Question

Factor the​ four-term polynomial by grouping.
12x³-8x²+15x-10

Answer 1

`12x^3-8x^2+15x-10=4x^2(3x-2)+5(3x-2)=(4x^2-5)(3x-2)`

Answer 2

To factor the four-term polynomial 12x³-8x²+15x-10 by grouping, we can follow these steps:

1. Group the terms in pairs:

12x³-8x² + 15x-10

2. Factor out the greatest common factor (GCF) from each pair separately:

4x²(3x - 2) + 5(3x - 2)

3. Notice that we now have a common binomial factor of (3x - 2). We can factor it out:

(3x - 2)(4x² + 5)

So, the factored form of the polynomial 12x³-8x²+15x-10 is (3x - 2)(4x² + 5).

Factoring by grouping involves identifying common factors within pairs of terms and factoring them out. By doing so, we simplify the expression and make it easier to work with or solve.