show that (2x+1),(x-3),(3x+1) are factors of the polynomial 6x^3-13x^2-14x-3
Answers
Answer:
Given:
expressions (2x+1),(x-3),(3x+1)
and polynomial 6x^3-13x^2-14x-3
To prove:
(2x+1),(x-3),(3x+1) are factors of the polynomial 6x^3-13x^2-14x-3
Solving Question:
We know the factor theorem it says that if 'a' is the factor of the polynomial p(x) then p(a) = 0
We would use the same formula here to prove.
first find value of 'x'
⇒ 2x+1=0
or 2x = -1
or, x = -1/2
second
⇒x-3=0
or, x= 3
Third,
⇒ 3x+1=0
or, 3x = -1
or, x = -1/3
Solution:
substitute values of' x'
6x³ -13x² -14x-3
⇒6(-1/2)³ - 13(-1/2)² -14*(-1/2)-3
⇒6((-1/8) -13(1/4) +14/2-3
⇒ -6/8 -13/4+14/2-3
⇒ l.c m = 8
⇒( -6 -26 + 56 -24)/8
⇒ 0 /8
⇒ 0
∴ 2x +1 is a factor
Then take 'x = 3
6x³-13x²-14x-3
⇒ 6(3)³ -13(3)²-14*3 -3
⇒ 162 - 117 - 42 -3
⇒ 162-162
⇒ 0
∴x -3 is a factor.
Then, take x = -1/3
6x³-13x²-14x-3
⇒ 6(-1/3)³ - 13(-1/3)²-14(-1/3) -3
⇒-6/27 -13/9 +14/3 -3
⇒ l.c.m = 27
⇒ (-6 -39 +126 -81)/27
⇒(-126+126)/27
⇒ 0
∴ 3x+1 is a factor.
Hence, (2x+1),(x-3),(3x+1) are factors of the polynomial 6x^3-13x^2-14x-3
Step-by-step explanation:
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