Examine whether 2x + 3 is a factor of 2x^3 + | vedclass

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Question

(A) Let $p(x) = 2x^3 + 21x^2 + 67x + 60$.To check if $2x + 3$ is a factor,we find its zero by setting $2x + 3 = 0$,which gives $x = -\frac{3}{2}$.Acco

Vedclass · Accepted Answer

Yes

Vedclass · Answer

(A) Let $p(x) = 2x^3 + 21x^2 + 67x + 60$.To check if $2x + 3$ is a factor,we find its zero by setting $2x + 3 = 0$,which gives $x = -\frac{3}{2}$.According to the factor theorem,if $p(-\frac{3}{2}) = 0$,then $2x + 3$ is a factor.$p(-\frac{3}{2}) = 2(-\frac{3}{2})^3 + 21(-\frac{3}{2})^2 + 67(-\frac{3}{2}) + 60$$= 2(-\frac{27}{8}) + 21(\frac{9}{4}) - \frac{201}{2} + 60$$= -\frac{27}{4} + \frac{189}{4} - \frac{402}{4} + \frac{240}{4}$$= \frac{-27 + 189 - 402 + 240}{4}$$= \frac{429 - 429}{4} = 0$.Since $p(-\frac{3}{2}) = 0$,$2x + 3$ is a factor of the given polynomial.

Examine whether $2x + 3$ is a factor of $2x^3 + 21x^2 + 67x + 60$ or not.

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