Answer:
[tex](x-7)(x-\sqrt{5})(x+\sqrt{5})[/tex]
Step-by-step explanation:
The given expression is
[tex]x^3-7x^2-5x+35[/tex]
Factor the first two and the last two.
[tex]x^2(x-7)-5(x-7)[/tex]
[tex](x-7)(x^2-5)[/tex]
Apply difference of two squares to the leftmost factor.
[tex](x-7)(x-\sqrt{5})(x+\sqrt{5})[/tex]
Answer:
[tex]x^3 - 7x^2 - 5x + 35=(x-7)(x-\sqrt{5})(x+\sqrt{5})[/tex]
Step-by-step explanation:
We are given a expression:
[tex]x^3 - 7x^2 - 5x + 35[/tex]
[tex]x^3 - 7x^2 - 5x + 35\\\\=x^2(x-7)-5(x-7)\\\\=(x^2-5)(x-7)[/tex]
We know that [tex]a^2-b^2=(a-b)(a+b)[/tex]
So, [tex]x^2-5=x^2-(\sqrt{5})^2 \\\\=(x-\sqrt{5})(x+\sqrt{5})[/tex]
So, [tex]x^3 - 7x^2 - 5x + 35=(x-7)(x-\sqrt{5})(x+\sqrt{5})[/tex]
