Question

if p (x) =g(x) .q(x) + r(x),degree of p(x) =6,degree g(x) =3,then degree of q(x) is ​

Answer 1

Answer:

3

Step-by-step explanation:

In the equation degree of p(x) is 6

Now as degree of g(x) is 3

for the degree of g(x) * q(x) to be 6

q(x) has to be 3 in order to match with degree of p(x) also degree of r(x) will be 6 for solving the equation

Answer 2

Degree of q(x) = 3

Given :

p(x) = g(x) q(x) + r(x)

Degree of p(x) = 6 , Degree g(x) = 3

To find :

Degree of q(x)

Concept :

Division Algorithm

Let f(x) and g(x) be two polynomials of degree n and m respectively and n ≥ m . Then there exist two uniquely determined polynomials q(x) and r(x) satisfying

f(x) = g(x) q(x) + r(x)

Where the degree of q(x) is n - m and r(x) is either a zero polynomial or the degree of r(x) is less than m

Solution :

Step 1 of 2 :

Write down Degree of p(x) and g(x)

By the given

Degree of p(x) = 6

Degree g(x) = 3

Step 2 of 2 :

Find Degree of q(x)

Degree of f(x) = 3

Degree of g(x) = 2

p(x) = g(x) q(x) + r(x)

By Division Algorithm

Degree of q(x)

= Degree of p(x) - Degree g(x)

= 6 - 3

= 3

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ Evaluate f(x) = x4 - 7x2 + 2x - 6 at x = 1

https://brainly.in/question/32494746

2..The polynomial f(x) = x⁴ - 2x³ - px² + q is divisible by (x-2)². Find the values p and q. Hence, solve the equation.

https://brainly.in/question/27895807