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Q: What is the complete factor of 33xsquared minus 61x plus 10?

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Yes.

(x-4)

There are no rational factors.

(3y - 5)(y + 5)

(a - 2)(a^2 + 6)

(b-c)(a+b)-ac

(x + 3)(3x - 2)

Same mathematical signs equal plus Different mathematical signs equal minus Plus Plus = Plus (+)(+) = + Minus Minus = Plus (-)(-) = + Plus Minus = Minus (+)(-) = - Minus Plus = Minus (-)(+) = - So the direct answer to your question would be: plus minus equals minus

To factor a trinomial square take the square roots of the end terms and join them with a plus sign if the middle term is preceded by a plus or with a minus if the middle term is preceded by a minus.

There are no rational factors.

There is no rational factorisation.

2(a + 7)(a - 6)

That doesn't factor neatly. Applying the quadratic formula, we find two imaginary solutions: 1 plus or minus i where i is the square root of negative one.

No.

6(b - ac + b2 - bc)

6(ab - ac + b2 - bc)

(3x - 4)(2x^2 + 6x + 5)

A plus + a plus is a plus.

(x2 plus 40) (x minus 1)

x squared minus 12 x plus 36 = (x - 6)(x - 6)

(x - 3)(x - 18)

(3x - 4)(4x - 3)

(2x+5)(4x-7)

(x + 7)(x - 6)

(3x - 1)(2x - 7)