IGCSE Math B 3.E Algebraic division Topic Practice

Given that (x-3) is a factor of $5 x^{3}+2 x^{2}+k x+36$ where k is a constant,

Given that, for all values of x,
$$5x^3+2x^2-63x+36=(x-3)(ax^2+bx+c),$$
where a, b and c are constants,
find the value of a, the value of b and the value of c.

21(x+2) is a factor of $6 x^{3}+31 x^{2}+k x+30$

Factorise fully $6 x^{3}+31 x^{2}+53 x+30$

Answer parts (a) and (b).

Hence, factorise completely $2x^3+9x^2-11x-30$.
Show clear algebraic working.

$$f(x)=2x^3+9x^2-14x-9.$$

Express $\frac{f(x)}{2x+1}$ in the form $(x+a)^2+b$, where a and b are integers to be found.

28(x+2) is a factor of $6 x^{3}-x^{2}+k x-10$, where k is a constant.

Hence, factorise completely $6 x^{3}-x^{2}-31 x-10$

27(x+1) is a factor of $x^{3}+k x^{2}+x+6$ where k is a constant.

Using this value of k, factorise completely $x^{3}+k x^{2}+x+6$