Solve. 8x^{2}+10x-3/2x^{2}-7x-15

maduregimc

maduregimc

Answered question

2021-12-13

Solve.
8x2+10x32x27x15

Answer & Explanation

Papilys3q

Papilys3q

Beginner2021-12-14Added 34 answers

Step 1
We have to evaluate:
8x2+10x32x27x15
In this case we have to factorize the numerator and denominator.
So factorizing the numerator by middle term splitting method, we get
8x2+10x3=8x2+12x2x3
(here we have used 8×3=12×2)
Now taking common from terms,
8x2+10x3=8x2+12x2x3
=4x(2x+3)-1(2x+3)
=(2x+3)(4x-1)
Hence, factorization of numerator is (2x+3)(4x-1).
Now finding factorization of the denominator by middle term splitting method,
2x27x15=2x210x+3x15
(here we have used 15×2=10×3)
Now taking common from terms,
2x2
7x15=2x210x+3x15
=2x(x-5)+3(x-5)
=(x-5)(2x+3)
Hence, factorization of denominator is (x-5)(2x+3).
Step 2
Therefore whole expression can be written as:
8x2+10x32x27x15=(2x+3)(4x1)(x5)(2x+3)
=(4x1)(x5)
Hence, reduced form of the expression is (4x1)(x5).

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