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A polynomial containing two nonzero terms is called a ________.
Let a = 3x and b = 5 (3x)³ - (5)³ - 3×3x×5(3x- 5) = 27x³ - 125 -45x ( 3x -5) = 27x³ -125 - 135x² + 225x = 27x³ - 135x² + 225x - 125
X+ 1/x = 7 then, cubing both side = (x +1/x)³ = (7)³ = x³ + 1/x³ + 3×X×1/X (x+1/x) = 343 = x³ +1/x³ +3(7) = 343 =x³ +1/x³ +21 =343 = x³ +1/x³ =343 - 21 = x³ +1/x³ = 322
Degree is the highest exponent of any value in an equation. Here, this highest exponent is 4. Therefore, 4 is the degree of the given equation.
A polynomial containing three nonzero terms is called a ________.
use factor theorem as x+2 is factor of
x³-2ax²+16 so put x = -2 and equate the equation to 0
so putting x = -2
(-2)³-2a(-2)²+16 =0
-8-8a+16=0
-8a = -8
a = 8/8= 1
So,
a = 1
ANSWER :- b
Solution :- (0.75 * 0.75 * 0.75 + 0.25 * 0.25 * 0.25)/(0.75 * 0.75 - 0.75 * 0.25 + 0.25 * 0.25)
= (0.421875 + 0.015625)/(0.5625 - 0.1875 + 0.0625)
= (0.4375)/(0.4375)
= 1
If one of the factor of x2 + x – 20 is (x + 5). Find the other
Let f(x) = px2 + 5 x + r
If (x - 2) is a factor of f (x), then by factor theorem
f(2) = 0 | x - 2 = 0 ⇒ x = 2
⇒ p(2)2 + 5(2) + r = 0
⇒ 4p + r + 10 = 0 ...(1)
If is a factor of f (x), then by factor theorem,
Subtracting (2) from (1), we get
3p - 3r = 0
⇒ p = r
The remainder when the polynomial x4+2x3−3x2+x−1 is divided by (x−2) is
The remainder obtained when the polynomial p(x) is divided by (b – ax) is
ANSWER :- b
Solution :- b-ax=0
b=ax
b/a=x
i.e. remainder is p(b/a)
x³+y³+15xy-125
=x³ + y³ +3 xy ×5 - 125
=x³ + y³ +3xy(x+y) - (5)³
= (x+y) ³ - (5)³
=(5)³ - (5)³
=0
If the polynomial x3−6x2+ax+3 leaves a remainder 7 when divided by (x−1), then the value of ‘a’ is
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