# Algebra questions need help

**Question description**

1.
Find all zeros of
the polynomial *P(x) = 3x ^{ 4} + 26 x^{ 3} +
74 x^{ 2} + 74 x + 15* knowing that P(x) has two
rational zeros.

2.
Polynomial *P(x)
= x ^{ 3} + x^{ 2} + c x + d* has x
- 2 as a factor and when divided by x - 1, the remainder is equal to 3. Find
the constant c and d.

3.
P(x) is an even
fourth degree polynomial function such that P(-2) = 0, P(x + 3) has a zero at x
= 4 and P(0) = -9. Find P(x).

4.
The
polynomial *P(x) = 2 x ^{ 4} + 3 x^{ 3} -
16 x^{ 2} - 17 x + 12* has zeros at x = 1/2 and x =
-3. Find the other zeros.

5.
Factor the
following polynomials:

a) *f(x) = x ^{ 3} - x^{ 2} - 4 x + 4*

b)

*f(x) = 2 x*

^{ 2}- x^{ 3}c)

*f(x) = x*

^{ 2}- 2 x^{ 4}d)

*f(x) = -(x*

^{ 2}- 2 x - 3)^{ 2}e)

*f(x) = x*

^{ 4}+ 3 x^{ 3}+ 3 x^{ 2}+ x10. A polynomial of degree 4 has a negative leading coefficient and simple zeros (i.e. zeros of multiplicity 1) at x = 2, x = -2, x = 1 and x = - 1. Is the y intercept below the x axis or above the x axis?

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