Where, f(x) = x3 - x2?- 14x + 24
Answers
Answer:
P(x) = x³ - x² - 14 x + 24
factors of 24 are possible rational roots of P(x), if at all rational roots exist.
so roots are possibly : + 1, 2, 3, 4, 6,8, 12, 24 or -1, -2, -3, -4, -6, -8, -12, -24
check with 1, -1, 2 .. x = 2 ⇒ P(2) = 0
let, P(x) = (x - 2) [ x² - a x + (24/-2) ]
then compare coefficients of x² term or x term, then
-a x² - 2 x² = - 1 x² ⇒ a = -1
2 a x -12 x = - 14 x ⇒ a = -1
P(x) = ( x -2 ) ( x² +x-12) =
find factors of -12 that have difference of -1.
so -4 and 3 are roots of x² +x -12
P(x) = (x - 2 ) ( x + 4 ) ( x - 3)
Answer:
please mark as brainlist please
Step-by-step explanation:
Explanation:
We start from the given 3rd degree polynomial
x
3
+
x
2
−
14
x
−
24
Use the monomial
−
14
x
It is equal to
−
4
x
−
10
x
x
3
+
x
2
−
4
x
−
10
x
−
24
Rearrange
x
3
−
4
x
+
x
2
−
10
x
−
24
Regroup
(
x
3
−
4
x
)
+
(
x
2
−
10
x
−
24
)
Factoring
x
(
x
2
−
4
)
+
(
x
+
2
)
(
x
−
12
)
x
(
x
+
2
)
(
x
−
2
)
+
(
x
+
2
)
(
x
−
12
)
Factor out the common binomial factor
(
x
+
2
)
(
x
+
2
)
[
x
(
x
−
2
)
+
(
x
−
12
)
]
Simplify the expression inside the grouping symbol [ ]
(
x
+
2
)
[
x
2
−
2
x
+
x
−
12
]
(
x
+
2
)
(
x
2
−
x
−
12
)
Factoring the trinomial
x
2
−
x
−
12
=
(
x
+
3
)
(
x
−
4
)
We now have the factors
(
x
+
2
)
(
x
+
3
)
(
x
−
4
)
Final answer
x
3
+
x
2
−
14
x
−
24
=
(
x
+
2
)
(
x
+
3
)
(
x
−
4
)
God bless ....I hope the explanation is useful.