Factorize out a monomial
key notes:
To factorize 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
Factorize out the highest common factor.
If the highest common factor is 1, just retype the polynomial.
3p2+9p=—————-
First, factorize each monomial and find the common factors.
3p2=3 . p . p
9p=3 . 3 . p
The common factors are 3 and p. Multiply them to find the highest common factor.
3 . p=3p
The highest common factor is 3p.
Now factorize out 3p.
3p2+9p
=3p . p+3p . 3
=3p(p+3)
The factorized form of the polynomial is 3p(p+3).
Factorize out the highest common factor.
If the highest common factor is 1, just retype the polynomial.
3t3+9t2 =——–
First, factorise each monomial and find the common factors.
3t3=3 . t . t . t
9t2=3 . 3 . t . t
The common factors are 3, t and t. Multiply them to find the highest common factor.
3 . t . t=3t2
The highest common factor is 3t2.
Now factorise out 3t2.
3t3+9t2
=3t2 . t+3t2 . 3
=3t2(t+3)
The factorised form of the polynomial is 3t2(t+3).
Factorize out the highest common factor.
If the highest common factor is 1, just retype the polynomial.
4z3+6z2 =———-
First, factorise each monomial and find the common factors.
4z3=2 . 2 . z . z . z
6z2=2 . 3 . z . z
The common factors are 2, z and z. Multiply them to find the highest common factor.
2 . z . z=2z2
The highest common factor is 2z2.
Now factorise out 2z2.
4z3+6z2
=2z2 . 2z+2z2 . 3
=2z2(2z+3)
The factorised form of the polynomial is 2z2(2z+3).
let’s practice!
