Question

- 5x² + 28x - 24 ans ​

Answer 1

Step-by-step explanation:

Here, f(x)=2x3+5x2–28x–15

So, x+5=0⇒x=−5

Thus, remainder =f(−5)

=2(−5)3+5(−5)2–28(−5)–15

=−250+125+140–15

=−265+265

=0

Therefore, (x+5) is a factor of f(x).

Now, performing division of polynomial f(x) by (x+5) we get

So, 2x3+5x2–28x–15=(x+5)(2x2–5x–3)

Further, on factorisation

=(x+5)[2x2–6x+x–3]

=(x+5)[2x(x–3)+1(x–3)]=(x+5)(2x+1)(x–3)

Thus, f(x) is factorised as (x+5)(2x+1)(x–3)

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