If x2 – x – 42 = (x + k) (x + 6) then find the value of k.

1.	If x2 – x – 42 = (x + k) (x + 6) then find the value of k.
Answer» x² – x – 42 = (x + k) (x + 6) ⇒ x² – 7x + 6x – 42 = (x + k) (x + 6) ⇒x (x – 7) + 6 (x – 7) = (x + k) (x + 6) ⇒ (x – 7) (x + 6) = (x + k) (x + 6) On comparison k = – 7

Answer»

x² – x – 42 = (x + k) (x + 6)

⇒ x² – 7x + 6x – 42 = (x + k) (x + 6)

⇒x (x – 7) + 6 (x – 7) = (x + k) (x + 6)

⇒ (x – 7) (x + 6) = (x + k) (x + 6)

On comparison

k = – 7

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