Question

Would greatly appreciate if any of you can answer the question in the attached image with full explanation including a strategy for solving it. Thanks in advance!

Answer 1

• B) a = - 3

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Multiply both sides by ax - 2 to clear fractions:

• 24x² + 25x - 47 = (ax - 2)(- 8x - 3) - 53
• 24x² + 25x - 47 = - 8ax² - 3ax + 16x + 6 - 53
• 24x² + 25x - 47 = - 8ax² - (3a - 16)x - 47

Comparing both sides we can guess that -8a = 24 ⇒ a = - 3, then:

• - (3*(-3) - 16) = - (- 9 - 16) = - (-25) = 25.

We see both coefficients match, hence a = - 3 is a right choice.