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PLZ HELP: Write each trinomial in the form a(x+b)^2 or a(x-b)^2:
5x^2 + 15x + 11.25
10x^2 +20x +10
1/4x^2 + x + 1
3x^2 + 5x + 25/12
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Sagot :

msm555

Answer:

solution given:

A. 5x^2 + 15x + 11.25

taking common 5

5(x²+3x+11.25/5)

since 11.25/5=2.25=(3/2)^2

5(x²+2*x*3/2 +(3/2)²)

5(x+3/2)²

5(x+1.50)²

B.10x^2 +20x +10

taking common 10

10(x²+2x+1)

since x²+2x+1 is in a form of x²+2xy+y²

so

10(x+1)²

C. 1/4x^2 + x + 1

taking common 1/4

while taking common we must balance the equation

1/4(x² +4x+4)

since x²+4x+1 is in a form of x²+2xy+y²: x²+2*x*2 +2²

so

1/4(x+2)²

D. 3x^2 + 5x + 25/12

taking common 3

3(x²+5/3 x +25/(12*3))

3(x²+2* x*5/6+25/36)

since x²+2* x*5/6+25/36  is in a form of x²+2xy+y²: x²+2*x*5/6 +(5/6)²

so

3(x+5/6)²

Step-by-step explanation:

semsee45

Answer:

Expand the two given forms:

[tex]\begin{aligned}\implies a(x+b)^2 & =a(x+b)(x+b)\\& =a(x^2+2bx+b^2)\end{aligned}[/tex]

[tex]\begin{aligned}\implies a(x-b)^2 & =a(x-b)(x-b)\\& =a(x^2-2bx+b^2)\end{aligned}[/tex]

Therefore, to write each given trinomial in one of the given forms:

  • a = coefficient of x²
  • b = half the coefficient of x after a has been factored out

[tex]\textsf{For }\quad 5x^2+15x+11.25:[/tex]

Factor out the coefficient of x² (common term 5):

[tex]\implies 5(x^2+3x+2.25)[/tex]

Factor the perfect trinomial:

[tex]\implies 5\left(x+\dfrac{3}{2}\right)^2[/tex]

[tex]\textsf{For }\quad 10x^2+20x+10:[/tex]

Factor out the coefficient of x² (common term 10):

[tex]\implies 10(x^2+2x+1)[/tex]

Factor the perfect trinomial:

[tex]\implies 10\left(x+1\right)^2[/tex]

[tex]\textsf{For }\quad \dfrac{1}{4}x^2+x+1:[/tex]

Factor out the coefficient of x² (common term 1/4):

[tex]\implies \dfrac{1}{4}(x^2+4x+4)[/tex]

Factor the perfect trinomial:

[tex]\implies \dfrac{1}{4}\left(x+2\right)^2[/tex]

[tex]\textsf{For }\quad 3x^2+5x+\dfrac{25}{12}:[/tex]

Factor out the coefficient of x² (common term 3):

[tex]\implies 3 \left(x^2+\dfrac{5}{3}x+\dfrac{25}{36} \right)[/tex]

Factor the perfect trinomial:

[tex]\implies 3\left(x+\dfrac{5}{6}\right)^2[/tex]

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