check whether 2x³–5x²+4x–3 is a multiple of ( x–2 ) or not
Answers
Answer:
Hello !,
p(x)=
(x-2) => factor.
x= 2 =>zero of p(x).
hence, p(2)=
= 2(8) -5(4)+ 8 -3
= 16 -20 +8 -3
= -4 +8 -3 = 4 -3
= 1.
Therefore (x-2) isn't a factor of p(x) ,
and so p(x) isn't a multiple of (x-2).
2x³ - 5x² + 4x - 3 is not a multiple of x - 2
Given :
The polynomial 2x³ - 5x² + 4x - 3
To find :
Check whether 2x³ - 5x² + 4x - 3 is a multiple of x - 2 or not
Solution :
Step 1 of 3 :
Write down the given polynomial
Let the given polynomial = p(x)
Then p(x) = 2x³ - 5x² + 4x - 3
Step 2 of 3 :
Find the remainder when 2x³ - 5x² + 4x - 3 is divided by x - 2
Let g(x) = x - 2
For Zero of the polynomial g(x) we have
g(x) = 0
⇒ x - 2 = 0
⇒ x = 2
So the remainder when 2x³ - 5x² + 4x - 3 is divided by x - 2
= p(2)
= 2 × 2³ - 5 × 2² + 4 × 2 - 3
= 16 - 20 + 8 - 3
= - 4 + 5
= 1
Step 3 of 3 :
Check whether 2x³ - 5x² + 4x - 3 is a multiple of x - 2 or not
Since the remainder = 1 ≠ 0
Hence 2x³ - 5x² + 4x - 3 is not a multiple of x - 2
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