Find the value of a such that (x-4) is a factor of 5x³-7x²-ax-28.
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Let, f (x) = 5x³ - 7x² - ax - 28 be the given polynomial.
By factor theorem, If (x - 4) is a factor of f (x) then f (4) = 0 :
Now, f (x) = 5x³ - 7x² - ax - 28
⇒f (4) = 5(4)³ - 7(4)² + a (4) - 28
⇒ 0 = 5 × 64 - 7 × 16 + 4a - 28
⇒ 0 = 320 - 112 + 4a - 28
⇒0 = 180 - 4a
⇒5a = 180
⇒a = 180/5
⇒a = 45
Hence, (x – 4) is a factor of f (x), if a is 45.
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