How do you factor #-2x^2 + 1x + 1#?

Question

Eva Abramson · Accepted Answer

Set the expression = 0 and use the ABC formula
Find factors by using #(x - x_1)(x-x_2)#
#-2x^2 + x + 1 = (x+1/2)(x-1)#

Start by setting the expression equal to zero, then use the ABC-formula. The ABC-formula is: #(-b+-sqrt(b^2 - 4ac))/(2a)# Insert the values for a, b and c (which are the coefficients(red) in your expression: #color(red)(-2)x^2 + color(red)(1)x + color(red)(1)# #x =(-1 +- sqrt(1^2 - 4 * (-2) * 1)) / (2*(-2)) to (-1 +- sqrt(1+8)) / (-4) to (-1+-3)/-4# #x_1 = (-1 + 3)/-4= 2/-4 = -1/2# #x_2 = (-1 - 3)/-4= (-4) /(-4) = 1# Put these values into #(x-x_1)(x-x_2)# #(x-(-1/2))(x-1)# #(x+1/2)(x-1)#

Jace Anderson · Answer

undefined To factor the expression $ -2x^2 + x + 1 $, we look for two numbers that multiply to $ -2 \times 1 = -2 $ and add to $ 1 $. Those numbers are $ -1 $ and $ 2 $. Then, we rewrite the middle term using these numbers: $ -2x^2 - x + 2x + 1 $. Now, we group the terms: $ (-2x^2 - x) + (2x + 1) $. Next, we factor out the greatest common factor from each group: $ -x(2x + 1) + 1(2x + 1) $. Finally, we factor out the common binomial factor $ (2x + 1) $: $ (2x + 1)(1 - x) $. So, the factored form of $ -2x^2 + x + 1 $ is $ (2x + 1)(1 - x) $.