The factors of the expression are (2x+3)(x-7).
Factorization is the breaking or decomposition of an entity (a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number. Factorize an expression involves take out the greatest common factor (GCF) of all the terms.
For the given situation,
The expression is [tex]2x^{2} -11x-21[/tex]
The complete factorization of the expression is as,
⇒ [tex]2x^{2} -11x-21=0[/tex]
⇒ [tex]2x^{2} -14x+3x-21=0[/tex]
⇒ [tex]2x(x-7)+3(x-7)=0[/tex]
⇒ [tex](2x+3)(x-7)=0[/tex]
The value of x can be found as
⇒ [tex]2x+3 = 0[/tex] or [tex]x-7 = 0[/tex]
⇒ [tex]x=\frac{-3}{2}[/tex] or [tex]x=7[/tex]
Then -3/2 and 7 are the zeroes of the expression.
Hence we can conclude that the complete factorization of the expression are (2x+3)(x-7).
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