Question

If f(x) =5x⁵+a×x³+3x²-4x-6 with a=-8 is devided by x-1, find the remainder find the reminder​

Answer 1

я написал решение на листочке

Answer 2

To find the remainder when the polynomial \( f(x) = 5x^5 + a \cdot x^3 + 3x^2 - 4x - 6 \) with \( a = -8 \) is divided by \( x - 1 \), you can use the Remainder Theorem.

The Remainder Theorem states that if you divide a polynomial \( f(x) \) by \( x - c \), the remainder is \( f(c) \).

In this case, \( c = 1 \) because we are dividing by \( x - 1 \). Therefore, you need to substitute \( x = 1 \) into the polynomial \( f(x) \) to find the remainder.

First, substitute \( x = 1 \) into the expression for \( f(x) \):

\[ f(1) = 5(1)^5 + (-8)(1)^3 + 3(1)^2 - 4(1) - 6 \]

Simplify the expression:

\[ f(1) = 5 - 8 + 3 - 4 - 6 \]

\[ f(1) = -10 \]

So, the remainder when \( f(x) \) is divided by \( x - 1 \) is \( -10 \).