Question

Solve pla do not spams

Answer 1

Step-by-step explanation:

Given:

3x³-x²-3x+1

To find:

Factors using factor theorem.

Solution:

We know that if x-a is a factor of polynomial p(x), then f(a)=0.

Step 1: Analyze the given cubic polynomial

Put x=1

$\begin{gathered}p(x) = 3 {x}^{3} - {x}^{2} - 3x + 1 \\ \\ p(1) = 3( {1)}^{3} - ( {1)}^{2} - 3(1) + 1 \\ \\ p(1) = 3 - 1 - 3 + 1 \\ \\ p(1)= 0 \\ \end{gathered}$

Thus,

(x-1) is a factor of p(x).

Step 2: Divide p(x) by (x-1)

$\begin{gathered}x - 1 \: )3 {x}^{3} - {x}^{2} - 3x + 1(3 {x}^{2} + 2x - 1\\ 3 {x}^{3} - 3 {x}^{2} \: \: \: \: \: \: \: \: \: \: \: \\ ( - ) \: \: \: \: ( + ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ - - - - - - - - \\ 2 {x}^{2} - 3x \\ 2 {x}^{2} - 2x \\ ( - ) \: \: ( + ) \\ - - - - - - - - - \\ - x + 1 \\ - x + 1 \\ ( + ) \: \: ( - ) \\ - - - - - - \\ 0 \\ - - - - - - \end{gathered}$

Step 3: Find factors of quotient polynomial

$\begin{gathered}3 {x}^{2} + 2x - 1 \\ \\ 3 {x}^{2} + 3x - x - 1 \\ \\ 3x(x + 1) - 1(x + 1) \\ \\ (3x - 1)( x + 1) \\ \end{gathered}$

Step 4: Factors of polynomial are

$\begin{gathered}(x - 1)(x + 1)(3x - 1) \\ \end{gathered}$

Final answer:

$\begin{gathered}\bold{\red{3{x}^{3} -{x}^{2}-3x - 1 =(x - 1)(x + 1)(3x - 1)}}\\\end{gathered}$

Answer 2

spamssssssssssssonlyforrrrrrrrrrrrbutsorryyyyyyyyy

Step-by-step explanation:

IWANTPOINTS