Question

Add the following polynomials and find the degree of the resultant polynomial.
(i) p(x)=6x2-7x+2 q(x) = 6x3-7x+15
(ii) h(x)= 7x3- 6x +1 f(x) =7x2+ 17x -9
(iii) f(x)= 16x 5x4-5x2+9 g(x) =-6x3+=7x-15

Answer 1

$1)p(x) + g(x) = 6 {x}^{2} - 7x + 2 + 6 {x}^{3} - 7x + 15 \\ = 6 {x}^{3} + 6 {x}^{2} - 14x + 17 \\ degree \: 3$
$h(x) + f(x) = 7 {x}^{3} - 6x + 1 + 7 {x}^{2} + 17x - 9 \\ = 7 {x}^{3} + 7 {x}^{2} + 11x - 8 \\ degree \: 3$
$f(x) + g(x) = 16 {x}^{5} + {x}^{4} - 5 {x}^{2} + 9 - 6 {x}^{3} + 7x - 15 \\ = 16 {x}^{5} + {x}^{4} - 6 {x}^{3} - 5 {x}^{2} + 7x - 6 \\ degree \: 5$

Answer 2

p(X)=6x2-7x+15

p(X)+q(X)=12x2-14+17

=6×3=7x+15