Question

The hcf of two polynomials is (x + 3) and their lcm is x3 – 7x + 6. if one of the polynomials is (x2 + 2x – 3), then the other is​

Answer 1

Answer:

h(x)=(x+3) is HCF of p(x) and q(x).

So, both the polynomials will contain (x+3) as one of the factor.

Now, q(x)=x2+x−6=(x+3)(x−2) (i)

m(x) is LCM of p(x) and q(x). So, it will also contain (x+3) as one of the factor.

∴ m(x)=x3−7x+6=(x+3)f(x)

We first find f(x),

By using long division method, we get

f(x)=(x2−3x+2)

∴ m(x)=(x+3)(x2−3x+2)=(x+3)(x−2)(x−1)

Now, p(x) has (x+3) as one of the factor.

Since, LCM contains (x−1) and q(x) does not contains (x−1) as one of the factors. So, p(x) will have (x−1) and it will be another factor.

As it is given that, p(x) has negative leading coefficient, so we have

p(x)=−(x+3)(x−1)=−(x2+2x−3)=−x2−2x+3