Question

Multiply the following polynomials and find the degree of the resultant polynomial:
(i) p(x)=x2-9 q(x)= 6x2+7x-2
(ii) f(x) = 7x + 2 g(x) = 15x - 9
(iii) h(x)=6x2-7x +1 f(x) = 5x - 7

Answer 1

$1)p(x) \times q(x) = ( {x}^{2} - 9) \times (6 {x}^{2} + 7x - 2) \\ = 6 {x}^{4} + 7 {x}^{3} - 2 {x}^{2} - 54 {x}^{2} - 63x + 18 \\ = 6 {x}^{4} + 7 {x}^{3} - 56 {x}^{2} - 63x + 18 \\ degree \: 4$
$2)f(x) \times g(x) = (7x + 2) \times (15x - 9) \\ = 105 {x}^{2} - 63x + 30x - 18 \\ = 105 {x}^{2} - 33x - 18 \\ degree \: 2$
$3)h(x) \times f(x) = (6 {x}^{2} - 7x + 1) \times (5x - 7) \\ = 30 {x}^{3} - 42 {x}^{2} - 35 {x}^{2} + 9x + 5x - 7 \\ = 30 {x}^{3} - 77 {x}^{2} + 14x - 7 \\ degree \: 3$

Answer 2

hi

here's ur answer!!

1)p(x)×q(x)=(x

2

−9)×(6x

2

+7x−2)

=6x

4

+7x

3

−2x

2

−54x

2

−63x+18

=6x

4

+7x

3

−56x

2

−63x+18

degree4

\begin{gathered}2)f(x) \times g(x) = (7x + 2) \times (15x - 9) \\ = 105 {x}^{2} - 63x + 30x - 18 \\ = 105 {x}^{2} - 33x - 18 \\ degree \: 2\end{gathered}

2)f(x)×g(x)=(7x+2)×(15x−9)

=105x

2

−63x+30x−18

=105x

2

−33x−18

degree2

\begin{gathered}3)h(x) \times f(x) = (6 {x}^{2} - 7x + 1) \times (5x - 7) \\ = 30 {x}^{3} - 42 {x}^{2} - 35 {x}^{2} + 9x + 5x - 7 \\ = 30 {x}^{3} - 77 {x}^{2} + 14x - 7 \\ degree \: 3\end{gathered}

3)h(x)×f(x)=(6x

2

−7x+1)×(5x−7)

=30x

3

−42x

2

−35x

2

+9x+5x−7

=30x

3

−77x

2

+14x−7

degree3

hope it helps you