factoring practice questions **check the domain\n$x^{2}-2x - 8 = 0$\n$x^{2}+7x - 18 = 0$\n$x^{2}-3x =…

factoring practice questions **check the domain\n$x^{2}-2x - 8 = 0$\n$x^{2}+7x - 18 = 0$\n$x^{2}-3x = 10$\n$x^{2}+8x = 65$\n$x^{2}+16x = - 15$\n$-x + x^{2}=56$\n$x^{2}-9 = 0$\n$x^{2}+28 = 11x$\n$-x + x^{2}=12$\n$x^{2}-121 = 0$

factoring practice questions **check the domain\n$x^{2}-2x - 8 = 0$\n$x^{2}+7x - 18 = 0$\n$x^{2}-3x = 10$\n$x^{2}+8x = 65$\n$x^{2}+16x = - 15$\n$-x + x^{2}=56$\n$x^{2}-9 = 0$\n$x^{2}+28 = 11x$\n$-x + x^{2}=12$\n$x^{2}-121 = 0$

Answer

Explanation:

Step1: Rearrange the equation

For the equation (-x + x^{2}=56), rewrite it in standard quadratic form (ax^{2}+bx + c = 0). So, (x^{2}-x - 56=0).

Step2: Factor the quadratic

We need to find two numbers (m) and (n) such that (m\times n=-56) and (m + n=-1). The numbers are (m = 7) and (n=-8) since (7\times(-8)=-56) and (7+(-8)=-1). Then (x^{2}-x - 56=(x + 7)(x-8)=0).

Step3: Solve for (x)

Set each factor equal to zero:

  • If (x + 7=0), then (x=-7).
  • If (x - 8=0), then (x = 8).

Answer:

(x=-7) or (x = 8)