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1 vote
Factor x³ + x² − 3x − 3.

2 Answers

3 votes

Answer:

(x^2-3)(x+1)

Explanation:

we can split this into 2 equations

x^3+x^2

-3x-3

first one we can take x^2 out of the equations

x^2(x+1)

second one we can take out -3 of the equation

-3(x+1)

now we can combine them

(x^2-3)(x+1)

hopes this helps

User WilliamMayor
by
8.3k points
7 votes

Answer:


(x+1)(x+\sqrt3)(x-\sqrt3)

Explanation:

We need to factor out ,


\longrightarrow x^3 + x^2 -3x -3 = p(x) \ \ \rm[say]\\

Look out for factors of 3 , which could be , ±1 or ±3 . That is : 1 , -1 , 3 , -3

Substitute these factors one by one in the given cubic polynomial and look out for that value for which the expression becomes 0 .

Substitute
x = 1 ,


\longrightarrow 1^3 + 1^2 -3(1) -3 \\


\longrightarrow 2 -3-3 = -4 \\eq 0\\

Again substitute
x = -1 , we have ;


\longrightarrow (-1)^3+(-1)^2-3(-1)-3\\


\longrightarrow -1 + 1 +3 - 3 = \boxed{0 } \\

This implies
x +1 is a factor of the given cubic polynomial. Now on dividing the polynomial by
x +1 , we have; ( see attachment)


\longrightarrow p(x) = (x+1)(x^2-3)\\

Now we can further factorise
x^2-3 as ,


\longrightarrow x^2 - 3 \\

can be written as ,


\longrightarrow x^2-(\sqrt3)^2 \\

on using identity
a^2-b^2=(a-b)(a+b) , we have;


\longrightarrow (x+\sqrt3)(x-\sqrt3) \\

So the final factorised form of the given cubic polynomial is ,


\longrightarrow \underline{\underline{ p(x)= (x+1)(x+\sqrt3)(x-\sqrt3)}} \\

and we are done!

User Tmpearce
by
7.8k points

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