Question

If x + k is the GCD of x2 − 2x − 15 and x3 + 27, find the value of k.

Answer 1

Hey Mate...
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x2 − 2x − 15

= x2 − 5x + 3x − 15 [− 5x + 3x = −2x, − 5x × 3x = −15x2]

= x(x − 5) + 3(x − 5)

= (x − 5) (x + 3)

x3 + 27

= (x)3 + (3)3

= (x + 3) (x2 − 3x + 9) [a3 + b3 = (a + b) (a2 − ab + b2)]

∴GCD of x2 − 2x − 15 and x3 + 27 is x + 3.

It is given that x + k is the G.C.D of x2 − 2x − 15 and x2 + 27.

Comparing x + 3 with x + k, we get k = 3.

Thus, the value of k is 3.

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Answer 2

Holla ^_^

☸ Required Answer is ⬇⬇ ⬇⬇ ⬇

Given Equation,

⭕ ▶ x²-2x-15

By factorisation method,

▶ x² -5x +3x -15

▶ x (x -5 ) +3 (x-5)

▶ (x+3) (x-5) .

⭕ Equation no. 2
▶ x³ + 27

▶ x³ + 3³

▶ (x+3) ( x² -3x +9) .


Therefore, GCD of both equation is (x+3).

Given GCD of x²-2x-15 is x+k .

By Comparing both GCD, we get k =3

✔ Value of k =3 .


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