Apr 25 2013

Exercise 01. Factoring polynomials.

High school (age 13 to 14)

Exercise.- Factor the following polynomial expressions completely:

a) $25x^2+70x+49$

b) $81x^2-54x+9$

c) $81x^2-9$

d) $9x-49x^2$

e) $(3x+5)^2-(2x+9)^2$

Solutions:

a) $(5x+7)^2$ b) $(9x-3)^2$ c) $(9x+3)(9x-3)$ d) $x(9-49x)$ e) $(5x+14)(x-4)$

Apr 23 2013

Solved exercise for quadratic equations

Exercise. Solve the following quadratic equations:

a) $x^2+3x+2=0$ b) $2x^2+5x+2=0$ c) $x^2+5x+14=10$

d) $3x^2-x-2=0$ e) $2x^2+6x+15=11$ f) $2x^2+4x+10=0$

g) $-2x^2+3x+5=0$ h) $x^2+8x+7=0$ i) $x^2-6x-7=0$

j) $2x^2-7x-4=0$

Solutions:
a) $-1 y -2$ b) $\dfrac{-1}{2} y -2$ c) $-1 y -4$ d) $1 y \dfrac{-2}{3}$ e) $-1 y -2$ f) has no solution in R g) $-1 y 5/2$ h) $-1 y -7$ i) $7 y -1$ j) $4 y \dfrac{-1}{2}$

Apr 21 2013

Pythagorean Theorem

Pythagorean Theorem: In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

Pythagoras PlanetPi visit. Pythagoras taught Naturalis to operate with triangles rectangle. We propose the following exercise you can try to solve after studying the example.

Example: If $a = 5, b = 12$ then $c^2=a^2+b^2 \Rightarrow c^2=5^2+12^2 \Rightarrow$ $c^2=25+144 \Rightarrow c= \sqrt{169}$ , so $c=13$