Math, asked by samarthmjn14, 1 month ago

f(x)= x³-4x²-11x+30, find f(2) (a) 16 (b) o (C) 28 (d) -16​

Answers

Answered by Anonymous
4

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 ☺️☺️☺️

Attachments:
Answered by lohitjinaga
1

Answer:

(a) 16

Step-by-step explanation:

f(x)= x³-4x²-11x+30, find f(2) (a) 16 (b) o (C) 28 (d) -16

Similar questions