Answer:
6^5
Step-by-step explanation:
Answer:
f(2)=0. The third option is correct.
Step-by-step explanation:
Suppose we have a polynomial called f(x) and we know (x-2) is a factor of f. This means that we can express f(x) as:
f(x)=(x-2)\cdot g(x)
Being g(x) another unknown function.
Option 1: f(0)=(0-2)\cdot g(0)=-2\cdot g(0). Since we don't know the value of g(0), we cannot assure f(0)=-2. Incorrect
Option 2: f(-2)=(-2-2)\cdot g(-2)=-4\cdot g(-2). Since we don't know the value of g(-2), we cannot assure f(-2)=0. Incorrect
Option 3: f(2)=(2-2)\cdot g(2)=0\cdot g(0)=0. Regardless of the value of g(0), f(0) must be 0. Correct
Option 4: f(0)=(0-2)\cdot g(0)=-2\cdot g(0). Since we don't know the value of g(0), we cannot assure f(0)=2. Incorrect
Answer:
Remainder 209
Step-by-step explanation:
f(x)= 4x⁵+5x⁴+1
x-2=0⇒x=2
Putting x=2 in the above equation
f(x)= 4(2)⁵ +5(2)⁴+1
f(x)= 4(32) +5(16) +1
f(x)= 128 +80+1
f(x)= 209
Answer:
a = -2
Simplifying 5 + -2(4a + 1) + 3a = 13 Reorder the terms: 5 + -2(1 + 4a) + 3a = 13 5 + (1 * -2 + 4a * -2) + 3a = 13 5 + (-2 + -8a) + 3a = 13 Combine like terms: 5 + -2 = 3 3 + -8a + 3a = 13 Combine like terms: -8a + 3a = -5a 3 + -5a = 13 Solving 3 + -5a = 13 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5a = 13 + -3 Combine like terms: 3 + -3 = 0 0 + -5a = 13 + -3 -5a = 13 + -3 Combine like terms: 13 + -3 = 10 -5a = 10 Divide each side by '-5'. a = -2
