Question

18. Without actual division, show that (x2 – 3x² - 13x +15) is exactly
divisible by (x2 + 2x - 3).​

Answer 1

Answer:

hope it helps you✌✌

Step-by-step explanation:

X2 +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,

x3−3x 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