Maths Core WMA01/WMA02: FACTOR THEOREM Topical Past Paper Questions

$$ \mathrm{f}(x)=(x+k)(3x^{2}+4x-16)+32, $$ where k is a constant (a) Write down the remainder when f(x) is divided by (x + k). (1) When $ f(x) $ is divided by $ (x + 1) $, the remainder is 15 (b) Show that k = 2 (3) (c) Hence factorise f(x) completely. (4)

$$ \mathrm{f}(x)=ax^{3}-8x^{2}+bx+6 $$ where a and b are constants. When $ f(x) $ is divided by $ (x + 1) $ there is no remainder. When $ f(x) $ is divided by $ (x - 2) $ the remainder is -12 (a) Find the value of a and the value of b. (5) (b) Factorise f(x) completely. (4)

$$ \mathrm{f}(x)=-4x^{3}+16x^{2}-13x+3 $$ (a) Use the remainder theorem to find the remainder when $ f(x) $ is divided by $ (x-1) $. (2) (b) Use the factor theorem to show that $ (x-3) $ is a factor of $ f(x) $. (2) (c) Hence fully factorise $f(x)$. (4) Figure 1 Figure 1 shows a…