what are the factors of the polynomial 2x^2+x-10

Question

whpalmer4 · Answer

To factor the polynomial $2x^2+x-10$, take a look at the leading coefficient, which is 2.  Our first components of our factors must have a product of 2, so we'll have something like
$$(2x + ____)(x + ____)$$
Next, look at the final term, -10.  This will be produced by the product of the two blanks.  Our choices here are the factors of -10: -1,10; -2, 5; -5,2; -10,1, 1,-10;2,-5; 5,-2; 10,-1.
Which choice?  The third constraint is that the 2nd member of the pair * 2, plus the first member of the pair must equal 1 because that is the value of the coefficient of the middle term.  2(-2)+5 = -4+5 = 1, so that's the set to choose, giving us
$$2x^2+x-10 = (2x+5)(x-2)$$If we multiply out our factorization to check (always a good idea):
$$(2x+5)(x-2) = 2x^2-4x+5x-10 = 2x^2+x-10\checkmark$$