The document provides 4 examples of factorizing polynomials by finding their roots. For each polynomial Q(x), S(x), P(x), and E(x), the document lists the roots, factors the polynomial into linear terms, and writes the factored form. The examples demonstrate how to use the quadratic formula to find roots of a polynomial and factor it into linear terms multiplied together.

1. 1) Q(x) x4 -5x2 + 4
x = ± 4; ± 2; ± 1 x = ± 2; ± 1
1 0 -5 0 4
2 2 4 -2 -4
1 2 -1 -2 0
-2 -2 0 2
1 0 -1 0
A = 1 B = 0 C = -1
x = -b ± √ b2 - 4 . A . C / 2a x = - (0) ± √ (0)2 - 4 . 1 . (-1) / 2 . 1
x = √4/2 = ± 2/2 2 / 2 = 1 -2 / 2 = -1
Q(x) = (x-2) . (x+2) . (x-1) . (x+1)
Alumnos:
nAJID Colmenarez
José Arango
Ricardo Gongalez
Fabiola Peña
Carlos Torrealba
Equipo 7
5to "B"
Guía de estudio de
"Raices de un polinomio"

2. 2) S(x) 2x3 -7x2 +8x -3
x = ± 3; ± 1 x = ± 2; ± 1
2 -7 8 -3
-1 2 -5 3
2 -5 3 0
A = 2 B = -5 C = -3
x = -b ± √ b2 - 4 . A . C / 2a x = - (-5) ± √ (-5)2 - 4 . 2 . (-3) / 2 . 2
x = 5 ± √ 25-24 / 4 x = 5 ± √ 1 / 4 5 + 1 / 4 = 6 / 4 = 3 / 2
5 - 1 / 4 = 4 / 4 = 1
S(x) = (x-1) . (x-3 / 2) . (x-1)
3) P(x) 2x4 +x3 -8x2 -x +6
x = ± 6; ± 3; ± 2; ± 1 x = ± 2; ± 1
2 1 -8 -1 6
-2 -4 6 4 -6
2 -3 -2 3 0
-1 -2 5 -3 0
2 -5 3 0
A = 2 B = -5 C = 3
x = -b ± √ b2 - 4 . A . C / 2a x = - (-5) ± √ (-5)2 - 4 . 2 . 3 / 2 . 2
x = 5 ± √ 25-24 / 4 x = 5 ± √ 1 / 4 5 + 1 / 4 = 6 / 4 = 3 / 2
5 - 1 / 4 = 4 / 4 = 1
P(x) = (x+2) . (x+1) . (x-3/2) . (x-1)

3. 4) E(x) x4 +x3 -11x2 -9x +18
x = ± 18; ± 9; ± 3; ± 1
1 1 -11 -9 18
3 3 12 3 -18
1 4 1 -6 0
-2 -2 -3 6
1 1 -3 0
A = 1 B = 1 C = -3
x = -b ± √ b2 - 4 . A . C / 2a x = - 2 ± √ (2)2 - 4 . 1 . (-3) / 2 . 1
x = -2 ± √ 4 + 12 / 2 x = -2 ± √ 16 / 2 = -2 ± 4 /2
-2 -4 / 2 = -6 / 2 = -3 -2 +4 / 2 = 2 / 2 = 1
E(x) = (x-3) . (x+2) . (x-1) . (x+3)