :

5y² + 7x

Solution :

Given, 5y² + 7x

5y² is that term containing y².

Coefficient of y² is 5.

Problem 3 :

2x²y – 15xy² + 7y²

Solution :

Given, 2x²y – 15xy² + 7y²

– 15xy² is that term containing y².

7y² is that term containing y².

Coefficient of y² is -15x.

Coefficient of y² is 7.

Problem 4 :

The expressions bx² + 11x and x(4x + a) - 3x where a and b are constants, are equivalent. What is the value of a + b ?

a)  12     b)  15    c)  18    d) 21

Solution :

bx² + 11x = x(4x + a) - 3x

bx² + 11x = 4x² + ax - 3x

bx² + 11x = 4x² + (a - 3)x

Equating the corresponding term coefficients, we get

b = 4 and a - 3 = 11

a = 11 + 3

a = 14

a + b = 14 + 4

= 18

So, the values of a + b is 18.

Problem 5 :

The expressions (ax + 5)(bx - 5) where a and b are constants can be rewritten as cx² + 15x - 25 where c is a constant. What is the value of b - a ?

Solution :

(ax + 5)(bx - 5) = cx² + 15x - 25

abx² - 5ax + 5bx - 25 = cx² + 15x - 25

abx² + (5b - 5a)x - 25 = cx² + 15x - 25

ab = c

5b - 5a = 15

Dividing it by 5, we get

b - a = 15/5

b - a = 3

So, the value of b - a is 3.

Problem 6 :

ax - b = 3(2x + 1)

In the given equation a and b are constants. The equation has no solution. Which of the following could be the values of a and b ?

a) a = 2, b = -3    b)  a = 2 and b = 3

c)  a = 6, b = -3    d) a = 6 and b = 3

Solution :

ax - b = 3(2x + 1)

ax - b = 6x + 3

Equating the coefficients of corresponding terms, we get

a = 6 and -b = 3

a = 6 and b = -3