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saveliy_v [14]
3 years ago
5

What is the quotient: (6x4 + 15x3 + 10x2 + 10x + 4) ÷ (3x2 + 2)?

Mathematics
2 answers:
mario62 [17]3 years ago
7 0
<span>                  2x^2 + 5x + 2
3x^2 + 2    </span><span>6x^4 + 15x^3 + 10x^2 + 10x + 4
             -    6x^4                + 4x^2
                             15x^3 + 6x^2 + 10x + 4
             -               15x^3            + 10x
                                           6x^2 + 4
                                           6x^2 + 4

Therefore, </span><span>(6x^4 + 15x^3 + 10x^2 + 10x + 4) ÷ (3x^2 + 2) = </span><span>2x^2 + 5x + 2</span>

Kryger [21]3 years ago
4 0

Answer:  Option 'C' is correct.

Step-by-step explanation:

Since we have given that

\frac{\left(6x^4+15x^3+10x^2+10x+4\right)}{\left(3x^2+2\right)}

Now, we will find the quotient by factoring the numerator:

\mathrm{Use\:the\:rational\:root\:theorem}\\a_0=4,\:\quad a_n=6\\\\\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:4,\:\quad \\\mathrm{The\:dividers\:of\:}a_n:\quad 1,\:2,\:3,\:6\\\\\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:4}{1,\:2,\:3,\:6}\\\\-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2\\\\=\left(x+2\right)\frac{6x^4+15x^3+10x^2+10x+4}{x+2}\\\\=\frac{6x^4+15x^3+10x^2+10x+4}{x+2}=6x^3+3x^2+4x+2\\\\

Now, we will factor it again:

=\left(6x^3+3x^2\right)+\left(4x+2\right)\\\\=2\left(2x+1\right)+3x^2\left(2x+1\right)\\\\=\left(2x+1\right)\left(3x^2+2\right)

At last we get our factorised form :

=\left(x+2\right)\left(2x+1\right)\left(3x^2+2\right)\\\\=\frac{\left(x+2\right)\left(2x+1\right)\left(3x^2+2\right)}{3x^2+2}\\\\=\left(x+2\right)\left(2x+1\right)\\\\=2x^2+5x+2

Hence, Option 'C' is correct.

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