# MULTIPLYING POLYNOMIALS WORKSHEET

Question 1 :

Multiply the following polynomials and find the degree of the resultant polynomial:

(i)  p(x)  =  x2 - 9 and q(x)  =  6x2 + 7x - 2

(ii)  f(x)  =  7x + 2 and g(x)  =  15x - 9

(iii)  h(x)  =  6x2 - 7x + 1 and f(x)  =  5x - 7

Question 2 :

The cost of a chocolate is Rs. (x + y) and Amir bought (x + y) chocolates. Find the total amount paid by him in terms of x and y. If x = 10, y = 5 find the amount paid by him.

Question 3 :

The length of a rectangle is (3x+2) units and it’s breadth is (3x–2) units. Find its area in terms of x. What will be the area if x = 20 units.

Question 4 :

p(x) his a polynomial of degree 1 and q(x) is a polynomial of degree 2. What kind of the polynomial p(x) × q(x) is ?

Question 1 :

Multiply the following polynomials and find the degree of the resultant polynomial:

(i)  p(x)  =  x2 - 9 and q(x)  =  6x2 + 7x - 2

Solution :

p(x) ⋅ q(x)  =  (x2 - 9) (6x2 + 7x - 2)

=  6x4 + 7x3 - 56x2 - 63x + 18

Degree of the resultant polynomial is 4.

(ii)  f(x)  =  7x + 2 and g(x)  =  15x - 9

Solution :

=  105x2 - 33x - 18

Degree of the resultant polynomial is 2.

(iii)  h(x)  =  6x2 - 7x + 1 and f(x)  =  5x - 7

Solution :

=  30x3 - 77x2 + 54x - 7

Degree of the resultant polynomial is 3.

Question 2 :

The cost of a chocolate is Rs. (x + y) and Amir bought (x + y) chocolates. Find the total amount paid by him in terms of x and y. If x = 10, y = 5 find the amount paid by him.

Solution :

In order to find the total amount paid by him, we have to multiply the cost of 1 chocolate by the number of chocolate he buys.

Cost of 1 chocolate  =  x + y

Number of chocolates he buys  =  x + y

Total amount  =  (x + y) (x + y)

=  (x + y) ---(1)

=  x2 + 2xy + y2

By applying the values of x and y, we get

=  (10 + 5)2

=  152

=  225

Hence he has to pay Rs. 225.

Question 3 :

The length of a rectangle is (3x+2) units and it’s breadth is (3x–2) units. Find its area in terms of x. What will be the area if x = 20 units.

Solution :

Length of the rectangle  =  3x + 2

Breadth of the rectangle  =  3x - 2

Area of rectangle  =  (3x + 2)(3x - 2)

=  9x2 - 6x + 6x - 4

=  9x2 - 4

If x = 20

Area of rectangle  =  9(20)2 - 4

=  9(400) - 4

=  3600 - 4

=  3596

Question 4 :

p(x) his a polynomial of degree 1 and q(x) is a polynomial of degree 2. What kind of the polynomial p(x) × q(x) is ?

Solution :

The degree of the polynomial p(x) is 1

Degree of the polynomial q(x) is 2.

The product of polynomial is 3.

Hence it is a cubic polynomial.

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