Can you please help me factor these trinomials and binomials,

Question

I am just confused with factoring Trinomials with a coefficient that is not 1 in general : 

14t^2 -9t +1 

3x^2 + 2x -5 

Also, I am having trouble with trinomials that do not start with a variable such as : 

1 - 8ab -20a^2b^2 

& 

9 - 10x^2 +x^4

Answer 1

1)

Given expression is 14t² - 9t + 1

= 14t² - 7t - 2t + 1

= 7t ( 2t - 1 ) - 1 ( 2t - 1 )

= ( 2t - 1 ) ( 7t - 1 )

Solution : 14t² - 9t + 1 = ( 2t - 1 ) ( 7t - 1 ).

Answer 2

2)

Given expression is 3x² + 2x - 5

= 3x² + 5x - 3x - 5

= x ( 3x + 5 ) - 1 (3x + 5 )

= ( 3x + 5 ) ( x - 1 )

Solution : 3x² + 2x - 5 = ( 3x + 5 ) ( x - 1 ).

Answer 3

3)

Given expression is  1 - 8ab - 20a²b²

= 1 - 8ab - 20 (ab)²

= 1 - 10ab + 2ab - 20 (ab)²

= 1 ( 1 - 10ab ) + 2ab ( 1 - 10ab )

= ( 1 - 10ab ) ( 1 + 2ab )

Solution : 1 - 8ab - 20a²b²  = ( 1 - 10ab ) ( 1 + 2ab ).

Answer 4

4)

Given expression is   9 - 10x² + x⁴

= 9 - 10x² + (x²)²

= 9 - 9x² - x²  + (x²)²

= 9 ( 1 - x² ) - x² ( 1 - x²)

= ( 1 - x² ) ( 9 - x² )

= ( 1² - x² ) ( 3² - x² )

Apply formula : a² - b² = ( a + b )( a – b )

= ( 1 + x ) ( 1 - x ) ( 3 + x ) ( 3 - x )

Solution : 9 - 10x² + x⁴  = ( 1 + x ) ( 1 - x ) ( 3 + x ) ( 3 - x ).