Question

Factorise x^2 - 31x + 220.

Answer 1

Simplifying

x2 + -31x + 220 = 0

Reorder the terms:

220 + -31x + x2 = 0

Solving

220 + -31x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.

(11 + -1x)(20 + -1x) = 0

Subproblem 1

Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying

11 + -1x = 0

Solving

11 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-11' to each side of the equation.

11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0

0 + -1x = 0 + -11

-1x = 0 + -11

Combine like terms: 0 + -11 = -11

-1x = -11

Divide each side by '-1'.

x = 11

Simplifying

x = 11

Subproblem 2

Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying

20 + -1x = 0

Solving

20 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-20' to each side of the equation.

20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0

0 + -1x = 0 + -20

-1x = 0 + -20

Combine like terms: 0 + -20 = -20

-1x = -20

Divide each side by '-1'.

x = 20

Simplifying

x = 20

Solution

x = {11, 20}

Answer 2

${x}^{2} - 31x + 220 \\ write \: 31x \: as \: a \: difference \:\\ {x}^{2} - 11x - 20x + 220 \\ factor \: out \: x \: from \: the \: expression \\ x(x - 11) - 20x + 220 \\ factor \: out \: - 20 \: from \: the \: expression \\ x(x - 11) - 20( x - 11) \\ (x - 11)(x - 20)$
Hope it will help you