EXERCISE - 2.4
1. Determine which of the following polynomials has (x + 1) as a factor.
3--x+1
(i) x4 - x + x2 - x + 1
(i) x + 2x + 2x2 + x + 1
(iv) x - x2 - (3 - 13)x+ V3
2. Use the Factor Theorem to determine whether g(x) is factor of f(x) in each of
following cases
(6) f(x) = 5x + x? - 5x - 1, g(x) = x + 1
(ii
) f(x) = x + 3x2 + 3x + 1, g(x) = x + 1
(ii) f(x) = x - 4x² + x + 6, g(x) = x - 2
(iv) f(x) = 3x + x2 - 20x + 12, g(x) = 3x - 2
(1) Ax) = 4x + 20x² + 33x + 18, g(x) = 2x + 3
3. Show that (x - 2), (x + 3) and (x - 4) are factors of x - 3x2 - 10x + 24.
Show that (x + 4), (x - 3) and (x - 7) are factors of x2 - 6x² - 19x + 84.
Gif both (x - 2) and
are factors of px? + 5x + r, show that p=r.
2
Answers
Answered by
3
Answer:
1)Apply remainder theorem
x+1=0
x=−1
Put the value of x=−1 in all equations.
(i) x
3
+x
2
+x+1=(−1)
3
+(−1)
2
+(−1)+1=−1+1−1+1=0
Then x+1 is the factor of equation
(ii) x
4
+x
3
+x
2
+x+1=(−1)
4
+(−1)
3
+(−1)
2
+(−1)+1=1−1+1−1+1=1
This is not zero.Then x+1 is not the factor of equation
(iii) x
4
+3x
3
+3x
2
+x+1=(−1)
4
+3(−1)
3
+3(−1)
2
+(−1)+1=1
This is not zero.Then x+1 is not the factor of equation
(iv)x
3
−x
2
−(2+
2
)x+
2
=(−1)
3
−(−1)
2
−(2+
2
)(−1)+
2
=−1−1+2−
2
+
2
=0
This is zero. Then x+1 is the factor of equation
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