$$ 30 a^{2}-19 a s-63 s^{2} $$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $$ 30 a^{2}-19 a s-63 s^{2}=\square $$ (Factor completely.) B. The trinomial is not factorable.

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UpStudy AI · Accepted Answer

To factor 30a² - 19as - 63s², we first look for two numbers that multiply to (30)(-63) = -1890 while adding to -19. The numbers -54 and 35 work since -54 × 35 = -1890 and -54 + 35 = -19.

Now, rewrite the middle term using these numbers:
 30a² - 54as + 35as - 63s²

Group the terms:
 (30a² - 54as) + (35as - 63s²)

Factor out the greatest common factor from each group:
 6a(5a - 9s) + 7s(5a - 9s)

Now, factor out the common binomial (5a - 9s):
 (5a - 9s)(6a + 7s)

Since the factorization is complete, the correct choice is:

A. 30a² - 19as - 63s² = (5a - 9s)(6a + 7s)
$$ 30a^{2} - 19as - 63s^{2} = (5a - 9s)(6a + 7s) $$

\( 30 a^{2}-19 a s-63 s^{2} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( 30 a^{2}-19 a s-63 s^{2}=\square \) (Factor completely.) B. The trinomial is not factorable.

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