Question

x²-x+1 by factor theorm​

Answer 1

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f(x) = 0

x2 + 2x – 15 = 0

(x + 5) (x – 3) = 0

(x + 5) = 0 or (x – 3) = 0

x = -5 or x = 3

We can check if (x – 3) and (x + 5) are factors of the polynomial x2 + 2x – 15, by applying the Factor Theorem as follows:

If x = 3

Substitute x = 3 in the polynomial equation/.

f (x)= x2 + 2x – 15

⟹ 32 + 2(3) – 15

⟹ 9 + 6 – 15

⟹ 15 – 15

f (3) = 0

And if x = -5

Substitute the values of x in the equation f(x)= x2 + 2x – 15

⟹ (-5)2 + 2(-5) – 15

⟹ 25 – 10 – 15

⟹ 25 – 25

f (-5) = 0

✈︎Since the remainders are zero in the two cases, therefore (x – 3) and (x + 5) are factors of the polynomial x2 +2x -15