Factor the following polynomials. a) x^2-6x+9 b) x^2-25 c) 3x^2-21x+30

Tammy Todd

Tammy Todd

Answered question

2021-09-13

Factor the following polynomials.
a) x26x+9
b) x225
c) 3x221x+30

Answer & Explanation

Maciej Morrow

Maciej Morrow

Skilled2021-09-14Added 98 answers

The polynomials:
a) x26x+9
b) x225
c) 3x221x+30
Part a)
Consider the given polynomial:
x26x+9
Now, splitting the middle term, we get,
x26x+9
=x23x3x+9
=x(x3)3(x3)
=(x3)(x3)
Hence, the given polynomial is factorised as:
x26x+9=(x3)(x3)
Part b):
Consider the given polynomial:
x225=x252
Using the identity a2b2=(a+b)(ab), we get,
=(x+5)(x5)
Hence, the given polynomial is factorised as:
x225=(x+5)(x5)
Part c)
Consider the given polynomial:
3x221x+30
Now, splitting the middle term, we get,
3x221x+30
=3x215x6x+30
=3x(x5)6(x5)
=(x5)(3x6)
=3(x5)(x2)
Hence, the given polynomial is factorised as:
3x221x+30=3(x5)(x2)

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