Factor 3x^2 + x - 10 into the product of two binomials by grouping

(3x-5) (x+2)

(x + 2) (3x - 5)

Step-by-step explanation:

Given

3x² + x - 10

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x - term.

product = 3 * - 10 = - 30 and sum = + 1

The factors are + 6 and - 5

Use these factors to split the x - term

3x² + 6x - 5x - 10 ← factor by grouping first/second and third/fourth terms

= 3x (x + 2) - 5 (x + 2) ← factor out (x + 2) from each term

= (x + 2) (3x - 5)