1. Fully factor the following polynomials. Explain your thought process with your solution.

a. ?(?) = 2?³ ? 25?² + 53? ? 30 [3 marks]

b. ?(?) = ?³ + 3? ? 4 [3 marks]

2. Sketch the graph of the function ?(?) = ?(? ? 4)(? + 1) 2 (? ? 5). Explain your thinking. [4 marks]

3. Solve the equation 6?⁴ + ? = 5?³ + 2?² . [4 marks]

J ( X - - ( x - 4 ) ( X + 1 ) ( x - 5 ) To sketch the graph of fors , we goto the steps step ! : Identify 2- intercepts, To find x - intercepts we set of ( x) co i.e . , - ( - 4 ) ( X + 1) " ( X - 5) CO -) x = 4 , - 1 , 5 , So x-interceptsone at 2 = 4, - 1, 5. Step 2 :. Identify: 1- intercepts, To find y-intercepts we put x =0 which gives f (O ) = - (- 4 ) ( ) ( - 51 = - 20 80 y- intercept is y = -20 Step 3 : Determine the behavior at x-> observe that the leading term x in fly has negative sign , Do for 2 -10 Steph : Analyze the sign changes and multiplicity of factors : ( a ) x-4 : charges sign from ave as a goes R54 to 2 > 4b x- 5 : changes sign from :- ve to Ave as x goes frum 2