Please try to explain that when k is a value, the polynomial x ^ 2-x + K has a factor X + 2 ! don't copy and paste

Please try to explain that when k is a value, the polynomial x ^ 2-x + K has a factor X + 2 ! don't copy and paste

Let another factor be (x + a), then the original formula = (x + 2) (x + a) is simplified: x ^ 2 + (2 + a) x + 2a, because 2 + a = - 1, so a = - 3
How tiring it is to type

(1) 5x ^ 2-5x-60 = how many (2) 2x ^ 3-8x ^ 2-24x = how many (3) 2A ^ 2B ^ 2 + 14ab-60 = how many (4) x ^ 3-8x ^ 2y-20xy ^ 2?

(1)5x^2-5x-60
=5(x²-x-12)
=5(x+3)(x-4)
（2)2X^3-8X^2-24x
=2x(x²-4x-12)
=2(x-6)(x+2)
（3）2a^2b^2+14ab-60
=2(a²b²+7ab-30)
=2(ab+10)(ab-3)
（4）x^3-8x^2y-20xy^2
=x(x²-8xy-20y²)
=x(x+2y)(x-10y)

Given that the polynomial (a + 3) x ^ 3-2x ^ 2Y + y ^ 2 - (5x ^ 3 + y ^ 2 + 1) does not contain x ^ 3 term, calculate 1 / 2 (a ^ 3-2a ^ 2 + 4a-1)

(a+3)x^3-2x^2y+y^2-(5x^3+y^2+1)
=（a+3-5)x^3-2x^2y-1
If x ^ 3 is not included, then a + 3-5 = 0
a=2
1/2(a^3-2a^2+4a-1)
=1/2(8-8+8-1)
=7/2