Question

Can someone please help me with this

Answer 1

1.

1)

Put the given values of p and q in the factored form equation.

... f(x) = (x -(-1))(x -(-2)) . . . . p and q values put in

... f(x) = (x +1)(x +2) . . . . . . .simplified

2)

Multiplying the factors, we have

... f(x) = x(x +2) + 1(x +2) = x² +2x +1x +2

... f(x) = x² +3x +2

2.

We want to factor x³ -x² -6x. We notice first of all that x is a factor of all terms. Thus we have

... = x(x² -x -6)

Now, we're looking for factors of -6 that add up to -1. Those are -3 and 2. Thus the factorization is ...

... = x(x -3)(x +2)

3.

We want a description of the structure and an equivalent expression for

... 64x⁹ -216

We note that 64, 216, and x⁹ are all cubes, so this expression is ...

... the difference of cubes.

It can be rewritten to

... = 8((2x³)³ -3³)

and so can be factored as

... = 8(2x³ -3)(4x⁶ +6x³ +9)