Question

find the value of a such that (x-4) is a factor of 5x³-7x²-ax-28

please give the correct answer​

Answer 1

Answer:

Hence, (x – 4) is a factor of f (x), if a is 45.

Step-by-step explanation:

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Answer 2

Answer:

$given \: that \: (x - 4)is \: a \: factor \: of \: {5x}^{3} - {7x}^{3} - ax - 28 | to \: find \: out \: value \: of \: a$

Let the given polynomial be p(x).

According to the factor theorem, if (x−a) is a factor of f(x), then f(a)=0.

∴ p(4)=0

$Hence, p(4) \: = \: 5 {(4)}^{3} - 7 {(4)}^{2} </p><p>−a(4)−28=0$

⇒5(64)−7(16)−4a−28=0

⇒320−112−4a−28=0

⇒320−140−4a=0

⇒180−4a=0

⇒4a=180

$a = \frac{180}{4}$

∴ a=45

$Hence, if (x−4) is a factor of \: {5x}^{3} - {7x}^{3} - ax - 28, then \: the \: value \: of\: a is 45.$