Two mark example problems II — task. Mathematics State Board, Class 9.

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Answer variants:

$1 + 13 = 14 \neq 0$

the coefficients of equal powers is not equal to

$0$

the coefficients is equal to

$0$

all

$- 7 - 7 = - 14 \neq 0$

$-125$

$3x^2 - 11x + 40$

$1 - 7 + 13 - 7 = 0$

the coefficients of odd powers is not equal to

$0$

odd

even

1. Find the quotient and remainder when

$p(x) = (3x^3 - 2x^2 - 5 + 7x)$ is divided by

$d(x) = x + 3$ using synthetic division.

Answer:

Quotient

$=$

Remainder

$=$

2. Prove that

$(x - 1)$ is a factor of

$x^3 - 7x^2 + 13x - 7$ .

Answer:

Sum of coefficients of

powers of

$x$ including the constant

$=$

Since

, then

$(x - 1)$ is a factor of

$x^3 - 7x^2 + 13x - 7$ .

Hence, we proved.

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3. Two mark example problems II