HOW TO FIND THE DEGREE OF A POLYNOMIAL

Write the degree of each polynomial.

Problem 1 :

3x⁴ + 2xyz + 5x² - 4

Solution :

Find the degree of each term :

So, the greatest degree is 4.

Problem 2 :

-6s²tu³ + st + tu² + st³u + t³

Solution :

Find the degree of each term :

So, the greatest degree is 6.

Problem 3 :

-d² - d – 9d³

Solution :

So, the greatest degree is 3.

Problem 4 :

uv + 4u

Solution :

Find the degree of each term :

uv : degree 2

4u : degree 1

So, the greatest degree is 2.

Problem 5 :

6u² + u²vw – 2u³vw + 4u³

Solution :

So, the greatest degree is 5.

Problem 6 :

3m⁵n²

Solution :

3m⁵n² : degree 7

So, the greatest degree is 7.

Problem 7 :

p²q³r³ - p4qr² + 7 + qr + p6q

Solution :

So, the greatest degree is 8.

Problem 8 :

-8a² + abc + b²c² + ab

Solution :

So, the greatest degree, 4.

Problem 9 :

x – x⁶ + x² + x³ - x⁵

Solution :

So, the greatest degree is 6.

Problem 10 :

4r⁴ + r³s⁴t³ - r²s³t + t⁶ + 3

Solution :

So, the greatest degree is 10.

Problem 11 :

-q³rs² + 3 – q⁷r² + r²s⁴

Solution :

So, the greatest degree is 9.

Problem 12 :

w⁴xy⁵ – w⁶xy³ + 9w⁴x⁵y²

Solution :

So, the greatest degree is 11.

Problem 13 :

A polynomial of degree 7 is divided by a polynomial of degree 4. Find the degree of the quotient.

Solution :

Degree of the divisor of polynomial = 7

Degree of the dividend of the polynomial = 4

Degree of the quotient = 3

Problem 14 :

Write the degree of the given polynomials :

i) (2x + 4)³

ii) (t³ + 4) (t³ + 9)²

Solution :

i) (2x + 4)³

(a + b)³ = a³ + 3a²b + 3ab² + b³

a = 2x and b = 4

= (2x)³ + 3(2x)²(4) + 3(2x)(4)² + 4³

= 8x³ + 48x² + 96x + 64

Degree of the polynomial is 3.

ii) (t³ + 4) (t³ + 9)²

= (t³ + 4) [(t³)² + 2(t³) 9 + 9²]

= (t³ + 4) [t⁶ + 18t³ + 81]

= t⁹ + 18t⁶ + 81t³ + 4t⁶ + 72t³ + 324

= t⁹ + 22t⁶ + 153t³ + 324

So, the degree of the polynomial is 9.

Problem 15 :

Write the coefficient of x⁴ and x in 4x³ -5x⁴ +2x² + 3.

Solution :

4x³ - 5x⁴ + 2x² + 3

The given polynomial is not in the standard form, writing in the standard form, we get

= - 5x⁴ + 4x³ + 2x² + 3

Coefficient of x⁴ = -5

Coefficient of x = 0

Problem 16 :

Find the zeroes of f(z) = z² - 2z

Solution :

To find the zeroes of the polynomial, we set up f(z) = 0

z² - 2z = 0

z(z - 2) = 0

z = 0 and z = 2

Problem 17 :

Find the product using suitable identities: (4 + 5x)(4 - 5x).

Solution :

= (4 + 5x)(4 - 5x)

Looks like (a + b) (a - b), by multiplying it we get a² - b²

= 4² - (5x)²

= 16 - 25x²

Problem 18 :

What is the value of k in polynomial x² + 8x + k , if -1 is a zero of the polynomial?

Solution :

Let p(x) = x² + 8x + k

Since -1 is a zero of the polynomial, then p(-1) = 0

0 = (-1)² + 8(-1) + k

0 = 1 - 8 + k

0 = -7 + k

k = 7

So, the value of k is 7.