How did Mendel know the the tall pea plants in the first generation had a hidden factor for shortness?

Answer 1

By "test cross" you can know whether it homozygous dominant or heterozygous dominant...in homozygous both alleles code for the dominant trait, in heterozygous one allele is recessive (what you called a "hidden factor"). To perform the test cross, cross a homozygous recessive with the first generation.

Lets suppose tall pea tree in the first generation is hetrozygous dominant (Xx) and has alleles X (dominant) and x (recessive). When we cross it with homozygous recessive (xx)

X x

x :Xx xx

x :Xx xx

we get half offspring showing dominant trait (Xx) and half showing recessive (xx).

If the first generation was homozygous (which is not possible) the result would be

X X

x: Xx Xx

x: Xx Xx

all the offspring showing dominant trait and it doesn't really happen when we cross the first generation with homozygous recessive. It means that the genotype of first generation is heterozygous (has a hidden factor or a recessive allele x).

Note:You must know what the recessive and dominant allele means...In presence of a dominant allele, recessice character is not expressed but it is present is heterozygous. If both alleles are recessive (homozygous recessive) then the recessive trait is expressed. If both the alleles are dominant (homozygous dominant) obviusly the dominant trait is showed by the individual.

Answer 2

TT X tt

= Tt

======All phenotype expression would be tall plants, so a further cross is needed.