OCR A Level Maths - Pure

Factor Theorem - ANS-A polynomial f(x) has a factor (x - a) if and only if f(a) = 0 It has a factor (bx-a) if f(a/b) = 0 Sketching polynomials - ANS-Shape: Reflect in x-axis if there is a negative x Roots: - Crosses x-axis at any root e.g. (x+5) would mean crosses at negative 5 -However, if negative x is in the bracket e.g. (5-x) would mean crosses at positive 5 -Also a repeated root means the curve just touches at that point Sketching graphical inequality - ANS-Shade where the inequality is not satisfied and use the origin to determine this Transformation of curves - ANS-y = f(x)+a: Translation by 'a' units parallel to the y-axis y = f(x-a): Translation by 'a' units parallel to the x-axis y = af(x): Stretch parallel to the y-axis by a scale factor of 'a,' (1,3) goes to (1,3a) y = f(ax): Stretch parallel to the x-axis by a scale factor of '1/a,' (1,3) goes to (1/a,3) y=-f(x): Reflect f(x) in x-axis y=f(-x): Reflect f(x) in y-axis