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Twelfth Grade (Grade 12) Polynomials and Rational Expressions Questions

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Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.D.6

What is

$4x^3-2x^2+7x+5$ divided by

$(x+2)?$

$(4x^2-10x+27)-49/(x+2)$
$(4x^2-10x+27)$
$(4x^2-10x+27)+59/(x+2)$
$(4x^2-10x+27)-59/(x+2)$

Grade 12 Polynomials and Rational Expressions CCSS: HSN-CN.C.9

What is the maximum number of purely imaginary roots that the polynomial

$x^3-x^6-x-x^7$ can have?

Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.C.4

Is the following proof correct? If not, identify the first step that has an error.

$"Prove: " \ (x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2$

Left Side:

$(x^2+y^2)^2$
Step 1:

$(x^2+y^2)(x^2+y^2)$
Step 2:

$x^4-2x^2y^2+4x^2y^2+y^4$
Step 3:

$(x^2-y^2)^2+(2xy)^2$

The proof is correct.
Step 1 has an error.
Step 2 has an error.
Step 3 has an error.

Grade 12 Polynomials and Rational Expressions CCSS: HSN-CN.C.9

How many roots does the polynomial

$x^3-x^6-x-x^7$ have?

Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.C.5

How can one determine the coefficients of the Binomial Theorem expansion for

$(x+y)^n$ , where

$n$ is an integer? There may be more than one correct answer.

Pascal's Triangle
Binomial Permutation
$({:(n),(k):}), \ k=0,...,n$
$(n!)/(k!(n-k)!), \ k=0,...,n$

Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.D.6

What is the remainder of

$x^2+6x-2$ divided by

$x-5$ ?

$-7$
$x-53$
$53$
$-2$

Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.C.4

Is the following proof correct? If not, identify the first step that has an error.

$"Prove: " \ (x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2$

Left Side:

$(x^2 + y^2)^2$
Step 1:

$(x^4+y^4)$
Step 2:

$x^2+2x^2y^2+y^2$
Step 3:

$(x^2-y^2)^2+(2xy)^2$

The proof is correct.
Step 1 has an error.
Step 2 has an error.
Step 3 has an error.

Grade 12 Polynomials and Rational Expressions

Which of the following is a factor of the polynomial

$x^4 + 3x^2 - 17x + 6$ ?

x + 2
x + 3
x - 2
x - 3

Grade 12 Polynomials and Rational Expressions CCSS: HSN-CN.C.9

What is the maximum number of purely imaginary roots that the polynomial

$x^2-6-x^4-x^6$ can have?

Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.C.4

Is the proof correct? If not, identify the first step that has an error.

$"Prove: " \ (a+b)^2 = a^2 + 2ab + b^2$

Left Side:

$(a+b)^2$
Step 1:

$(a+b)(a+b)$
Step 2:

$a^2+ab+ab+b^2$
Step 3:

$a^2+2ab+b^2$

The proof is correct.
Step 1 has an error.
Step 2 has an error.
Step 3 has an error.

Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.D.6

What is the remainder of

$5x^2+2x-8$ divided by

$x-3$ ?

$-8$
$x-53$
$43$
$51$

Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.D.6

What is

$4x^2-6x+2$ divided by

$(2x-1) ?$

$(x-2)+2/(2x-1)$
$(2x-2)+2/(2x-1)$
$(2x-2)$
$(4x-1)+2/(2x-1)$

Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.D.6

What is the remainder of

$x^2-x-2$ divided by

$x+6$ ?

$-2$
$40$
$x-40$
$x+2$

Grade 12 Polynomials and Rational Expressions

$f(x)=2x^5+x^3-3x$ is .

even
odd
both even and odd
neither even nor odd

Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.D.6

What is

$13x^2+5x-8$ divided by

$(x+8) ?$

$(13x-104)+874/(x+8)$
$(13x-99)+784$
$(13x-8)$
$(13x-99)+784/(x+8)$

Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.D.6

What is

$x^2+14x-6$ divided by

$(x+7) ?$

$(x+7)+8/(x+7)$
$(x+7)-55/(x+7)$
$(x+7)-20/(x+7)$
$(x+7)$

Grade 12 Polynomials and Rational Expressions CCSS: HSN-CN.C.9

How many roots does the polynomial

$x^2-6-x^4-x^6$ have?

Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.D.6

What is the remainder of

$4x^2+2x-5$ divided by

$x-2$ ?

$-2$
$x-15$
$15$
$x+15$

Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.D.6

What is

$3x^2-7x-6$ divided by

$(x-3) ?$

$(3x+2)+6/(x-3)$
$3x+2$
$x-3$
$3x^2-8x-9$

Grade 12 Polynomials and Rational Expressions

Evaluate

$3x - 4y^2$ when x = (-2) and y = 4 (10-12).

-28
-4
-262
-38

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Twelfth Grade (Grade 12) Polynomials and Rational Expressions Questions