# Tutor profile: Kirsten S.

## Questions

### Subject: Pre-Calculus

Find the zeros of the following polynomial. $$x^3-x^2-6x=0$$

First, factor out an x from the left side of the equation. $$x(x^2-x-6)=0$$ Factor the quadratic $$x^2-x-6$$. $$x(x-3)(x+2)=0$$ Set each of the factors on the left side of the equation equal to 0 and solve for x. $$x=0 \Rightarrow x=0$$ $$x-3=0 \Rightarrow x=3$$ $$x+2=0 \Rightarrow x=-2$$ So we know that this graph either crosses or touches the x-axis at these three points.

### Subject: Calculus

$$\lim_{x \to 1}\frac{3x-7}{x+1}$$

Since plugging 1 in for the variable x does not give us a zero in the denominator, we can solve this limit directly. $$\lim_{x \to 1}\frac{3x-7}{x+1}$$= $$\frac{3(1)-7}{(1)+1}=\frac{-4}{2}=-2$$

### Subject: Algebra

Solve the equation $$3^{2-5x}=11$$

Below is a step-by-step solution to the question. $$3^{2-5x}=11$$ Apply log base 3 to both sides of the equation. $$log_33^{2-5x}=log_311$$ The $$log_3$$ and the base 3 of the exponential cancel leaving $$2-5x$$ on the left side of the equation. $$2-5x=log_311$$ Use the change of base formula to rewrite $$log_3(11)$$ in log base 10 form. $$2-5x=\frac{log(11)}{log(3)}$$ Solve for x. First, subtract 2 from both sides. $$-5x=\frac{log(11)}{log(3)}-2$$ Next, divide 5 on both sides. $$x=\frac{-log(11)}{5log(3)}+\frac{2}{5}$$

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