When factoring a quadratic trinomial, student a misinterprets the coefficient of the first term and decomposes it into 2 (x-1) (X-9), while student B misinterprets the constant term and decomposes it into 2 (X-2) (x-4). Please judge the correct quadratic trinomial and decompose it correctly

When factoring a quadratic trinomial, student a misinterprets the coefficient of the first term and decomposes it into 2 (x-1) (X-9), while student B misinterprets the constant term and decomposes it into 2 (X-2) (x-4). Please judge the correct quadratic trinomial and decompose it correctly

2 (x-1) (X-9) = 2x2-20x + 18, 2 (X-2) (x-4) = 2x2-12x + 16; because student a misread the coefficient of the first term and student B misread the constant term, the correct quadratic trinomial is: 2x2-12x + 18; then factor it into 2x2-12x + 18 = 2 (x-3) 2

When two students factorize a quadratic trinomial, one student misinterprets the coefficient of the first term and decomposes it into 2 (x-1) (X-9)
Another student, because he misread the constant term and decomposed it into 2 (X-2) (x-4), asked for a polynomial and factorized it

Let the original polynomial be 2x & # 178; + BX + C
2（x-1）（x-9）
=2(x²-9x-x+9)
=2(x²-10x+9)
=2x²-20x+18
∴c=18
2（x-2）（x-4）
=2(x²-6x+8)
=2x²-12x+16
The constant term is wrong
∴b=-12
The original polynomial is 2x & # 178; - 12x + 18
2x²-12x+18
=2(x²-6x+9)
=2(x-3)²

When factoring a quadratic trinomial, student a misinterprets the coefficient of the first term and decomposes it into 2 (x-1) (X-9), while student B misinterprets the constant term and decomposes it into 2 (X-2) (x-4). Please judge the correct quadratic trinomial and decompose it correctly

2 (x-1) (X-9) = 2x2-20x + 18, 2 (X-2) (x-4) = 2x2-12x + 16; because student a misread the coefficient of the first term and student B misread the constant term, the correct quadratic trinomial is: 2x2-12x + 18; then factor it into 2x2-12x + 18 = 2 (x-3) 2