Question
Divide the polynomial $3x^4 – 4x^3 – 3x –1$ by $x – 1$
✓
Answer
By long division, we have:
Since the remainder is $– 5.$
Now, the zero of $x – 1$ is $1.$
Therefore, putting $x = 1$ in $p(x)$, we have,
$p(1) = 3(1)^4 – 4(1)^3 – 3(1) – 1 = 3 – 4 – 3 – 1$
$= – 5$, which is the remainder
Since the remainder is $– 5.$
Now, the zero of $x – 1$ is $1.$
Therefore, putting $x = 1$ in $p(x)$, we have,
$p(1) = 3(1)^4 – 4(1)^3 – 3(1) – 1 = 3 – 4 – 3 – 1$
$= – 5$, which is the remainder
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