SAT Math: Polynomial Divisibility 2

1. $f(x)=4x^3 +12x^2 +8x$

$g(x)=2x^2 +6x+4$

The polynomials $f(x)$ and $g(x)$ are defined above. Which of the following polynomials is divisible by $4x+6$ ?

$h(x)=f(x)+g(x)$

$h(x)=f(x)+3g(x)$

$h(x)=2f(x)+3g(x)$

$h(x)=3f(x)+2g(x)$

2. For the polynomial $f(x)$ , the value of $f(5)$ is $-4$ . Which of the following must be true about $f(x)$ ?

$x-4$ is a factor of $f(x)$

$x+4$ is a factor of $f(x)$

$x+5$ is a factor of $f(x)$

The remainder when $f(x)$ is divided by $x-5$ is $-4$

3. $f(x)=3x^3 -9x^2 +cx -12$

In the polynomial above, $c$ is a constant. If the polynomial is divisible by $x-3$ , what is the value of $c$ ?

$1$

$2$

$3$

$4$

4. $y^5 -2y^4 -cy^2 +6y$

In the polynomial above, $c$ is a constant. If the polynomial is divisible by $y-2$ , what is the value of $c$ ?

$1$

$2$

$3$

$4$

5. $x^4 +3x^3 -13x^2 -cx$

In the polynomial above, $c$ is a constant. If the polynomial is divisible by $x-3$ , what is the value of $c$ ?

$6$

$9$

$15$

$18$

6. $f(x)=25x^3 +150x^2 +131x +c$

In the polynomial above, $c$ is a constant. If the polynomial is divisible by $x+5$ , what is the value of $c$ ?

$19$

$21$

$24$

$30$