Question

f(x)= 16x 5x4-5x²+9 g(x) =-6x³+=7x-15. Add the polynomials and find the degree of the resultant polynomial.

Answer 1

Given, f(x) = 16x + 5x⁴ - 5x² + 9
g(x) = -6x³ + 7x - 15

we have to add f(x) and g(x) ,

f(x) + g(x) = 16x + 5x⁴ - 5x² + 9 + (-6x³ + 7x - 15)

= 16x + 5x⁴ - 5x² + 9 - 6x³ + 7x - 15

= 5x⁴ - 6x³ - 5x² + 23x - 15

we know, degree of any polynomial P(x) is the highest power of x. for example :- if P(x) = x³ + x² + 6 is given then, degree of P(x) = 3 , because highest power of x is 3.

now, degree of Resultant polynomial is 4.
hence, answer is 4.

Answer 2

Hi ,

Given two polynomials are

f(x) = 16x + 5x⁴ - 5x² + 9 ,

g(x) = -6x³ + 7x - 15

Let the Resultant polynomial = p(x)

i ) p(x) = f(x) + g(x)

= 16x + 5x⁴ - 5x² + 9 + ( -6x³+7x-15 )

= 16x + 5x⁴ - 5x² + 9 - 6x³ + 7x - 15

= 5x⁴ - 6x³ - 5x² + 23x - 6

ii ) Degree of p( x ) = heighest degree

of the p( x )

= 4

I hope this helps you.

: )