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Eleventh Grade (Grade 11) Polynomials and Rational Expressions Questions

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Grade 11 Polynomials and Rational Expressions

Multiply the polynomials using the FOIL method:

$(-2x-2y)(7x+y)$ .

$-14x^2+6xy+2y^2$
$-14x^2-16xy-2y^2$
$14x^2-16xy-2y^2$
$14x^2-16xy+2y^2$

Grade 11 Polynomials and Rational Expressions

Multiply the binomials and use the FOIL method:

$(5x-4y)(x+8y)$ .

$5x^2-36xy-32y^2$
$5x^2+40xy+32y^2$
$5x^2+36xy-32y^2$
$5x^2-40xy-32y^2$

Grade 11 Polynomials and Rational Expressions

State the restrictions on x in the expression

$((x+7)(x-1))/((x-4)(x+7))$ .

$x ne 4$
$x ne 1, x ne 4$
$x ne -7, x ne 4$
$x ne -7, x ne 1, x ne 4$

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

Use synthetic division to divide the polynomials:

$(x^2-5x-24)/(x-8)$ .

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

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.A.1

Which polynomial has the factorization

$(x - 10)(x^2 + 10x + 100)?$

$x^3 - 1000$
$x^3 - 100$
$x^3 + 100$
$x^3 + 1000$

Grade 11 Polynomials and Rational Expressions

Find the values that make the rational expression undefined.

$(x^2+3)/(x(x+5)$

$x=0$ or $-5$
$x=0$ or $7$
$x=0$ or $5$
$x=2$ or $4$

Grade 11 Polynomials and Rational Expressions

Find the Greatest Common Factor (GCF) of the terms of the given polynomial.

Given:

$8x^6 + 32x^3$

$x^3$
$8x^3$
$4x^3$
$8x^6$

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

Use synthetic division to divide the polynomials:

$(3m^2+16m-12)/(m+6)$ .

$3m-2$
$m-2$
$3m-2+(8)/(m-2)$
$3m+2$

Grade 11 Polynomials and Rational Expressions

What is the equation for the vertical asymptote of

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

$x=-1$
$x=-2$
$x=1$
$x=2$

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

Use synthetic division to divide the polynomials:

$(x^3+64)/(x+4)$ .

$x^2+16$
$x^2-16x+4$
$x^2-4x+16$
$x^2-4$

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

Simplify the expression

$(x-7)/(x^2-x-42)$ .

$1/(x+7), \ x!=-6$
$1/(x+6), \ x!= 7$
$x+7, \ x!= -6, 7$
$x+6, \ x!= -6, 7$

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.7

Divide and simplify the expression

$(x-2)/(5x+10)-:(3)/(3x+6)$ .

$5/(x-2), \ \ x!=-2$
$(3(x-2))/(15(x+2)^2)$
$(x-2)/5, \ \ x!=-2$
$(3(x-2))/(15(x+2))$

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

Use synthetic division to divide the polynomials:

$(x^2-14x+45)/(x-5)$ .

$x+9$
$9-x$
$x+5$
$x-9$

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

Factor.

$27x^3 + 64$

$(3x-4)(9x^2 + 12x + 16)$
$(3x + 4)(9x^2 - 12x + 16)$
$(3x+4)(9x^2 + 12x + 16)$
$"Can't factor further"$

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.7

$(x^2-64)/(x(x+8))*x/(x-8)$ =

$1 , \ \ x!=-8,0,8$
$(x^3-64x)/((x+8)(x-8)), \ \ x!= 0$
$(x^2-8)/(x^2-64), \ \ x!= 0$

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

Simplify the expression

$(7x^2-63)/(x+3)$ .

$(x+3)/7, \ x!=-3$
$(7x^2-9)/(x), \ x!=-3$
$7(x+3), \ x!=-3$
$7(x-3), \ x!=-3$

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.7

Add and simplify.

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

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

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.7

Add and simplify.

$\ (x+2)/(x-1)+(x-3)/(x-1)$

$(x^2-x-6)/(x^2-2x+1)$
$(2x-1)/(x-1)$
$x^2-x-6$
$-1/2x$

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.7

Subtract and simplify the expression

$x/(x+2)-3/(x-2)$ .

$((x-6)(x+1))/(x^2-4)$
$(x-3)/(x+2)$
$(x-3)/(x^2-4)$
$(x+3)/(x+2)$

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

Use long division or synthetic division to divide the polynomials:

$(4x^2-9) -:(2x+3).$

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

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Eleventh Grade (Grade 11) Polynomials and Rational Expressions Questions