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