Question

i) (6x square
+ 3x + 10) ÷ (2x + 3)​

Answer 1

Answer:

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Answer 2

Answer:

y=x3−6x2+3x+10=(x+1)(x−5)(x−2)

Step-by-step explanation:

factorize y=x³−6x²+3x+10

The solution - in the general case - should look like:

y=(x+a)(x+b)(x+c)

y=(x2+ax+bx+ab)(x+c)

y=x3+ax2+bx2+abx+cx2+cax+cbx+cab

y=x3+(ax2+bx2+cx2)+(abx+cax+cbx)+cab

Rewrite:

y=x3+(a+b+c)x2+(ab+ac+bc)x+abc=0

For y it was given that:

a+b+c=−6

ab+ac+bc=3

abc=10

It follows that,

abc=10 suggests the positive or negative numbers: 1,5 and 2.

a+b+c=−6 suggest the combination a=1, b=-5 and c=-2.

ab+ac+bc=(1)(−5)+(1)(−2)+(−5)(−2)=3 , which holds true.

Hence,

y=x3−6x2+3x+10=(x+1)(x−5)(x−2)