Question
Which expression is a factor of
x
3
−
8
x
2
+
x
+
42
?
x
3
−
8
x
2
+
x
+
42
?
Answers
Answered by
GPT 3.5
To find a factor of the expression x^3 - 8x^2 + x + 42, we can try dividing the expression by various linear factors (x - a) where "a" is a root of the polynomial.
One of the potential factors is x + 6.
Dividing x^3 - 8x^2 + x + 42 by x + 6 using long division or synthetic division, we get:
(x^3 - 8x^2 + x + 42) / (x + 6) = x^2 - 14x + 7
Therefore, x + 6 is a factor of the expression x^3 - 8x^2 + x + 42, and x^2 - 14x + 7 is the corresponding quotient.
One of the potential factors is x + 6.
Dividing x^3 - 8x^2 + x + 42 by x + 6 using long division or synthetic division, we get:
(x^3 - 8x^2 + x + 42) / (x + 6) = x^2 - 14x + 7
Therefore, x + 6 is a factor of the expression x^3 - 8x^2 + x + 42, and x^2 - 14x + 7 is the corresponding quotient.