Division of a Polynomial by a Polynomial

1. $ab+bc+ca=-\frac{1}{2}$
2. $abc=\frac{1}{6}$
3. $ab+bc+ca=\frac{1}{2}$
4. $abc=\frac{1}{9}$

1. reflexive only
2. transitive only
3. symmetric only
4. an equivalence relation

1. $-1$
2. $2$
3. $1$
4. $\frac{1}{2}$
5. $-\frac{1}{2}$

SImplify $3y^2(12y^3-6y^2+5y-1)$

1. $36y^7-18y^4+15y^3-3y^2$

2. $36y^6-18y^4+15y^3-3y^2$

3. $36y^5-18y^4+15y^3-3y^2$

4. $36y-18y^4+15y^3-3y^2$

If a + b + c = 12 and $a^2+b^2+c^2=50$; find ab + bc + ca

1. 24

2. 94

3. 48

4. 47

1. $\frac{7x^3}{yz}$
2. $\frac{7x^2}{y^{2}z}$
3. $\frac{7x^2}{yz}$
4. $\frac{7x}{yz}$

1. 2y+3
2. -24y + 3
3. y-2
4. 0

1. $\frac{w(z+x)}{2}$
2. $\frac{w(z-x)}{2}$
3. $\frac{x(z-x)}{2}$
4. $\frac{x(z+x)}{2}$

Find the value of t for which the polynomial,
$p\left(x\right)=x^3+3x^2+2x+t$ gives 3 as remainder when
divided by $x-1$.

1. $(2b+2c)$
2. $(2b-c)$
3. $(b-2c)$
4. $(b+2c)$

Dividing $x(3x^2-27)$ by $3(x-3)$ gives $x^2+3x$.

1. x+3

2. x²+3x

1. $8$
2. $-6$
3. $3$
4. $0$

If a + b + c = 12 and $a^2+b^2+c^2=50$; find ab + bc + ca

1. x(x+1)

2. (x+3)

3. (x+2)

4. (x + 2) (x + 3)

1. $-180$
2. $-170$
3. $-160$
4. $-150$

1. $\frac{3}{5a+b}$
2. $\frac{5}{3a+b}$
3. $\frac{3}{5a-b}$
4. $\frac{3}{a+5b}$

1. $1$
2. $0$
3. $-1$
4. $2$

1. $-17$
2. $17$
3. $-29$
4. $29$
5. Cannot be determined from the information given

For an expression to be divisible by another algebraic expression the divisor should be a factor of the dividend.

1. True

2. False

1. $-(7p-q)(p+5q)$
2. $-(7p+q)(p+5q)$
3. $(7p-q)(p+5q)$
4. $(7p+q)(p-5q)$

Dividing $\left(\right(a+b{)}^2+(a-b{)}^2)$ by $(a^2+b^2)$ gives ___

1. $x$
2. $0$
3. $y+5$
4. $x-3$