Answer:
43
Step-by-step explanation:
Using the remainder theorem, that is
The remainder on dividing f(x) by (x - h) is the value of f(h)
here division by (x - 3) hence evaluate f(3) for remainder
f(3) = 3² + 14(3) - 8 = 9 + 42 - 8 = 43 ← remainder
As per the remainder theorem, a polynomial P(x) is divided by (x-t) then the remainder is equal to P(t). When f(x) = x2 + 14x − 8 is divided by (x − 3), the value of the remainder is 43. The correct option is A.
According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial.
We can find the value of the remainder, when f(x) = x² + 14x − 8 is divided by (x − 3) by using the remainder theorem.
Now, as per the remainder when f(x) = x² + 14x − 8 is divided by (x − 3) will be equal to f(3). Therefore, the value of the remainder will be,
f(x) = x² + 14x − 8
f(3) = (3)² + 14(3) − 8
= 9 + 42 - 8
= 43
Hence, when f(x) = x2 + 14x − 8 is divided by (x − 3), the value of the remainder is 43.
Learn more about the Remainder Theorem here:
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