Problem

Factor \(9x^{2}-30x+25=0\) as the square of a binomial. Use the middle term to determine the sign, then solve the repeated factor and state the zero’s multiplicity.

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end roots=a=3x,b=5; middle check=−2ab=−30x; squared factor=(3x−5)²=0; repeated zero=-5; multiplicity2; graph meaning=tangent at the copied value

end roots=a=3x,b=5; middle check=-2ab=-30x; factored=(3x−5)²=0; repeated zero=x=5/3; multiplicity=2; graph meaning=tangent x-intercept(5/3,0)

Roots 3x and 5; middle check +2(3x)(5) = +30x; squared factor (3x + 5)² = 0; repeated zero x = −5/3; multiplicity 2; expansion 9x² + 30x + 25.

end roots=a=3x,b=5; middle check=−2ab=−30x; squared factor=(3x−5)²=0; zeros=5/3 and 5/3; multiplicity=1 each; graph meaning=two distinct x-intercepts

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