Factor out the greatest common factor for each polynomial Ex

Factor out the greatest common factor for each polynomial. Examples 1 and 2. Factor the polynomial by grouping.

28 r⁴ s² +7r³ s -35r⁴ s³

we write factors of 28,7 and 35

28 = 7*2*2*1 , 7 = 7*1 , 35 = 7*5*1

we can see that \"7\" is common in all of them so we pull out \"7\"

r⁴ ,r³ ,r⁴

we can write r⁴ as r³ * r¹ (here \"r\" is the base and \"4\" is the exponent ) (we add exponents if base are same)

so r³ is common in all 3 so we pull out r³

similarly \"s\" is common so we pull out \"s\"

28 r⁴ s² +7r³ s -35r⁴ s³ we get

7r³s (4rs + 1 - 5rs²) answer (7r³s is the greatest common factor)

(4z-5)(3z-2) - (3z-9)(3z-2)

we can see that (3z-2) is common so we pull out this as greatest common factor

we get

(3z-2)((4z-5) - (3z-9))

(3z-2)(4z-5 - 3z + 9) if there is a (\"-\" sign before a bracket the sign of the variables gets reversed )

(3z-2)(z+4) answer

14)

15 -5m² -3r² +m²r²

we group two terms as one group

(15 - 5m² ) + (-3r² + m²r²)

now we pull out \"5\" from 1st group and \"-r²\" from second group

5(3 - m²) - r²(3 - m²) (negative number * postive number = negative number ) eg: 2*(-3) = -6

now (3-m²) is common so we pull out as greatest common factor

(3-m²)(5-r²) answer