Question

Find the LCM of p2 - 39 + 2, p2 - 4. ​

Answer 1

Answer:

p3-2-39

Step-by-step explanation:

p2-39+2,p2-4

p2-39+2,(p-2)2

p3-2-39

hope this answer help u..plzz support

Answer 2

Hi friend ,

so in order to get the lcm of these polynomials,

you should first  know what is the following :

1) FACTORIZATION: it means to convert  it into the form where all its components are separated by a multiplication symbol only . For example : to factorise x^2 -5x + 6 , we can do it by middle term splitting method , ie. x^2-3x-2x+6  => x(x-3)-2(x-3) => (x-3)*(x-2) hence its factorized .

2)how to find the hcf and lcm of two no. : if I have to find the hcf & lcm of 6 and 9 then we would break them into prime factors and then find out . 6=3*2 and 9=3*3 so, here hcf is 3 and lcm is 18 .

3)what is HCF and LCM : HCF is the lowest power of common factor  of the two or three or as many no. and LCM is the  product of all highest power of all prime factors of the numbers .For the above example the common product for the lowest power is 3 and the highest power is 2*3*3 .

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coming to the question

it says about two polynomials

p^2 - 3p + 2                [there is a typing error I guess coz it should be p not 9]

p^2 - 4

so ,

first factorize both the equations

p^2-3p+2

=p^2-2p-1p +2

=p(p=2)-1(p-2)

=(p-2)*(p-1)

it is factorized

now ,

p^2-4

=(p-2)(p+2)                                       [it is in the form a^2-b^2 =(a-b)(a+b)]

now we see ,

p^2-3p+2 = (p-2)*(p-1)

p^2-4=(p-2)(p+2)

here (p-2) is common hence it would be the HCF of the two polynomials.

now

LCM = (p-2)(p-1)(p+2) = p^3-p^2 -4p + 4