Makakuha ng maaasahan at pangkomunidad na mga sagot sa IDNStudy.com. Magtanong at makakuha ng detalyadong sagot mula sa aming komunidad ng mga eksperto na may kaalaman.

Find the factors of the following polynomials​

Find The Factors Of The Following Polynomials class=

Sagot :

Answer:

1.x2-13x-39

Step-by-step explanation:

yan lng po alam ko

Solution/s:

1.

[tex] \displaystyle x^3 + 13x^2 + 30x = ? [/tex]

[tex] \displaystyle \textsf{Factor out x:} [/tex]

[tex] \displaystyle = x(x^2 + 13x + 30) [/tex]

[tex] \displaystyle \textsf{Factor quadratic trinomial:} [/tex]

[tex] \displaystyle = \boxed{\green{ x(x+10)(x+3) }} [/tex]

[tex] \displaystyle \textsf{(Optional)Let us solve for x:} [/tex]

[tex] \displaystyle \textsf{Equate to 0:} [/tex]

[tex] \displaystyle = x=0,(x+10=0),(x+3=0) [/tex]

[tex] \displaystyle = x=0,(x=-10),(x=-3) [/tex]

[tex] \displaystyle = \boxed{ x=0, -10, -3} [/tex]

[tex] \displaystyle x^3 + 13x^2 + 30x = x(x+10)(x+3) [/tex]

2.

[tex] \displaystyle x^3 + 4x^2 + 5x + 2 = ? [/tex]

[tex] \displaystyle \textsf{Factor out x:} [/tex]

[tex] \displaystyle x^3 + 4x^2 + 5x + 2 [/tex]

[tex] \displaystyle \textsf{Let us find the possible roots:} [/tex]

[tex] \displaystyle \pm  2 \textsf{\ and\ } \pm 1 [/tex]

[tex] \displaystyle \textsf{Let us try: \ } \pm 1 [/tex]

[tex] \displaystyle 1^3 + 4(1)^2 + 5(1) + 2 = 0 \quad ? [/tex]

[tex] \displaystyle 1 + 4 + 5 + 2 = 0 \quad ? [/tex]

[tex]\displaystyle 12 \ne 0 \quad \times \[/tex]

[tex] \displaystyle (-1)^3 + 4(-1)^2 + 5(-1) + 2 = 0 \quad ? [/tex]

[tex] \displaystyle -1 + 4 + -5 + 2 = 0 \quad ? [/tex]

[tex]\displaystyle 0 = 0 \quad \checkmark \[/tex]

[tex]\displaystyle \textsf{-1 is a solution, therefore x+1 is a factor:}[/tex]

[tex] \displaystyle = (x+1)(x^2+3x+2) [/tex]

[tex] \displaystyle \textsf{Now let us factor the quadratic trinomial:} [/tex]

[tex] \displaystyle = \boxed{\green{ (x+1)(x+1)(x+2) }} [/tex]

[tex] \displaystyle x^3 + 4x^2 + 5x + 2 = (x+1)(x+1)(x+2) [/tex]