Question

Find the remainder when 2
x
2 – 5
x
+7 is divided by x – 1, without actual division.

Answer 1

Answer:

4

Step-by-step explanation:

${2x}^{2} - 5x + 7 = 0 \\ divided \: by \\ x - 1 \\ it \: can \: be \: do \: with \: remainder \: therom \\ put \: x = 1 \: in \: above \: equation \\ 2 {(1)}^{2} - 5(1) + 7 \\ = - 3 + 7 \\ = 4 \\ remainder \: is \: 4 \: when \: it \: devided \: by \: \\ x - 1$

I think that is correct answer

Answer 2

Answer:

4

Step-by-step explanation:

given polynomial is 2x² -5x +7

lets try to get the polynomial into ( x-1) form.

2x²-5x+7 = 2x²-2x -3x +7

= 2x(x-1) -3x +3+4

= 2x(x-1) -3(x-1) +4

so here first element of polynomial i.e. 2x(x-1) is directly divisible by x-1.

likewise, second element I.e. -3(x-1) is also directly divisible by x-1.

so, the remainder is 4