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Eleventh Grade (Grade 11) Polynomials and Rational Expressions Questions

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Grade 11 Polynomials and Rational Expressions

Find the LCD for the rational expression

$5/(2y)+4/(3y^2)$ .

$3y^2$
$2y^2$
$y^2$
$6y^2$

Grade 11 Polynomials and Rational Expressions

What is the dividend in the polynomial division problem

$(x^7+x^5-10x^3+12)/ (x+2)$ ?

$x+2$
$x^7+x^5−10x^3+12$
$x^7+x^5$
$-10x^3$

Grade 11 Polynomials and Rational Expressions

$4k^2 - 100$

$(2k + 10)(2k + 10)$
$(2k -10)(2k - 10)$
$(2k + 10)(2k - 10)$
$(4k + 10)(k -10)$

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.B.2

Given polynomial

$q(x)$ , such that

$q(4)=0$ , what is a possible answer for

$q(x)$ divided by

$x-4 ?$

$3x^2 + 3 - 4/(x-4)$
$x-10$
$x^2 + 1 + 2/(x-4)$
$x + 2 - 4/(x-4)$

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5

Approximate

$1.92^7$ with the Binomial Theorem, using only the first 3 terms of the expansion, by rewriting

$1.92$ as

$2 - 0.08$ .

92.16
96.4608
96.17408
4.3008

Grade 11 Polynomials and Rational Expressions

Find the LCD for the rational expression

$5/(x+6)+3/(x+3)$ .

$x+3$
$(x+6)(x+3)$
$(x+6)$
$(x-6)(x-3)$

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.B.2

For polynomial

$f(x)$ , if

$f(0)=0$ , which of the following MUST be a factor of

$f(x) ?$

$x$
$x-4$
$x-1$
$x+1$

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.4

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

$"Prove: " x^4 - y^4 = (x-y)(x+y)(x^2+y^2)$

$"Right Side: " (x-y)(x+y)(x^2+y^2)$

$"Step 1: " (x-y)(x^3 + xy^2 + x^2y + y^3)$

$"Step 2: " (x-y)(x^3 + y^3)$

$"Step 4: " x^4 - y^4$

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

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6

Simplify.

$(x^2y-x^5y^7+x^8y^4)/(x^2y)$

$1-x^3y^6+x^6y^3, \ \ \ \ x,y!=0$
$x^4y^2-x^7y^8+x^10y^5, \ \ \ \ x,y!=0$
$x^6y^3-x^3y^6-1, \ \ \ \ x,y!=0$
$xy-x^3y^6+x^6y^3, \ \ \ \ x,y!=0$

Grade 11 Polynomials and Rational Expressions

Factor:

$a^2x+3ax+2x-a^2y-3ay-2y$

$(y-x)(a+3)$
$(x-y)(a-5)(2)$
$(x-y)(a+2)(a+1)$
$(y-x)(2-a)(1-a)$

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.4

Sam claims that for any two consecutive integers, the difference of the larger number squared and the smaller number squared is always odd. He writes an identity he says proves this, which is

$(n+1)^2 - n^2 = 2n-1$ . Is this true? If not, choose the reason why.

It is true.
$2n-1$ is not always an odd number.
It is not an identity.
It is only true for some numbers.

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5

Expand the binomial

$(x-3)^4$ using Pascal's Triangle.

$x^4+12x^3+54x^2+108x+81$
$x^4-12x^3+54x^2-108x+81$
$x^4-12x^3-54x^2-108x-81$
$x^4-12x^3+18x^2-36x+81$

Grade 11 Polynomials and Rational Expressions

Write the dividend of the polynomial division problem

$(x^2-5x-5x^3+x^4)-: (5+x)$ in standard form.

$-5x^3+x^4+x^2-5x$
$x^4-5x^3+x^2-5x$
$x^2+x^4-10x^3$
$-5x+x^4-5x^3+x^2$

Grade 11 Polynomials and Rational Expressions

What type of divisor must be used to divide polynomials using synthetic division?

Trinomial Divisor
Binomial Divisor
Linear Divisor
Polynomial Divisor

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.4

Which of the following is a correct polynomial identity that illustrates the statement "the sum of any integer and its value squared is an even number"?

$n^2 + n = 2n$
$n^2 + n = n/2$
$n^2 + n = n(n+1)$
$n^2 + n = n^2(1+n)$

Grade 11 Polynomials and Rational Expressions

The common denominator for the problem

$8/(x+1) + 10/(x+2)$ is

$(x+1) (x+2)$ .

True
False

Grade 11 Polynomials and Rational Expressions

Factor completely.

$p^5+2p^2-p^3-2$

$(p^3+2)(p^2-1)$
$(p^3+2)(p+1)(p-1)$
$(p^3+2)(p-1)^2$
$(p^3+2)$

Grade 11 Polynomials and Rational Expressions

Divide:

$(x^4+2x^3+2x^2+2x+1)/(x+1)$

$x^3+x^2+x+1$
$x^3+x^2+1$
$x^2+x+1$
$x^3+x^2+x-1$

Grade 11 Polynomials and Rational Expressions

For which values of

$x$ is

$sqrt(9-x^2)/(3-x)$ real?

$-3 < x < 3$
$-3 < x <= 3$
$-3 <= x <= 3$
$-3 <= x < 3$

Grade 11 Polynomials and Rational Expressions

Find the LCD for the rational expressions

$1/(4x+11) and x/(16x^2-121)$ .

$(4x+11)(4x+11)$
$(4x+11)(4x-11)$
$(4x-11)(4x-11)$
$(4x+11i)(4x-11i)$

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Eleventh Grade (Grade 11) Polynomials and Rational Expressions Questions