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

Question

PRoperties of exponents, operations with polynomials.

Answer 1

    (x - 4)(2x² - x + 3)

First, multiply the first term in the first set of parentheses by everything in the second set of parentheses, and multiply the second term in the first set of parentheses by everything in the second set of parentheses. Then subtract :

    (x(2x² - x + 3)) - (4(2x² - x + 3))

    (x·2x² - x·x + x·3) - (4·2x² - 4·x + 4·3) 

When multiplying when multiplying two terms with the same base, you add the exponents.  

     For example,     xⁿ · x^m = x^n+m 

  (2x³ - x² + 3x) - (8x² - 4x + 12) ==>  (2x³ - x² + 3x) + (-8x² + 4x - 12)

Next, add like terms.

   2x³ - x² + 3x - 8x² + 4x - 12    =    2x³ - 9x² + 7x - 12

Thus, the answer is 2x³ - 9x² + 7x - 12