This is what they teach us at school! Part 3

Algebra Level 3

Find the sum of the values of $a$ and $b$ if $x^2-5x+6$

is a factor of $3x^3+ax^2+bx+12$

The answer is -5.

2 solutions

Brian Charlesworth
Jul 2, 2014

Assuming that the second polynomial p(x) is degree 3 instead of degree 2, then we know that p(2) = p(3) = 0.

This means that 4a + 2b = -36 and that 9a + 3b = -93. Solving these simultaneously gives us a = -13 and b = 8, and so a + b = $\boxed{-5}$ .

@Mardokay Mosazghi I think that you made a typo on the second polynomial; I believe it should be degree 3. :)

Brian Charlesworth - 6 years, 11 months ago

dang it sorry @brian charlesworth just edited it thanks.

Mardokay Mosazghi - 6 years, 11 months ago

No problem. Thanks for posting the set of questions. :)

Brian Charlesworth - 6 years, 11 months ago

How do you get the terms 4a - 2b and 9a - 3b when in the polynomial, the middle terms are ax^2 + bx? Why wouldn't it be 4a + 2b and 9a + 3b?

Ryan Tamburrino - 6 years, 11 months ago

You're right, Ryan. I think I made a quick edit to my original post and wasn't careful with the changes I made. I've made the appropriate changes now; the values for a and b are unchanged. Thanks for the noticing my mistake. :)

Brian Charlesworth - 6 years, 11 months ago

Reinaldo Limantara
Aug 6, 2014

as we can see that the integer in the 3rd degree equation is 3x^3, and the constant is 12. By factorizing, we get (x-3)(x-2). In order for x^2 to become 3x^3, it needs to be multiplied by 3x, and 6 multiplied by 2 to get 12, there fore we can say that 3x^3 + ax^2 + bx + 12 = (x-3)(x-3)(3x+2) --> 3x^3 - 13x^2 + 8x + 12, therefore a + b = -5

This is what they teach us at school! Part 3

The answer is -5.

2 solutions

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