[tex]2x^{2}-8x+8[/tex]
Factor the polynomial.
2([tex]x^{2}-4x+4[/tex])
2(x-2)[tex]^{2}[/tex]
Factor the other Polynomial.
3[tex]x^{2}+27x-30[/tex]
[tex]3(x^{2}+9x-10)[/tex]
[tex]3(x+10)(x-1)[/tex]
This is your answer.
[tex]6(x-2)^{2}(x+10)(x-1)[/tex]
The LCM of the pair of polynomials [tex]2x^{2} -8x+8[/tex] and [tex]3x^{2} +27x-30[/tex] is
6(x-1)[tex](x-2)^{2}[/tex](x+10) which is option b.
The full form of LCM is lowest common multiple. It is smallest common multiple of two integers a and b. It is the smallest positive integer that can be divisible by a and b.
The given polynomials are [tex]2x^{2} -8x+8[/tex] and [tex]3x^{2} +27x-30[/tex]. To find the LCM of these two polynomials we first need to make factors of these polynomials which is done under:
[tex]2x^{2} -8x+8[/tex]=[tex]2x^{2}[/tex]-4x-4x+8
=2x(x-2)-4(x-2)
=(2x-4)(x-2)
=2(x-2)(x-2)
=2[tex](x-2)^{2}[/tex]
[tex]3x^{2} +27x-30[/tex]=[tex]3x^{2}[/tex]+30x-3x-30
=3x(x+10)-3(x+10)
=(3x-3)(x+10)
=3(x-1)(x+10)
LCM=2[tex](x-2)^{2}[/tex]*3(x-1)(x+10)
=6[tex](x-2)^{2}[/tex](x-1)(x+10)
Hence the LCM of polynomials [tex]2x^{2} -8x+8[/tex] and [tex]3x^{2} +27x-30[/tex] is [tex]6(x-2)^{2} (x-1)(x+10)[/tex].
Learn more about LCM at https://brainly.com/question/233244
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