Use all available methods to factor each of the following polynomials completely, and then sketch the graph of each one. See Example 1. 9. f(x)= x° +4x +x' - 10x² – 4x+8 10. p(x)= 2x' -x² - 8x-5 %3D %3D 11. s(x) = -x* +2x° +8x² – 10x – 15 12. f(x)=-x' +6x² – 12x +8 13. H(x)= x* - x' - 5x² +3x+6 14. h(x)=x -11x* +46x³ – 90x² +81x– 27 %3D 15. f(x)= 2x³ +11x² + 20x+ 12 16. g(x)= x* + 3x° – 5x² -21x-14 %3D Use all available methods to solve each polynomial equation. Use the Linear Factors Theorem to make sure you find the appropriate number of solutions, counting multiplicity. 17. x +4x* +x³ = 10x² +4x-8 18. x* +15 = 2x³ +8x² – 10x %3D %3D 19. x* +x +3x² +5x-10 = 0 20. x -9x2 = 30– 28x %3D %3D 21. x +x* - x³ +7x² - 20x+12 = 0 22. 2x* - 5x3 – 2x² +15x = 0 %3D 23. x +15x +16 = x* + 15x²+16x 24. x - 5 = 5x² - 9x %3D Use all available methods (in particular, the Conjugate Roots Theorem, if applicable) to factor each of the following polynomials completely, making use of the given zero if one is given. See Example 2. 25. f(x)= x*-9x +27x2 -15x-52; 3-2i is a zero. |3D 26. g(x)= x² -(1-i)x² -(8-i)x+(12-6i); 2-i is a zero. %3D%X= 27. f(x)= x' -(2+3i)x² -(1-3i)x+(2+6i); 2 is a zero. 28. p(x)= x* - 2x+14x²-8x+40; 2i is a zero. %3D 29. n(x)= x*-4x +6x² +28x-91; 2+3i is a zero. %3D 30. G(x)= x*-14x +98x² - 686x+240o1; 7i is a zero. 31. f(x)= x* - 3x +5x-x-10 25r4 40r3 402 33r+16

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.