4x⁴ + 0x³ +0x⁵ + 5x+7
4x⁴ + 5x + 7
Here, the highest power is 4.
Therefore, the degree of given polynomial is 4.

5x − 4x²+3
−4x² + 5x + 3
Putting x= -1 in the given polynomial, we get
−4 (−1)²+5(−1) +3
= −4−5+3
= −9+3
= −6

P(x) = x + 3
And p (-x) = -x + 3
Then, p(x) + p (-x)
= x + 3 – x + 3
= 6

p(x) = 5x – 2
To find zero of the polynomial, we write
5x – 2 = 0
5x = 2
x = 2/5

2x² +7x – 4
2x² +8x – x −4
2x(x + 4) – 1(x + 4)
(2x – 1)(x + 4)
2x – 1 = 0 and x + 4 = 0
x = 1/2 and x = -4
Therefore, one zero of the given polynomial is 1/2

x⁵¹+51 is divided by x + 1.

It means x = -1 will be one of the value. By putting this value, we can obtain the remainder.

Using remainder theorem,

(−1)⁵¹ + 51

= −1 + 51

= 50

If x+1 is a factor of p(x) = 2x²+kx+1,
then by putting x=-1, the value of p(x) will be 0.
p(-1) = 0
2x²+kx+1= 0
2(−1)²+k(−1)+1= 0
2−k+1= 0
k = 3

(249)² – (248)²

(249 + 248)(249 – 248)   [Using identity a²−b² = (a + b) (a−b)]

= 497 × 1

= 497

9x²−3x−20

9x²−15x+12x−20

= 3x (3x−5) + 4(3x−5)

= (3x + 4) (3x – 5)

If a + b + c = 0, then

a³+b³+c³−3abc = (a+b+c)(a²+b²+c²-ab-bc-ca)

a³+b³+c³−3abc = 0

a³+b³+c³ = 3abc