Mathematics: PLS HELP QUICK **50 POINTS** it’s a timed quiz , pls hurry

Factor theorem: .Synthetic division: .Step-by-step explanation:Factor TheoremBy the factor theorem, a monomial of the form (where is a constant) is a factor of polynomial if and only if .In this question, the monomial is , which is equivalently . . .Hence, by the factor theorem, , which is equivalent to , is a factor of .Synthetic Division.The remainder is when dividing by . Hence, is a factor of ....

PLS HELP QUICK **50 POINTS** it’s a timed quiz

Ответ:

gustinya000

25.07.2021

Mathematics

It starts at 0.

You subtract it by -3; it lands at -3

and then by -1.5; it land at -4.5

the answer is the first one.

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Ответ:

belle200163

30.12.2021

Mathematics

Factor theorem: f(-5) = 0 .

Synthetic division: $f(x) = (x + 5)\, (2\, x^2 -3\, x + 1)$ .

Step-by-step explanation:

Factor Theorem

By the factor theorem, a monomial of the form (x - a) (where is a constant) is a factor of polynomial f(x) if and only if f(a) = 0 .

In this question, the monomial is (x + 5) , which is equivalently (x - (-5)) . a = -5 .

$\begin{aligned}& f(-5) \\ &= 2 \times (-5)^{3} + 7 \times (-5)^{2}- 14\times (-5) + 5\\ &= -250 + 175 + 70 + 5 \\ &= 0\end{aligned}$ .

Hence, by the factor theorem, (x + 5) , which is equivalent to (x - (-5)) , is a factor of f(x) .

Synthetic Division

$\begin{aligned}& f(x) \\ &= 2\, x^{3} + 7\, x^{2} - 14\, x + 5 \\ &= \underbrace{(x + 5) \, (2\, x^2)}_{2\, x^{3} + 10\, x^{2}} - 3\, x^{2} - 14\, x + 5 \\ &= \underbrace{(x + 5) \, (2\, x^2)}_{2\, x^{3} + 10\, x^{2}} + \underbrace{(x + 5)\, (-3\, x)}_{-3\, x^{2} - 15\, x} + (x + 5) \\ &= (x + 5)\, (2\, x^{2} - 3\, x + 1)\end{aligned}$ .

The remainder is when dividing f(x) by (x + 5) . Hence, $(x + 5)\!$ is a factor of $f(x)\!$ .

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PLS HELP QUICK 50 POINTS
it’s a timed quiz , pls hurry

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