Question

3. If 2x3 + ax2 + bx - 6 has a factor (2x + 1) and
+,
leaves the remainder 12 when divided by (x + 2).
Calculate the values of a and b, hence factorise the
expression completely.​

Answer 1

Answer:

a=57/5

b=29/5

Step-by-step explanation:

Let p(x) = 2x³+ ax²+ bx - 6 has a factor (2x + 1)

taking 2x+1=0

x=-1/2

Then p(-1/2)=0

2*(1/2)³+a(1/2)²+b*1/2-6=0

2/8 + a/4 +b/2-6=0

2+2a+4b-48=0

2a+4b=46........................(1)

Now p(x) leaves the remainder 12 when divided by (x + 2).

so x+2=0,x=-2

Thus from remainder theorem

p(-2)=12

or 2*(-2)³+a*(-2)²+b(-2)-6=12

-16+4a-2b-6=12

4a-2b=34

Or 2a-b=17............................(2)

Subtracting (2) from(1)

4b+b=46-17=29

b=29/5

From(2)

2a-29/5=17

10a-29=85

10a=114

a=114/10=57/5

Answer 2

Answer:

a = 57/5

b = 29/5

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