without actual division prove that x^3 - 3 x^2 - 13 x + 15 is exactly divisible by X ^2 + 2 x - 3
Answers
= x(x + 3)-1(x + 3)
= (x + 3)(x - 1)
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checking whether (x + 3) and (x - 1) are the factors or not,
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Taking x + 3 = 0 So, x = -3
Putting the value of x in given equation,
x^3 - 3x^2 - 13x + 15 = 0
(-3)^3 - 3(-3)^2 - 13(-3) + 15 = 0
-27 - 3(9) + 39 + 15 = 0
-27 -27 + 39 + 15 = 0
-54 + 54 = 0
0 =0
Hence, (x + 3) is the factor,
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checking for (x -1) x = 1
Putting the value of x in given equation,
x^3 - 3x^2 - 13x + 15 = 0
(1)^3 - 3(1)^2 - 13(1) + 15 =0
1 - 3 - 13 + 15 = 0
-15 + 15 = 0
0 =0
Hence, (x - 1) is also a factor.
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Then, x^2 + 2x - 3 is the factor of given equation
i hope this will help you
(-:
Answer:
x^2 + 2x - 3 is the factor of given equation
Step-by-step explanation:
x^2 + 2x - 3 = x^2 + 3x - x -3
= x(x + 3)-1(x + 3)
= (x + 3)(x - 1)
===============================
checking whether (x + 3) and (x - 1) are the factors or not,
==========================
Taking x + 3 = 0 So, x = -3
Putting the value of x in given equation,
x^3 - 3x^2 - 13x + 15 = 0
(-3)^3 - 3(-3)^2 - 13(-3) + 15 = 0
-27 - 3(9) + 39 + 15 = 0
-27 -27 + 39 + 15 = 0
-54 + 54 = 0
0 =0
Hence, (x + 3) is the factor,
=======================
checking for (x -1) x = 1
Putting the value of x in given equation,
x^3 - 3x^2 - 13x + 15 = 0
(1)^3 - 3(1)^2 - 13(1) + 15 =0
1 - 3 - 13 + 15 = 0
-15 + 15 = 0
0 =0
Hence, (x - 1) is also a factor.
=========================
Then, x^2 + 2x - 3 is the factor of given equation
i hope this will help you