use the Factor Theorem to show that
Answers
Answer:
a) let f(x) = x³ + 2x² +2x +1
Given x + 1
so, x = (-1)
putting value of x in
f(x)= x³ + 2x² +2x +1
= (-1)³ + 2 (-1)² + 2(-1) + 1
= (-1) + 2(1) -2 + 1
= (-1) + 2 - 2 + 1
= 0
f(x) = 0
therefore x³ + 2x² +2x +1 is facter of x+1
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b) let f(x) = x³ - 3x² + 4x - 4
Given x - 2
so, x = 2
putting value of x in
f(x) = x³ - 3x² + 4x - 4
= (2)³ - 3(2)² + 4(2) - 4
= 8 - 3(4) + 8 - 4
= 8 - 12 + 8 - 4
= 16 - 16
= 0
f(x) = 0
therefore x³ - 3x² + 4x - 4 is factor of x - 2
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c) let f(x) = x³ - 3x² + x - 3
Given x - 3
so, x = 3
putting value of x in
f(x) = x³ - 3x² + x - 3
= (3)³ - 3(3)² + 3 - 3
= 27 - 3(9) + 3 - 3
= 27 - 27 +3 - 3
= 0
f(x) = 0
therefore x³ - 3x² + x - 3 is factor of x-3
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d) let f(x) = x⁴ + 5x³ + 2x² + 7x - 15
Given x+5
so, x = (-5)
putting value of x in
f(x) = x⁴ + 5x³ + 2x² + 7x - 15
= (-5)⁴ + 5(-5)³ + 2(-5)² + 7(-5) - 15
= 625 + 5(-125) + 2(25) - 35 - 15
= 625 - 625 + 50 - 50
= 0
f(x) = 0
therefore x⁴ + 5x³ + 2x² + 7x - 15 is factor of x + 5
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