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1. suppose p(x)=x^3-2x^2+13x+k. The remainder of the division of p(x) by (x+1) is -8. What is the remainder of the division of p(x) by (x-1)?

2.What value of h is needed to complete the square for the equation x^2+10x-8=(x-h)^2-33?

3.A system of equations is shown below

y=|x-3|

y=1/2x

What is the distance between the points of intersection of the system?

May 13, 2020

#1
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1.

suppose $$p(x)=x^3-2x^2+13x+k$$.

The remainder of the division of $$p(x)$$ by $$(x+1)$$ is $$-8$$.

What is the remainder of the division of $$p(x)$$ by $$(x-1)$$?

$$\begin{array}{|lrcll|} \hline & p(x) &=& q_1(x)(x+1)-8 \quad | \quad p(x)=x^3-2x^2+13x+k \\ x=-1: & x^3-2x^2+13x+k &=& q_1(x)(x+1)-8 \\ & -1-2-13+k &=& q_1(x)\cdot 0-8 \\ & -16+k &=& -8 \\ & k &=& 16 -8 \\ & \mathbf{k} &=& \mathbf{8} \\ \hline & p(x) &=& q_2(x)(x-1)+r \quad | \quad p(x)=x^3-2x^2+13x+k \\ x=1: & x^3-2x^2+13x+k &=& q_2(x)(x-1)+r \\ & 1-2+13+k &=& q_2(x)\cdot 0+r \\ & 12+k &=& r \quad | \quad k=8 \\ & 12+8 &=& r \\ & \mathbf{r} &=& \mathbf{20} \\ \hline \end{array}$$

May 13, 2020