Question

Help with Factoring?

Answer 1

Some steps to rewrite the expression x3 - 4x + x2 - 4 as a product of three factors are shown below:

Step 1: x3 - 4x + x2 - 4
Step 2: x3 + x2 - 4x - 4
Step 3: x2(x + 1) - 4(x + 1)

Which of the following best shows the next two steps to rewrite the expression?

Step 4: (x2 - 4)(x + 1); Step 5: (x - 2)(x + 2)(x + 1)

Step 4: (x2 + 4)(x + 1); Step 5: (x + 2)(x + 2)(x + 1)

Step 4: (x2 - 4)(x + 1); Step 5: (x + 2)(x + 2)(x + 1)

Step 4: (x2 + 4)(x + 1); Step 5: (x - 2)(x + 2)(x + 1)

Answer 2

@ganeshie8 can u plz help?

Answer 3

It looks like it is probably A

Answer 4

Step by step solution :
Step 1 :

Simplify x3+x2-4x - 4

Checking for a perfect cube :

1.1 x3+x2-4x-4 is not a perfect cube
Trying to factor by pulling out :

1.2 Factoring: x3+x2-4x-4

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: x3+x2
Group 2: -4x-4

Pull out from each group separately :

Group 1: (x+1) • (x2)
Group 2: (x+1) • (-4)
-------------------
Add up the two groups :
(x+1) • (x^2-4)
Which is the desired factorization
Trying to factor as a Difference of Squares :

Factoring: x^2-4

Theory : A difference of two perfect squares, \(\huge\ A^2 - B^2\) can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =
\(\huge\ A^2 - AB + BA - B62\) =
\(\huge\ A^2 - AB + AB - B^2\) =
\(\huge\ A^2\) - \(\huge\ B^2\)

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 4 is the square of 2
Check : \(x^2\) is the square of \(x1\)

Factorization is : (x + 2) • (x - 2)
Final result :

\((x + 2) • (x - 2) • (x + 1)\)

Answer 5

Oh k Thank You! Lol

Answer 6

np :) took time but i hoped i pleased you

Answer 7

Lol Thank You Again!