I. Check or Wrong. 1. A polynomial expression PM is an expression of the form a sub n-1 xn-l + + a sub 1 x + a sub D where n is a nonnegative integer and each coefcient are real numbers. 2. A polynomial of degree n In x is an algebraic expression that contains a specic number of terms each of which is of the form axAn. where a is A real number and n is a whole number. 3. A polynomial with three terms is called a binomial. 4. The degree of a term in a polynomial in it refers to the exponent of x. 5. A polynomial having a degree of 0 is called a constant polynomial. 6. The degree of a polynomial refers to the highest degree among the degrees of the terms in the polynomial. 7. The terms of a polynomial written in decreasing powers of the variable x is said to be in standard form. 8. To add two or more polynomials means to combine their similar terms. 9. Terms are similar if they have different variable and have the same exponents. 10. The Remainder is the quantity left after a number or expression can no longer be divided exactly by another number or expression. II. Factor the given expressions. A. Factoring the greatest common factor 1.1.8x\" - 4x3 + 1le2 2. Xiy' + am 4- 51r5ya B. Factoring Quadratic Polynomial 3. x2 + 2x 15 4. X2 - 17x + 6 III. Discuss the two methods In dividing polynomials. 1. Long Division 2. Synthetic Division IV. Divide the following expression using the long method. 1. (x' - 3x3 + 11x1 - 3x +10)+(3(1 + 1) 2. (x5 +4x'+2x3- 5x2+4x+12)+(x2+4x+4) 3. (3+2x3- 10x3x')+(x3) V. Divide the following expression using the synthetic method. 1. (a:3 + 2x1 + 4x 5) + (1+3) 2. (lea - 12x1 + 17x 12) + (2x 3) 3.(9x'-3x'-9x+5)+(3x+2) VI. Fill in the blanks with words and symbols that will best complete the statement given. Provide reasons forthe given statements. Suppose the polynomial PM is divided by (x r ), as follows: |P(x)] -: (x r) = Ob!) + [Re (x r)] 1. If PM is of degree n, then Dix) is degree of (blank). The remainder R is a constant because (blank). Statements 2. PM = (x r) - lel + R 3. P(r)=(rr) - Q(r) +R 4. Ptr) = (0) . er) + R 5. PM = R VII. The proof Is a consequence of the remainder theorem. Fill in the blanks to complete the statement. 1.x-r Is a factor of P(x) if and only if the remainder R of P(x)+(xr) is (blank). 2. By the Remainder Theorem, R: 0 if and only if (blank). 3. Thus (xr) is a factor of Phi), if and only if (blank)