algebraic, question 3, grade 9

21/06/2016 Grade 9 2,522

3)

Given A(x) =  {(3x+2)^2}-{(x-2)^2}  and B(x) = 2{x^2}-8-(x+2)(-2x+6)

  1. Write A(x) as a product of 3 factors then deduce its roots.
  2. Factorize B(x)
  3. Expand B(x) and solve B(x)+20 = 0.
  4. let F(x) =   \frac{{A(x)-2B(x)}}{{A(x)}}

i) Find the domain of definition of F(x).

ii) Verify that F(x) =  \frac{5}{{4x}}

iii) Solve F(x) =  \frac{{- 5}}{8}

iv) Evaluate  F(\sqrt3)

5) Consider E(x) =  (a-b){x^3}+2a{x^2}-{b^2}x+x

Find a&b if E(x) is identical to 0.