Question

Given a polynomial and one of its factors find the remaining factors of the polynomial some of the factors may not be binomials 16x3-48x2-49x+147;x-3

Answer 1

The other factors are (4x + 7) and (4x - 7).

Explanation:

One of the factor of the polynomial
`16x^(3) - 48x^(2) - 49x + 147` is given to be (x - 3). We have to find the other factors of this polynomial.

Now,
`16x^(3) - 48x^(2) - 49x + 147`

=
`16x^(2) (x - 3) - 49(x - 3)`

=
`(x - 3)( 16x^(2) - 49)`

=
`(x - 3)[(4x)^(2) - 7^(2)]`{Since we know the formula,
`(a^(2)-b^(2) ) = (a + b)(a - b)`}

=
`(x - 3)(4x + 7)(4x - 7)`

Therefore, the other factors are (4x + 7) and (4x - 7). (Answer)