Exam 5: Polynomials: Factoring

Provide an appropriate response. -In factoring a trinomial in $\mathrm{z}$ as $(\mathrm{z}+\mathrm{a})(\mathrm{z}+\mathrm{b})$ , what must be true of $\mathrm{a}$ and $\mathrm{b}$ , if the coefficient of the last term of the trinomial is positive?

(Essay)

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Question 141

Find the $x$ -intercepts of the graph of the equation. (The grids are intentionally not included.) - $y=2 x^{2}-7 x-49$ $Find the x -intercepts of the graph of the equation. (The grids are intentionally not included.) - y=2 x^{2}-7 x-49$

(Multiple Choice)

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Question 142

Factor by grouping. - $2 x^{3}-18 x^{2}-5 x+45$

(Multiple Choice)

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Question 143

Factor completely. - $36 \mathrm{~m}^{2}-\frac{25}{16}$

(Multiple Choice)

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Question 144

Factor. - $16-72 x+81 x^{2}$

(Multiple Choice)

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Question 145

Factor. - $4 x^{3}+4 x^{2}-24 x$

(Multiple Choice)

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Question 146

Provide an appropriate response. -Explain the error in the following: $x^{2}+2 x-15=(x-5)(x+3)$

(Essay)

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Question 147

Factor completely. - $10 x^{4}+21 x^{2}+9$

(Multiple Choice)

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Question 148

Solve using the principle of zero products. - $x(2 x+4)=0$

(Multiple Choice)

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Question 149

Factor completely. - $45 x^{2}-60 x+20$

(Multiple Choice)

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Question 150

Solve the problem. -The height of a box is 10 inches. The length is three inches more than the width. Find the width if the volume is 400 cubic inches.

(Multiple Choice)

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Question 151

Factor. - $6 x^{2}-5 x t-4 t^{2}$

(Multiple Choice)

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Question 152

Factor by grouping. - $x^{3}-7 x^{2}-10 x+70$

(Multiple Choice)

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Question 153

Factor. - $12 z^{3}+7 z^{2}-12 z$

(Multiple Choice)

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Question 154

Factor completely. - $49 x^{2}+84 x+36$

(Multiple Choice)

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Question 155

Factor by grouping. - $x^{3}-3 x^{2}+4 x-12$

(Multiple Choice)

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Question 156

Factor completely. - $4 y^{4}-9$

(Multiple Choice)

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Question 157

Factor completely. - $16 x^{2}-25$

(Multiple Choice)

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Question 158

Factor completely. - $25 m^{2}-\frac{25}{9}$

(Multiple Choice)

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Question 159

Solve the problem. -Within a group of $n$ people, the number of possible handshakes, $N$ , is given by $\mathrm{N}=\frac{1}{2}\left(\mathrm{n}^{2}-\mathrm{n}\right)$ . How many handshakes are possible at a meeting if 10 people are present?

(Multiple Choice)

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Question 160

Provide an appropriate response. -In factoring a trinomial in $\mathrm{z}$ as $(\mathrm{z}+\mathrm{a})(\mathrm{z}+\mathrm{b})$ , what must be true of $\mathrm{a}$ and $\mathrm{b}$ , if the coefficient of the last term of the trinomial is positive?

Find the $x$ -intercepts of the graph of the equation. (The grids are intentionally not included.) - $y=2 x^{2}-7 x-49$ $Find the x -intercepts of the graph of the equation. (The grids are intentionally not included.) - y=2 x^{2}-7 x-49$

Factor by grouping. - $2 x^{3}-18 x^{2}-5 x+45$

Factor completely. - $36 \mathrm{~m}^{2}-\frac{25}{16}$

Factor. - $16-72 x+81 x^{2}$

Factor. - $4 x^{3}+4 x^{2}-24 x$

Provide an appropriate response. -Explain the error in the following: $x^{2}+2 x-15=(x-5)(x+3)$

Factor completely. - $10 x^{4}+21 x^{2}+9$

Solve using the principle of zero products. - $x(2 x+4)=0$

Factor completely. - $45 x^{2}-60 x+20$

Solve the problem. -The height of a box is 10 inches. The length is three inches more than the width. Find the width if the volume is 400 cubic inches.

Factor. - $6 x^{2}-5 x t-4 t^{2}$

Factor by grouping. - $x^{3}-7 x^{2}-10 x+70$

Factor. - $12 z^{3}+7 z^{2}-12 z$

Factor completely. - $49 x^{2}+84 x+36$

Factor by grouping. - $x^{3}-3 x^{2}+4 x-12$

Factor completely. - $4 y^{4}-9$

Factor completely. - $16 x^{2}-25$

Factor completely. - $25 m^{2}-\frac{25}{9}$

Solve the problem. -Within a group of $n$ people, the number of possible handshakes, $N$ , is given by $\mathrm{N}=\frac{1}{2}\left(\mathrm{n}^{2}-\mathrm{n}\right)$ . How many handshakes are possible at a meeting if 10 people are present?

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Rational Expressions and Equations

Systems of Equations

Radical Expressions and Equations

Quadratic Equations

Equations of Lines and Simplifying Radical Expressions

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Exam 5: Polynomials: Factoring

Provide an appropriate response. -In factoring a trinomial in z\mathrm{z}z as (z+a)(z+b)(\mathrm{z}+\mathrm{a})(\mathrm{z}+\mathrm{b})(z+a)(z+b) , what must be true of a\mathrm{a}a and b\mathrm{b}b , if the coefficient of the last term of the trinomial is positive?

Find the xxx -intercepts of the graph of the equation. (The grids are intentionally not included.) - y=2x2−7x−49y=2 x^{2}-7 x-49y=2x2−7x−49

Factor by grouping. - 2x3−18x2−5x+452 x^{3}-18 x^{2}-5 x+452x3−18x2−5x+45

Factor completely. - 36 m2−251636 \mathrm{~m}^{2}-\frac{25}{16}36 m2−1625​

Factor. - 16−72x+81x216-72 x+81 x^{2}16−72x+81x2

Factor. - 4x3+4x2−24x4 x^{3}+4 x^{2}-24 x4x3+4x2−24x

Provide an appropriate response. -Explain the error in the following: x2+2x−15=(x−5)(x+3)x^{2}+2 x-15=(x-5)(x+3)x2+2x−15=(x−5)(x+3)

Factor completely. - 10x4+21x2+910 x^{4}+21 x^{2}+910x4+21x2+9

Solve using the principle of zero products. - x(2x+4)=0x(2 x+4)=0x(2x+4)=0

Factor completely. - 45x2−60x+2045 x^{2}-60 x+2045x2−60x+20

Solve the problem. -The height of a box is 10 inches. The length is three inches more than the width. Find the width if the volume is 400 cubic inches.

Factor. - 6x2−5xt−4t26 x^{2}-5 x t-4 t^{2}6x2−5xt−4t2

Factor by grouping. - x3−7x2−10x+70x^{3}-7 x^{2}-10 x+70x3−7x2−10x+70

Factor. - 12z3+7z2−12z12 z^{3}+7 z^{2}-12 z12z3+7z2−12z

Factor completely. - 49x2+84x+3649 x^{2}+84 x+3649x2+84x+36

Factor by grouping. - x3−3x2+4x−12x^{3}-3 x^{2}+4 x-12x3−3x2+4x−12

Factor completely. - 4y4−94 y^{4}-94y4−9

Factor completely. - 16x2−2516 x^{2}-2516x2−25

Factor completely. - 25m2−25925 m^{2}-\frac{25}{9}25m2−925​

Solve the problem. -Within a group of nnn people, the number of possible handshakes, NNN , is given by N=12(n2−n)\mathrm{N}=\frac{1}{2}\left(\mathrm{n}^{2}-\mathrm{n}\right)N=21​(n2−n) . How many handshakes are possible at a meeting if 10 people are present?

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Rational Expressions and Equations

Systems of Equations

Radical Expressions and Equations

Quadratic Equations

Equations of Lines and Simplifying Radical Expressions

Filters

Provide an appropriate response. -In factoring a trinomial in $\mathrm{z}$ as $(\mathrm{z}+\mathrm{a})(\mathrm{z}+\mathrm{b})$ , what must be true of $\mathrm{a}$ and $\mathrm{b}$ , if the coefficient of the last term of the trinomial is positive?

Find the $x$ -intercepts of the graph of the equation. (The grids are intentionally not included.) - $y=2 x^{2}-7 x-49$ $Find the x -intercepts of the graph of the equation. (The grids are intentionally not included.) - y=2 x^{2}-7 x-49$

Factor by grouping. - $2 x^{3}-18 x^{2}-5 x+45$

Factor completely. - $36 \mathrm{~m}^{2}-\frac{25}{16}$

Factor. - $16-72 x+81 x^{2}$

Factor. - $4 x^{3}+4 x^{2}-24 x$

Provide an appropriate response. -Explain the error in the following: $x^{2}+2 x-15=(x-5)(x+3)$

Factor completely. - $10 x^{4}+21 x^{2}+9$

Solve using the principle of zero products. - $x(2 x+4)=0$

Factor completely. - $45 x^{2}-60 x+20$

Factor. - $6 x^{2}-5 x t-4 t^{2}$

Factor by grouping. - $x^{3}-7 x^{2}-10 x+70$

Factor. - $12 z^{3}+7 z^{2}-12 z$

Factor completely. - $49 x^{2}+84 x+36$

Factor by grouping. - $x^{3}-3 x^{2}+4 x-12$

Factor completely. - $4 y^{4}-9$

Factor completely. - $16 x^{2}-25$

Factor completely. - $25 m^{2}-\frac{25}{9}$

Solve the problem. -Within a group of $n$ people, the number of possible handshakes, $N$ , is given by $\mathrm{N}=\frac{1}{2}\left(\mathrm{n}^{2}-\mathrm{n}\right)$ . How many handshakes are possible at a meeting if 10 people are present?