Math 2 Factoring Practice PDF
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Jawad Berro
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This document includes various math problems related to factoring. It covers factoring with a common factor, area models for factoring, and some problems related to sketching the graph of a function, which are commonly found as secondary school math exercises.
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# Math 2 ## GCF Factoring ### Factor the common factor out of each expression. 1. 30x<sup>4</sup> - 9x - 6 3(10x<sup>3</sup> - 3x - 2) 2. 27x<sup>2</sup> - 9x 9x(3x - 1) 3. 18x<sup>3</sup> + 3x<sup>2</sup> + 18x 3x(6x<sup>2</sup> + x<sup>2</sup> + 6) 4. 14x<sup>2</sup> + 49x + 28...
# Math 2 ## GCF Factoring ### Factor the common factor out of each expression. 1. 30x<sup>4</sup> - 9x - 6 3(10x<sup>3</sup> - 3x - 2) 2. 27x<sup>2</sup> - 9x 9x(3x - 1) 3. 18x<sup>3</sup> + 3x<sup>2</sup> + 18x 3x(6x<sup>2</sup> + x<sup>2</sup> + 6) 4. 14x<sup>2</sup> + 49x + 28 7(2x<sup>2</sup> + 7x + 4) 5. 28x<sup>5</sup> - 12x<sup>4</sup> 4x<sup>2</sup>(7x - 3) 6. 2n<sup>5</sup> - 2n<sup>3</sup> + 2n<sup>2</sup> 2n<sup>2</sup>(n<sup>3</sup> - n + 1) 7. 6n<sup>5</sup> - 8n<sup>2</sup> + 6n 2n(3n<sup>4</sup> - 4n + 3) 8. x<sup>2</sup> + 5x<sup>3</sup> + 5x<sup>4</sup> x<sup>2</sup>(1 + 5x + 5x<sup>2</sup>) 9. 16x<sup>3</sup> + 56x + 80 8(2x<sup>3</sup> + 7x + 10) 10. 32n<sup>4</sup> + 8n<sup>3</sup> 8n<sup>3</sup>(4n + 1) ## Factoring Practice Day 2 ### Draw an AREA MODEL and DIAMOND to Factor each completely. 1. x<sup>2</sup> + 6x - 16 (x - 2)(x + 8) 2. x<sup>2</sup> + 13x + 36 (x + 4)(x + 9) 3. x<sup>2</sup> + 18x + 80 (x + 8)(x + 10) 4. x<sup>2</sup> + 12x + 20 (x + 10)(x + 2) 5. x<sup>2</sup> - 9x + 20 (x - 5)(x - 4) 6. x<sup>2</sup> + 18x + 77 (x + 11)(x + 7) 7. x<sup>2</sup> - 20x + 64 (x - 16)(x - 4) 8. x<sup>2</sup> - 6x - 72 (x - 12)(x + 6) ## Factoring: with a Leading Coefficient ### Draw an AREA MODEL and DIAMOND to Factor each completely. 1. 3x<sup>2</sup> + 20x - 7 (3x - 1)(x + 7) 2. 5x<sup>2</sup> - 24x - 5 (x - 5)(5x + 1) 3. 2x<sup>2</sup> - 7x - 9 (x + 1)(2x - 9) 4. 3x<sup>2</sup> + 13x + 14 (3x + 7)(x + 2) 5. 7x<sup>2</sup> - 3x - 10 (x + 1)(7x - 10) 6. 2x<sup>2</sup> + 7x + 5 (x + 1)(2x + 5) ## Sketch the graph of each function. 1. y = x<sup>2</sup> + 6x + 5 2. y = x<sup>2</sup> + 8x + 15 3. y = x<sup>2</sup> + 6x + 8 4. y = x<sup>2</sup> + 4x + 3 ## Area Models ### Draw an AREA MODEL to represent the problem below. Write the final answer in Standard Form (highest exponent term first) 1. (6x + 8)(5x + 3) 30x<sup>2</sup> + 58x + 24 2. (8x + 2)(5x + 4) 40x<sup>2</sup> + 42x + 8 3. (2x + 1)(5x + 5) 10x<sup>2</sup> + 15x + 5 4. (4x - 1)(x + 3) 4x<sup>2</sup> + 11x -3 5. (3x + 2)(2x<sup>2</sup> - 3x + 5) 6x<sup>3</sup> - 5x<sup>2</sup> + 9x + 10 6. (5x + 2)(5x<sup>2</sup> + 4x - 2) 25x<sup>3</sup> + 30x<sup>2</sup> - 2x - 4 ## Intro To Factoring ### Draw an AREA MODEL to Factor each completely. 1. x<sup>2</sup> - 2x - 24 (x - 6)(x + 4) 2. x<sup>2</sup> - 5x + 6 (x - 3)(x - 2) 3. x<sup>2</sup> - 14x + 45 (x - 9)(x - 5) 4. x<sup>2</sup> - 4x - 12 (x - 6)(x + 2) 5. x<sup>2</sup> - 15x + 56 (x - 8)(x - 7) 6. x<sup>2</sup> - 2x - 8 (x - 4)(x + 2) ## Guided Notes **Example 2** **Factor: x<sup>2</sup> + 7x - 30** **Example 3** **Factor: x<sup>2</sup> - 15x + 56** **Try:** 1. x<sup>2</sup> + 6x - 40 (x + 10)(x - 4) 2. (x - 3)(x + 7) x<sup>2</sup> + 4x - 21 3. x<sup>2</sup> + 6x - 27 (x + 9)(x - 3) 4. x<sup>2</sup> + 11x + 28 (x + 4)(x + 7) 5. x<sup>2</sup> + 2x - 15 (x + 5)(x - 3) 6. x<sup>2</sup> - 2x - 80 (x - 10)(x + 8) ## Factoring: GCF & Area Models ### Factor each completely. 1. 5p<sup>2</sup> + 25p - 30 5(p<sup>2</sup> + 5p - 6) 5(p + 6)(p - 1) 2. 2b<sup>2</sup> - 18b + 36 2(b<sup>2</sup> - 9b + 18) 2(b - 6)(b - 3) 3. 2r<sup>2</sup> + 14r + 28 2(r<sup>2</sup> + 7r + 14) 2(r + 2)(r + 7) 4. 15x<sup>2</sup> + 42x - 9 3(5x<sup>2</sup> + 14x - 3) 3(5x - 1)(x + 3) 5. 18p<sup>2</sup> + 48p - 40 2(9p<sup>2</sup> + 24p - 20) 2(3p - 2)(3p + 10) 6. 16r<sup>2</sup> + 16r - 60 (4r - 6)(4r + 10) 7. 6v<sup>2</sup> - 42v - 48 6(v<sup>2</sup> - 7v - 8) 6(v - 8)(v + 1) 8. 3n<sup>2</sup> + 30n + 27 9. 18b<sup>2</sup> + 6b - 24 (18b - 24)(b + 1) 10. 15v<sup>2</sup> - 40v + 25
