The expression {x²-2x-15}{x²+8x+15}× (x²+4x-5) is equal to

Correct Answer is : x2−6x+5x² - 6x + 5x2−6x+5

Correct Answer is : x2−6x+5x² - 6x + 5x2−6x+5

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CTET Paper II (Mathematics and Science) 24 Dec 2021 Solved Paper

Question : 38 of 150

Marks: +1, -0

The expression

\frac{x^{2}-2x-15}{x^{2}+8x+15}\times (x^{2}+4x-5)

is equal to

Solution:

Concept:

Factor each quadratic expression and cancel common factors before multiplying.

Explanation:

First, factor the numerator and denominator of the first fraction.

x^{2}-2x-15 = (x-5)(x+3)

and

x^{2}+8x+15 = (x+3)(x+5)

The second factor is

x^{2}+4x-5 = (x+5)(x-1)

Now substitute:

\frac{(x-5)(x+3)}{(x+3)(x+5)} \times (x+5)(x-1)

Cancel

(x+3)

and

(x+5)

. We get

(x-5)(x-1)

Expand:

x^{2} - x - 5x + 5 = x^{2} - 6x + 5

Answer:

x^{2} - 6x + 5

(Option C)

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