<prompt> Acha fx na gx ziwe polynomia mbili za ujazo za monic, na r iwe nambari halisi. Mizizi miwili ya fx ni r 1 na r 7. Mizizi miwili ya gx ni r 3 na r 9, nafx - gx rkwa nambari zote halisi x. Pata r.  <response>: Na Factor Theorem,fx x - r - 1x - r - 7x - anagx x - r - 3x - r - 9x - bkwa baadhi ya nambari halisi a na b.Kishafx - gx x - r - 1x - r - 7x - a - x - r - 3x - r - 9x - b rkwa x. zoteKuweka x r 3, tunapata2-4r 3 - a r.Kuweka x r 9, tunapata82r 9 - a r.Kisha -8r - 24 8a r na 16r 144 - 16a r, hivyoanzaalign8a - 9r 24, -16a 15r -144.endalignInatatua, tunapata r 32. 