Question

factor the following expression completely 75x^4+35x^3-10x^2

Answer 1

75x^4 + 35x^3 - 10x^2

See your first post below for an example of how this is done.

Hint, factor out 5x^2 first, then factor the remaining expression.

You will never learn without practice :)

Answer 2

75x^4+35x^3-10x^2=(5x^2)*(15x^2+7x-2)

Factoring:

15x^2+7x-2

Using the factor pair (-3, 10) whose sum is 7, rewrite your equation replacing the term 7 x with
-3 x and 10 x.

15x^2+7x-2=15x^2-3x+10x-2

Now group the first two terms and the last two terms on the left hand side:

(15x^2-3x)+(10x-2)

Within each group, factor out common factors.

(15x^2-3x)+(10x-2)=3x*(5x-1)+2*(5x-1)

Notice that the two quantities in parentheses are the same. This means that the quantity, (5x-1), is a common factor and we can factor it out.

3x*(5x-1)+2*(5x-1)=(5x-1)*(3x+2)

15x^2+7x-2=(5x-1)*(3x+2)

75x^4+35x^3-10x^2=(5x^2)*(15x^2+7x-2)=

(5x^2)*(5x-1)*(3x+2)

Answer 3

Hvala