Question

for what value of a is (x-5) a factor of x^3-3x^2+ax-10

Answer 1

Hope u like my process
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f(x) = x³ - 3x² +ax - 10

For a equation, a factor comes when it is totally divided by it.

Thus if (x-5) is a factor of f(x),
Then,

f(x) =0 when x =5

So,..
$= > {x}^{3} - 3 {x}^{2} + ax - 10 = 0 \: \: \: .. < if \: \: \: x = 2 > \\ \\ or. \: \: {(5)}^{3} - 3 \times {(5)}^{2} + a \times 5 - 10 = 0 \\ \\ or. \: \: 125- 75 + 5a - 10 = 0 \\ \\ or. \: \: 5a = - 40\\ \\ or. \: \: a = -\frac{40}{5} = - 8$
So,

a = - 8
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Hope this is ur required answer

Proud to help you

Answer 2

Given,x^3-3x^2+ax-10
(x-5)is a factor of the above polynomial
x=5
Substitute 'x' value in the given polynomial
5^3-3(5)^2+5a-10=0
125-75+5a-10=0
5a= 40
Therefore, a=8