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Question - 1 :
(2x + 3) (6x + 3)
To find the degree of this, multiply it.
➙ (2x + 3) (6x + 3)
➙ 2x (6x + 3) + 3(6x + 3)
➙ 12x² + 6x + 18x + 9
➙ 12x² + 24x + 9
The degree of this polynomial is 2. ( It's a quadratic polynomial.)
Question - 2 :
Since the degree of the P(x) is 1, it's a monomial.
Used identities :
Question - 3 :
By long division method,
Remainder = 10
Question - 4 :
2x - 1 is a factor
⇒ 2x - 1 = 0
2x = 1
x = 1/2 = 0.5
It is a factor of 2x² + kx, so when we substitute x = 0.5 the result is zero.
2(0.5)² + k(0.5) = 0
2(0.25) + 0.5k = 0
0.5 + 0.5k = 0
0.5k = -0.5
k = -0.5/0.5
k = -1
∴ The value of k is "-1"
Question - 5 :
x = -2,
5(-2) + 4(-2)² + 3(-2)³ + 5
-10 + 4(4) + 3(-8) + 5
-10 + 16 - 24 + 5
-13
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