Synthetic Substitution and Division

Mathematics

9th - 12th Grade

CCSS covered

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15 questions

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

State if the given binomial is a factor of the given polynomial.
$8x^4-23x^3+5x^2+18\ ;\ x-2$

Yes

Tags

CCSS.HSA.APR.B.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

State if the given binomial is a factor of the given polynomial.
$p^5+4p^4-17p^3+18p^2-64p+40\ ;\ p+7$

Yes

Tags

CCSS.HSA.APR.B.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

State if the given binomial is a factor of the given polynomial.
$x^5+16x^4+58x^3-28x^2+50x+7\ ;\ x+7$

Yes

Tags

CCSS.HSA.APR.B.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

State if the given binomial is a factor of the given polynomial.
$m^3+4m^{2\ }-44m-3\ ;\ m-5$

Yes

Tags

CCSS.HSA.APR.B.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

State if the given binomial is a factor of the given polynomial.
$2n^3+13n^2+29n+36\ ;\ n+4$

Yes

Tags

CCSS.HSA.APR.B.2

FILL IN THE BLANKS QUESTION

5 mins • 1 pt

Use synthetic substitution to evaluate the given value and determine the remainder.
$f\left(x\right)=\ -5x^5-x^4+x^3-6x^2-1\ at\ x=-1$

(a)

Tags

CCSS.HSA.APR.B.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Use synthetic substitution to evaluate the given value and determine the remainder.
$f\left(x\right)=x^4+5x^3-9x^2-18x-5\ at\ x=-6$

-10

-7

-5

Tags

CCSS.HSA.APR.D.6

FILL IN THE BLANKS QUESTION

5 mins • 1 pt

Use synthetic substitution to evaluate the given value and determine the remainder.
$f\left(x\right)=x^3+7x^2-12x-1\ at\ x=-5$

(a)

Tags

CCSS.HSA.APR.D.6

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Use synthetic substitution to evaluate the given value and determine the remainder.
$f\left(x\right)=-4x^4+9x^3+8x^2+9x-13\ at\ x=3$

-11

Tags

CCSS.HSA.APR.D.6

10.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Divide the polynomial
$a^5+3a^4-4a^3-6a^2+3a-19$ by $a+2$

$a^4+a^3-6a^2+6a-9-\frac{1}{a+2}$

$a^4+a^3-6a^2+6a-7+\frac{2}{a+2}$

$a^4+a^3-6a^2+6a-12-\frac{5}{a+2}$

$a^4+a^3-6a^2+6a-12-\frac{3}{a+2}$

Tags

CCSS.HSA.APR.D.6

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Synthetic Substitution and Division

State if the given binomial is a factor of the given polynomial. 8x4−23x3+5x2+18 ; x−28x^4-23x^3+5x^2+18\ ;\ x-28x4−23x3+5x2+18 ; x−2

State if the given binomial is a factor of the given polynomial. p5+4p4−17p3+18p2−64p+40 ; p+7p^5+4p^4-17p^3+18p^2-64p+40\ ;\ p+7p5+4p4−17p3+18p2−64p+40 ; p+7

State if the given binomial is a factor of the given polynomial. x5+16x4+58x3−28x2+50x+7 ; x+7x^5+16x^4+58x^3-28x^2+50x+7\ ;\ x+7x5+16x4+58x3−28x2+50x+7 ; x+7

State if the given binomial is a factor of the given polynomial. m3+4m2 −44m−3 ; m−5m^3+4m^{2\ }-44m-3\ ;\ m-5m3+4m2 −44m−3 ; m−5

State if the given binomial is a factor of the given polynomial. 2n3+13n2+29n+36 ; n+42n^3+13n^2+29n+36\ ;\ n+42n3+13n2+29n+36 ; n+4

Use synthetic substitution to evaluate the given value and determine the remainder. f(x)= −5x5−x4+x3−6x2−1 at x=−1f\left(x\right)=\ -5x^5-x^4+x^3-6x^2-1\ at\ x=-1f(x)= −5x5−x4+x3−6x2−1 at x=−1 (a)

Use synthetic substitution to evaluate the given value and determine the remainder. f(x)=x4+5x3−9x2−18x−5 at x=−6f\left(x\right)=x^4+5x^3-9x^2-18x-5\ at\ x=-6f(x)=x4+5x3−9x2−18x−5 at x=−6

Use synthetic substitution to evaluate the given value and determine the remainder. f(x)=x3+7x2−12x−1 at x=−5f\left(x\right)=x^3+7x^2-12x-1\ at\ x=-5f(x)=x3+7x2−12x−1 at x=−5 (a)

Use synthetic substitution to evaluate the given value and determine the remainder. f(x)=−4x4+9x3+8x2+9x−13 at x=3f\left(x\right)=-4x^4+9x^3+8x^2+9x-13\ at\ x=3f(x)=−4x4+9x3+8x2+9x−13 at x=3

Divide the polynomial a5+3a4−4a3−6a2+3a−19a^5+3a^4-4a^3-6a^2+3a-19a5+3a4−4a3−6a2+3a−19 by a+2a+2a+2

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State if the given binomial is a factor of the given polynomial.
$8x^4-23x^3+5x^2+18\ ;\ x-2$

State if the given binomial is a factor of the given polynomial.
$p^5+4p^4-17p^3+18p^2-64p+40\ ;\ p+7$

State if the given binomial is a factor of the given polynomial.
$x^5+16x^4+58x^3-28x^2+50x+7\ ;\ x+7$

State if the given binomial is a factor of the given polynomial.
$m^3+4m^{2\ }-44m-3\ ;\ m-5$

State if the given binomial is a factor of the given polynomial.
$2n^3+13n^2+29n+36\ ;\ n+4$

Use synthetic substitution to evaluate the given value and determine the remainder.
$f\left(x\right)=\ -5x^5-x^4+x^3-6x^2-1\ at\ x=-1$

(a)

Use synthetic substitution to evaluate the given value and determine the remainder.
$f\left(x\right)=x^4+5x^3-9x^2-18x-5\ at\ x=-6$

Use synthetic substitution to evaluate the given value and determine the remainder.
$f\left(x\right)=x^3+7x^2-12x-1\ at\ x=-5$

(a)

Use synthetic substitution to evaluate the given value and determine the remainder.
$f\left(x\right)=-4x^4+9x^3+8x^2+9x-13\ at\ x=3$

Divide the polynomial
$a^5+3a^4-4a^3-6a^2+3a-19$ by $a+2$