f(x)= x³-4x²-11x+30, find f(2) (a) 16 (b) o (C) 28 (d) -16
Answers
Answer:
x
3
+4x
2
−11x−30
By Rational Root Theorem, all rational roots of a polynomial are in the form
q
p
, where p divides the constant term −30 and q divides the leading coefficient 1. One such root is −5. Factor the polynomial by dividing it by x+5.
(x+5)(x
2
−x−6)
Consider x
2
−x−6. Factor the expression by grouping. First, the expression needs to be rewritten as x
2
+ax+bx−6. To find a and b, set up a system to be solved.
a+b=−1
ab=1(−6)=−6
Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product −6.
1,−6
2,−3
Calculate the sum for each pair.
1−6=−5
2−3=−1
The solution is the pair that gives sum −1.
a=−3
b=2
Rewrite x
2
−x−6 as (x
2
−3x)+(2x−6).
(x
2
−3x)+(2x−6)
Factor out x in the first and 2 in the second group.
x(x−3)+2(x−3)
Factor out common term x−3 by using distributive property.
(x−3)(x+2)
Rewrite the complete factored expression.
(x−3)(x+2)(x+5)
Step-by-step explanation:
l hope it will help u ☺️☺️☺️
Answer:
(a) 16
Step-by-step explanation:
f(x)= x³-4x²-11x+30, find f(2) (a) 16 (b) o (C) 28 (d) -16