Simplify the polynomial by combining like terms. -\[\begin{array} { r } 5 x ^ { 5 } + 5 x ^ { 2 } \\ + \left( 2 x ^ { 5 } - 8 x ^ { 2 } \right) \\ \hline \end{array}\]

A) $7 x ^ { 10 } - 3 x ^ { 4 }$ B) $4 x ^ { 14 }$ C) $7 x ^ { 5 } - 3 x ^ { 2 }$ D) $4 \mathrm { x } ^ { 7 }$ A) $7 x ^ { 10 } - 3 x ^ { 4 }$ B) $4 x ^ { 14 }$ C) $7 x ^ { 5 } - 3 x ^ { 2 }$ D) $4 \mathrm { x } ^ { 7 }$

Exam 5: Polynomials and Polynomial Functions

Solve. -The outside dimensions of a picture frame are $38 \mathrm {~cm}$ and $31 \mathrm {~cm}$ . The area of the picture inside the frame is 690 square centimeters. Find the width of the frame. $Solve. -The outside dimensions of a picture frame are 38 \mathrm {~cm} and 31 \mathrm {~cm} . The area of the picture inside the frame is 690 square centimeters. Find the width of the frame.$

(Multiple Choice)

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Question 301

Factor the trinomial. - $15 x ^ { 2 } + 8 x - 16$

(Multiple Choice)

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Question 302

Evaluate the polynomial function. -If $f ( x ) = x ^ { 2 } + 9 x + 4$ , find $f ( a )$

(Multiple Choice)

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Question 303

Find all positive and negative integers b such that the trinomial is factorable. - $x ^ { 2 } + b x + 7$

(Multiple Choice)

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Question 304

Multiply. Assume that variables used as exponents represent positive integers. - $\left( \mathrm { x } ^ { \mathrm { a } } + 7 \right) \left( \mathrm { x } ^ { 2 \mathrm { a } } - 9 \right)$

(Multiple Choice)

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Question 305

Multiply. - $( 5 x + 11 y ) ^ { 2 }$

(Multiple Choice)

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Question 306

Simplify the polynomial by combining like terms. - $13 y ^ { 2 } + 6 y ^ { 2 }$

(Multiple Choice)

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Question 307

Use substitution to factor the polynomial completely. - $9 x ^ { 6 } + 6 x ^ { 3 } - 8$

(Multiple Choice)

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Question 308

Solve. -The area $A$ of a trapezoid with bases $b$ and $B$ and height $h$ is given by the formula $A = \frac { 1 } { 2 } b h + \frac { 1 } { 2 } B h . W r i t e$ an equivalent equation by factoring the expression $\frac { 1 } { 2 } b h + \frac { 1 } { 2 } \mathrm { Bh }$ .

(Multiple Choice)

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Question 309

Factor the polynomial completely. - $7 ( x - 3 ) ^ { 2 } - 76 ( x - 3 ) - 11$

(Multiple Choice)

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Question 310

Solve. -The longer leg of a right triangle is 14 inches longer than the other leg. Find the length of the two legs if the hypotenuse is 26 inches.

(Multiple Choice)

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Question 311

Subtract. - $\left( 8 x ^ { 7 } + 8 x ^ { 5 } - 16 \right) - \left( - 18 x ^ { 5 } + 4 x ^ { 7 } + 16 \right)$

(Multiple Choice)

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Question 312

Find the GCF of the list of monomials. -5, 15

(Multiple Choice)

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Question 313

Simplify the polynomial by combining like terms. - 5+5 + 2-8

(Multiple Choice)

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Question 314

Solve the equation. - $5 x ( 8 x - 5 ) = 0$

(Multiple Choice)

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Question 315

Factor the polynomial by grouping. - $a c + 5 a - 2 c - 10$

(Multiple Choice)

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Question 316

Subtract. - $\left( 3 x ^ { 7 } + 7 x ^ { 6 } + 5 \right) - \left( 6 x ^ { 7 } + 19 x ^ { 6 } + 14 \right)$

(Multiple Choice)

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Question 317

Fill in the blank with one of the words or phrases listed below. -A is a polynomial with three terms.

(Multiple Choice)

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Question 318

Multiply. - $( x + 1 ) ( x + 11 )$

(Multiple Choice)

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Question 319

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = x ^ { 2 } + 7 x + 2 ; 3$

(Multiple Choice)

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Question 320

Factor the trinomial. - $15 x ^ { 2 } + 8 x - 16$

Evaluate the polynomial function. -If $f ( x ) = x ^ { 2 } + 9 x + 4$ , find $f ( a )$

Find all positive and negative integers b such that the trinomial is factorable. - $x ^ { 2 } + b x + 7$

Multiply. Assume that variables used as exponents represent positive integers. - $\left( \mathrm { x } ^ { \mathrm { a } } + 7 \right) \left( \mathrm { x } ^ { 2 \mathrm { a } } - 9 \right)$

Multiply. - $( 5 x + 11 y ) ^ { 2 }$

Simplify the polynomial by combining like terms. - $13 y ^ { 2 } + 6 y ^ { 2 }$

Use substitution to factor the polynomial completely. - $9 x ^ { 6 } + 6 x ^ { 3 } - 8$

Solve. -The area $A$ of a trapezoid with bases $b$ and $B$ and height $h$ is given by the formula $A = \frac { 1 } { 2 } b h + \frac { 1 } { 2 } B h . W r i t e$ an equivalent equation by factoring the expression $\frac { 1 } { 2 } b h + \frac { 1 } { 2 } \mathrm { Bh }$ .

Factor the polynomial completely. - $7 ( x - 3 ) ^ { 2 } - 76 ( x - 3 ) - 11$

Solve. -The longer leg of a right triangle is 14 inches longer than the other leg. Find the length of the two legs if the hypotenuse is 26 inches.

Subtract. - $\left( 8 x ^ { 7 } + 8 x ^ { 5 } - 16 \right) - \left( - 18 x ^ { 5 } + 4 x ^ { 7 } + 16 \right)$

Find the GCF of the list of monomials. -5, 15

Simplify the polynomial by combining like terms. - 5+5 + 2-8

Solve the equation. - $5 x ( 8 x - 5 ) = 0$

Factor the polynomial by grouping. - $a c + 5 a - 2 c - 10$

Subtract. - $\left( 3 x ^ { 7 } + 7 x ^ { 6 } + 5 \right) - \left( 6 x ^ { 7 } + 19 x ^ { 6 } + 14 \right)$

Fill in the blank with one of the words or phrases listed below. -A is a polynomial with three terms.

Multiply. - $( x + 1 ) ( x + 11 )$

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = x ^ { 2 } + 7 x + 2 ; 3$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

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Exam 5: Polynomials and Polynomial Functions

Solve. -The outside dimensions of a picture frame are 38 cm38 \mathrm {~cm}38 cm and 31 cm31 \mathrm {~cm}31 cm . The area of the picture inside the frame is 690 square centimeters. Find the width of the frame.

Factor the trinomial. - 15x2+8x−1615 x ^ { 2 } + 8 x - 1615x2+8x−16

Evaluate the polynomial function. -If f(x)=x2+9x+4f ( x ) = x ^ { 2 } + 9 x + 4f(x)=x2+9x+4 , find f(a)f ( a )f(a)

Find all positive and negative integers b such that the trinomial is factorable. - x2+bx+7x ^ { 2 } + b x + 7x2+bx+7

Multiply. Assume that variables used as exponents represent positive integers. - (xa+7)(x2a−9)\left( \mathrm { x } ^ { \mathrm { a } } + 7 \right) \left( \mathrm { x } ^ { 2 \mathrm { a } } - 9 \right)(xa+7)(x2a−9)

Multiply. - (5x+11y)2( 5 x + 11 y ) ^ { 2 }(5x+11y)2

Simplify the polynomial by combining like terms. - 13y2+6y213 y ^ { 2 } + 6 y ^ { 2 }13y2+6y2

Use substitution to factor the polynomial completely. - 9x6+6x3−89 x ^ { 6 } + 6 x ^ { 3 } - 89x6+6x3−8

Factor the polynomial completely. - 7(x−3)2−76(x−3)−117 ( x - 3 ) ^ { 2 } - 76 ( x - 3 ) - 117(x−3)2−76(x−3)−11

Solve. -The longer leg of a right triangle is 14 inches longer than the other leg. Find the length of the two legs if the hypotenuse is 26 inches.

Subtract. - (8x7+8x5−16)−(−18x5+4x7+16)\left( 8 x ^ { 7 } + 8 x ^ { 5 } - 16 \right) - \left( - 18 x ^ { 5 } + 4 x ^ { 7 } + 16 \right)(8x7+8x5−16)−(−18x5+4x7+16)

Find the GCF of the list of monomials. -5, 15

Simplify the polynomial by combining like terms. - 5+5 + 2-8

Solve the equation. - 5x(8x−5)=05 x ( 8 x - 5 ) = 05x(8x−5)=0

Factor the polynomial by grouping. - ac+5a−2c−10a c + 5 a - 2 c - 10ac+5a−2c−10

Subtract. - (3x7+7x6+5)−(6x7+19x6+14)\left( 3 x ^ { 7 } + 7 x ^ { 6 } + 5 \right) - \left( 6 x ^ { 7 } + 19 x ^ { 6 } + 14 \right)(3x7+7x6+5)−(6x7+19x6+14)

Fill in the blank with one of the words or phrases listed below. -A is a polynomial with three terms.

Multiply. - (x+1)(x+11)( x + 1 ) ( x + 11 )(x+1)(x+11)

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - P(x)=x2+7x+2;3P ( x ) = x ^ { 2 } + 7 x + 2 ; 3P(x)=x2+7x+2;3

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Factor the trinomial. - $15 x ^ { 2 } + 8 x - 16$

Evaluate the polynomial function. -If $f ( x ) = x ^ { 2 } + 9 x + 4$ , find $f ( a )$

Find all positive and negative integers b such that the trinomial is factorable. - $x ^ { 2 } + b x + 7$

Multiply. Assume that variables used as exponents represent positive integers. - $\left( \mathrm { x } ^ { \mathrm { a } } + 7 \right) \left( \mathrm { x } ^ { 2 \mathrm { a } } - 9 \right)$

Multiply. - $( 5 x + 11 y ) ^ { 2 }$

Simplify the polynomial by combining like terms. - $13 y ^ { 2 } + 6 y ^ { 2 }$

Use substitution to factor the polynomial completely. - $9 x ^ { 6 } + 6 x ^ { 3 } - 8$

Factor the polynomial completely. - $7 ( x - 3 ) ^ { 2 } - 76 ( x - 3 ) - 11$

Subtract. - $\left( 8 x ^ { 7 } + 8 x ^ { 5 } - 16 \right) - \left( - 18 x ^ { 5 } + 4 x ^ { 7 } + 16 \right)$

Solve the equation. - $5 x ( 8 x - 5 ) = 0$

Factor the polynomial by grouping. - $a c + 5 a - 2 c - 10$

Subtract. - $\left( 3 x ^ { 7 } + 7 x ^ { 6 } + 5 \right) - \left( 6 x ^ { 7 } + 19 x ^ { 6 } + 14 \right)$

Multiply. - $( x + 1 ) ( x + 11 )$

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = x ^ { 2 } + 7 x + 2 ; 3$