Factorise xcube minus 2xsquare minus xplus2

Question

ScanSolve AI Tutor · Accepted Answer

To factorize the expression x³ − 2x² − x + 2, we can use the method of grouping. Step 1: Group the terms into two pairs. (x³ − 2x²) − (x − 2) Step 2: Factor out the common factor from each pair. From the first pair, x² is common. From the second pair, −1 is common. x²(x − 2) − 1(x − 2) Step 3: Notice that (x − 2) is a common factor in both terms. Factor out (x − 2). (x − 2)(x² − 1) Step 4: The term (x² − 1) is a difference of squares, which can be factored as (a² − b²) = (a − b)(a + b). Here, a = x and b = 1. (x − 2)(x − 1)(x + 1) The fully factorized expression is: (x − 2)(x − 1)(x + 1)

Factorise xcube minus 2xsquare minus xplus2

Answer

Step-by-step solution

Group the terms into two pairs.

Factor out the common factor from each pair.

Notice that $(x - 2)$ is a common factor in both terms.

The term $(x^2 - 1)$ is a difference of squares, which can be factored as $(a^2 - b^2) = (a - b)(a + b)$ .

Try one yourself

Still stuck on this one?

More Mathematics Questions

Factorise xcube minus 2xsquare minus xplus2

Answer

Step-by-step solution

Group the terms into two pairs.

Factor out the common factor from each pair.

Notice that (x−2)(x - 2)(x−2) is a common factor in both terms.

The term (x2−1)(x^2 - 1)(x2−1) is a difference of squares, which can be factored as (a2−b2)=(a−b)(a+b)(a^2 - b^2) = (a - b)(a + b)(a2−b2)=(a−b)(a+b).

Try one yourself

Still stuck on this one?

More Mathematics Questions

Notice that $(x - 2)$ is a common factor in both terms.

The term $(x^2 - 1)$ is a difference of squares, which can be factored as $(a^2 - b^2) = (a - b)(a + b)$ .