Y.2 Factorise out a monomial

Factorise out a monomial

Key Notes:

To factorise a polynomial, first find the highest common factor (HCF) of each monomial. Then factor out the highest common factor using the distributive property.

Learn with an example

👉 Factorise out the highest common factor. If the highest common factor is 1, just retype the polynomial.

4u³+10u²=——

First, factorise each monomial and find the common factors.

4u³=2 . 2 . u . u . u

10u²=2 . 5 . u . u

The common factors are 2, u and u. Multiply them to find the highest common factor.

2 . u . u=2u²

The highest common factor is 2u².

Now factorise out 2u².

4u3+10u2

=2u² . 2u+2u² . 5

=2u2(2u+5)

The factorised form of the polynomial is 2u²(2u+5).

👉 Factorise out the highest common factor. If the highest common factor is 1, just retype the polynomial.

4g²+6g=———

First, factorise each monomial and find the common factors.

4g²=2 . 2 . g . g

6g=2 . 3 . g

The common factors are 2 and g. Multiply them to find the highest common factor.

2 . g=2g

The highest common factor is 2g.

Now factorise out 2g.

4g²+6g

=2g . 2g+2g . 3

=2g(2g+3)

The factorised form of the polynomial is 2g(2g+3).

👉 Factorise out the highest common factor. If the highest common factor is 1, just retype the polynomial.

6w²–4w=——

First, factorise each monomial and find the common factors.

6w²=2 . 3 . w . w

–4w=–1 . 2 . 2 . w

The common factors are 2 and w. Multiply them to find the highest common factor.

2 . w=2w

The highest common factor is 2w.

Now factorise out 2w.

6w2–4w

=2w . 3w+2w . –2

=2w(3w–2)

The factorised form of the polynomial is 2w(3w–2).

let’s practice!