Question

f (x) = 3x3 − 5x2 − 58x + 40
(a) Find the remainder when f (x) is divided by (x − 3).

Answer 1

If x-3 is a factor

x-3=0

Thus , x=3

f(x)=3(3)^3-5(3)^2-58(3)+40

= 3(27)-5(9)-174+40

=81-45-174+40

=-98

Answer 2

The remainder when f(x) = 3x³ - 5x² - 58x + 40 is divided by x - 3 is - 98

Given :

f(x) = 3x³ - 5x² - 58x + 40

To find :

The remainder when f(x) = 3x³ - 5x² - 58x + 40 is divided by x - 3

Solution :

Step 1 of 3 :

Write down the given polynomials

Here it is given that f(x) = 3x³ - 5x² - 58x + 40 is divided by x - 3

f(x) = 3x³ - 5x² - 58x + 40

Let g(x) = x - 3

Step 2 of 3 :

Find zero of g(x)

For Zero of g(x) we have

g(x) = 0

⇒ x - 3 = 0

⇒ x = 3

∴ Zero of g(x) is 3

Step 3 of 3 :

Find the remainder

By Remainder Theorem the required Remainder when f(x) is g(x) is

$\sf = f(3)$

$\sf = 3 \times {( 3)}^{ 3} - 5 \times {( 3)}^{2} - 58 \times 3 + 40$

$\sf = 81 - 45 - 174 + 40$

$\sf = - 98$

Hence remainder when f(x) = 3x³ - 5x² - 58x + 40 is divided by x - 3 is - 98

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ Find the remainder when x³-ax²+6x-a is divided by x - a.

https://brainly.in/question/5714646

2. If polynomial 3x^3 – 2x^2 + 4x + 1 is divided by x - 2, then remainder is

https://brainly.in/question/31996931

#SPJ3