7
advanced-math

Factor: x29x+20x^2 - 9x + 20

A

(x4)(x5)(x - 4)(x - 5)

B

(x+4)(x+5)(x + 4)(x + 5)

C

(x2)(x10)(x - 2)(x - 10)

D

(x+1)(x+20)(x + 1)(x + 20)

Correct Answer: A

Choice A is the correct answer. We need to factor the trinomial into (x+m)(x+n)(x + m)(x + n) where mn=20mn = 20 and m+n=9m+n = -9.

  1. Since the product is positive and the sum is negative, both numbers must be negative.
  2. Pairs of factors for 20: (-1, -20), (-2, -10), (-4, -5).
  3. Sums: 120=21-1-20=-21, 210=12-2-10=-12, 45=9-4-5=-9.

The correct pair is -4 and -5, so the factorization is (x4)(x5)(x - 4)(x - 5).

Choice B is incorrect because the sum would be +9. Choice C is incorrect because the sum would be -12. Choice D is incorrect because the sum would be +21.