Factor this polynomial expression 10x^2-7x-12

(2x - 3)(5x + 4)

Step-by-step explanation:

Given

10x² - 7x - 12

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 = 10 × - 12 = - 120 and sum = - 7

The factors are - 15 and + 8

Use these factors to split the x- term

10x² - 15x + 8x - 12 ( factor the first/second and third/fourth terms )

= 5x(2x - 3) + 4(2x - 3) ← factor out (2x - 3) from each term

= (2x - 3)(5x + 4) ← in factored form

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363