Question

without actual division prove that
$x ^{3} - 3x {}^{2} - 13x + 15$
is exactly divisible by
$x {}^{2} + 2x - 3$

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Answer 1

Answer:

Mark Brainliest

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