 83.1: Factor each trinomial.
 83.2: Factor each trinomial.
 83.3: Factor each trinomial.
 83.4: Factor each trinomial.
 83.5: Factor each trinomial.
 83.6: Factor each trinomial.
 83.7: Solve each equation. Check the solutions.
 83.8: Solve each equation. Check the solutions.
 83.9: Solve each equation. Check the solutions.
 83.10: Solve each equation. Check the solutions.
 83.11: NUMBER THEORY Find two consecutive integers x and x + 1 with a prod...
 83.12: Factor each trinomial.
 83.13: Factor each trinomial.
 83.14: Factor each trinomial.
 83.15: Factor each trinomial.
 83.16: Factor each trinomial.
 83.17: Factor each trinomial.
 83.18: Factor each trinomial.
 83.19: Factor each trinomial.
 83.20: Factor each trinomial.
 83.21: Factor each trinomial.
 83.22: Factor each trinomial.
 83.23: Factor each trinomial.
 83.24: Solve each equation. Check the solutions.
 83.25: Solve each equation. Check the solutions.
 83.26: Solve each equation. Check the solutions.
 83.27: Solve each equation. Check the solutions.
 83.28: Solve each equation. Check the solutions.
 83.29: Solve each equation. Check the solutions.
 83.30: Solve each equation. Check the solutions.
 83.31: Solve each equation. Check the solutions.
 83.32: GEOMETRY The triangle has an area of 40 square centimeters. Find th...
 83.33: SUPREME COURT When the justices of the Supreme Court assemble each ...
 83.34: RUGBY For Exercises 34 and 35, use the following information. The l...
 83.35: RUGBY For Exercises 34 and 35, use the following information. The l...
 83.36: GEOMETRY Find an expression for the perimeter of a rectangle with t...
 83.37: GEOMETRY Find an expression for the perimeter of a rectangle with t...
 83.38: SWIMMING For Exercises 3840, use the following information. The len...
 83.39: SWIMMING For Exercises 3840, use the following information. The len...
 83.40: SWIMMING For Exercises 3840, use the following information. The len...
 83.41: REASONING Explain why, when factoring x 2 + 6x + 9, it is not neces...
 83.42: OPEN ENDED Give an example of an equation that can be solved using ...
 83.43: FIND THE ERROR Peter and Aleta are solving x 2 + 2x = 15. Who is co...
 83.44: CHALLENGE Find all values of k so that each trinomial can be factor...
 83.45: CHALLENGE Find all values of k so that each trinomial can be factor...
 83.46: CHALLENGE Find all values of k so that each trinomial can be factor...
 83.47: CHALLENGE Find all values of k so that each trinomial can be factor...
 83.48: Writing in Math Use the information about Tamikas garden on page 43...
 83.49: Which is a factor of x 2 + 9x + 18? A x + 2 B x  2 C x + 3 D x  3
 83.50: REVIEW An 8foot by 5foot section of wall is to be covered by squa...
 83.51: Solve each equation. Check the solutions.
 83.52: Solve each equation. Check the solutions.
 83.53: Solve each equation. Check the solutions.
 83.54: Find the GCF of each set of monomials.
 83.55: Find the GCF of each set of monomials.
 83.56: Find the GCF of each set of monomials.
 83.57: MUSIC Albertina practices the guitar 20 minutes each day. She wants...
 83.58: PREREQUISITE SKILL Factor each polynomial.
 83.59: PREREQUISITE SKILL Factor each polynomial.
 83.60: PREREQUISITE SKILL Factor each polynomial.
 83.61: PREREQUISITE SKILL Factor each polynomial.
 83.62: PREREQUISITE SKILL Factor each polynomial.
 83.63: PREREQUISITE SKILL Factor each polynomial.
Solutions for Chapter 83: Factoring Trinomials: x 2 + bx + c
Full solutions for Algebra 1, Student Edition (MERRILL ALGEBRA 1)  1st Edition
ISBN: 9780078738227
Solutions for Chapter 83: Factoring Trinomials: x 2 + bx + c
Get Full SolutionsChapter 83: Factoring Trinomials: x 2 + bx + c includes 63 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra 1, Student Edition (MERRILL ALGEBRA 1) , edition: 1. Since 63 problems in chapter 83: Factoring Trinomials: x 2 + bx + c have been answered, more than 24880 students have viewed full stepbystep solutions from this chapter. Algebra 1, Student Edition (MERRILL ALGEBRA 1) was written by and is associated to the ISBN: 9780078738227. This expansive textbook survival guide covers the following chapters and their solutions.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).