The factored form of each equations are [tex](4x - 1)^{2}[/tex] , [tex](x + 5)(x - 6)[/tex] , [tex](3x + 7)(3x - 7)[/tex] and [tex](3x - 1)(x + 6)[/tex]
Equation in factored form -
A polynomial equation in a complex form can be expressed in the factored form by multiplication of two terms of polynomial in a binomial system. For example, [tex]x^{2} - y^{2}[/tex] can be expressed in factor form as [tex](x + y)(x - y)[/tex].
How to solve each equations in the question in factored form ?
Taking one by one problem respectively -
- [tex]16x^{2} - 8x + 1[/tex] = [tex]16x^{2} - 4x - 4x + 1[/tex]
= [tex]4x(4x - 1) -1(4x - 1)[/tex]
= [tex](4x - 1)^{2}[/tex]
- [tex]x^{2} - x - 30[/tex] = [tex]x^{2} - 6x + 5x - 30[/tex]
= [tex]x(x - 6) + 5(x - 6)[/tex]
= [tex](x + 5)(x - 6)[/tex]
- [tex]9x^{2} - 49[/tex] = [tex](3x)^{2} - 7^{2}[/tex]
= [tex](3x + 7)(3x - 7)[/tex]
- [tex]3x^{2} + 17x - 6[/tex] = [tex]3x^{2} + 18x - x - 6[/tex]
= [tex]3x(x + 6) - 1(x + 6)[/tex]
= [tex](3x - 1)(x + 6)[/tex]
To learn more about factored expression, refer -
https://brainly.com/question/12788888
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