Q:

Factor the following: 4x^2 + 18x - 10 so far I factored out 2: 2(x^2 + 9x - 5) what's the next step?

Accepted Solution

A:
Your input: factor 4x2+18xβˆ’10.Factor the common term:(4x2+18xβˆ’10)=(2(2x2+9xβˆ’5))To factor the quadratic function 2x2+9xβˆ’5, we should solve the corresponding quadratic equation 2x2+9xβˆ’5=0.Indeed, if x1 and x2 are the roots of the quadratic equation ax2+bx+c=0, then ax2+bx+c=a(xβˆ’x1)(xβˆ’x2).Solve the quadratic equation 2x2+9xβˆ’5=0.The roots are x1=12, x2=βˆ’5 Therefore, 2x2+9xβˆ’5=2(xβˆ’12)(x+5).2(2x2+9xβˆ’5)=2(2(xβˆ’12)(x+5))Simplify: 4(xβˆ’12)(x+5)=2(x+5)(2xβˆ’1).Thus, 4x2+18xβˆ’10=2(x+5)(2xβˆ’1).Answer: 4x2+18xβˆ’10=2(x+5)(2xβˆ’1).