Answer:
1. 16x2−40x+25
Perfect Square Trinomial
2. x2−2x−8
Trinomial when A>1
3. 3x2+6xy+9xy2
Greatest Common Factor (GCF)
4. 64x2−100
Difference of Squares
5. 27x3+8y6
Sum of Cubes
6. 64x9−y3
Difference of Cubes
7. 6x2+19x+15
Trinomial when A=1
8. 6x3+3x2+8x+4
Grouping
Step-by-step explanation:
A trinomial is a polynomial which has three terms.
1. 16x2−40x+25
(4x)2 - 2(4x)(5) + (5)2
= (4x-5)2
Perfect Square Trinomial
2. x2−2x−8
= x2 - 4x+2x-8
= x(x-4) +2 (x-4)
= (x+2)(x-4)
Trinomial when A>1 ( when we will put x= 1 we will get a negative value)
3. 3x2+6xy+9xy2
=3x(x+2y+3y2)
(3x is common)
Greatest Common Factor (GCF)
4. 64x2−100
= (8x)2- (10)2
= (8x-10)(8x+10)
Difference of Squares
5. 27x3+8y6
=(3x)3+(2y2)3
= (3x+2y)(6x2-6xy+4y2)
Sum of Cubes
6. 64x9−y3
= (4x3)3- (y)3
Difference of Cubes
7. 6x2+19x+15
= 6x2 + 9x + 10x + 15
= 3x( 2x+3) + 5(2x+3)
= (2x+3)(3x+5)
Trinomial when A=1
8. 6x3+3x2+8x+4
Grouping
Grouping usually has four or more terms
6x3+3x2+8x+4
=3x2(2x+1) + 4(2x+1)
=(3x2+4) (2x+1)
