f(x) = ax

^{3}+ (b − ad)x^{2}+ (c − bd)x − cd = (ax

^{2}+ bx + c)(x − d)f(x) = 0 when x = d ⇒ x = 8.

Note

The quadratic term ax

^{2}+ bx + c has no real solution for the given values of a, b and c.Mary B.

asked • 10/12/17I'm so bad at these topics ): I need help with this and some explanation, thanks!

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f(x) = ax^{3} + (b − ad)x^{2} + (c − bd)x − cd

= (ax^{2} + bx + c)(x − d)

f(x) = 0 when x = d ⇒ x = 8.

Note

The quadratic term ax^{2} + bx + c has no real solution for the given values of a, b and c.

Michael J. answered • 10/12/17

Tutor

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Effective High School STEM Tutor & CUNY Math Peer Leader

Plug in the numbers.

f(x) = 26x^{3} + (-8 - (26*8))x^{2} + (21 - (-8*8))x - (21*8)

f(x) = 26x^{3} + (-8(1 + 26))x^{2} + (21 * 64)x - 168

f(x) = 26x^{3} + (-8*27)x^{2} + 1344x - 168

f(x) = 26x^{3} - 216x^{2} + 1344x - 168

Then, you want to use synthetic division to find a linear factor and a quadratic factor. When you do the division, the remainder should be zero.

Andrew M.

I actually came up with a list of 74 possible rational roots...

That's a lot of synthetic division ....

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10/13/17

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Andrew M.

10/13/17