Question

factorise using factor theorem 2x^3+7x^2-9

Answer 1

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Answer 2

Answer: The answer is $(x-1)(x+3)(2x+3).$

Step-by-step explanation: We are given to factorise the following cubic expression using the factor theorem:

$E(x)=2x^3+7x^2-9.$

Factor Theorem states that, if 'a' is a zero of a polynomial p(x), then (x - a) will be a factor of p(x).

Now, we will check one by one for the given cubic expression E(x).

For x = 1, we have

$E(1)=2\times 1^3+7\times 1^2-9=2+7-9=0.$

Therefore, (x - 1) is a factor of E(x).

So, we have

$E(x)=2x^2(x-1)+9x(x-1)+9(x-1)\\\\\Rightarrow E(x)=(x-1)(2x^2+9x+9)\\\\\Rightarrow E(x)=(x-1)(2x^2+6x+3x+9)\\\\\Rightarrow E(x)=(x-1)\{2x(x+3)+3(x+3)\}\\\\\Rightarrow E(x)=(x-1)(x+3)(2x+3).$