Algebra 2 Review
Introduction :
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics (Source: Wikipedia) in this topic we discussed about algebra 2 review introduction and algebra 2 review examples.
Algebra 2 Review Example problem: 1
Find the coefficients of a4, a3, a2 and a terms in the product of 7a3 – 6a2 – 9a + 8 and 5a2 – 3a + 5 without doing actual multiplication.
Solution: To get the coefficient of a4:
Coefficient of a4 term in X × Constant term in Y = 0 × 5 = 0.
Coefficient of a3 term in X × Coefficient of a term in Y = 7 × – 3 = –21.
Coefficient of a2 term in X × Coefficient of a2 term in Y = – 6 × 5 = –30.
Coefficient of a term in X × Coefficient of a3 term in Y = – 9 × 0 = 0.
Constant term in X × Coefficient of a4 term in Y = 8 × 0 = 0.
So the coefficient of a4 in the product of X × Y is 0 + (–21) + (–30) + 0 + 0 = –51.
To get the coefficient of a3:
Coefficient of a3 term in X × Constant term in Y = 7 × 5 = 35.
Coefficient of a2 term in X × Coefficient of a term in Y = – 6 × – 3 = 18.
Coefficient of a term in X × Coefficient of a2 term in Y = – 9 × 5 = –45.
Constant term in X × Coefficient of a3 term in Y = 8 × 0 = 0.
So the coefficient of a3 in X × Y is 35 + 18 + (– 45) + 0 = 8.
To get the coefficient of a2:
Coefficient of a2 term in X × Constant term in Y = – 6 × 5 = –30.
Coefficient of a term in X × Coefficient of a term in Y = –9 × –3 = 27.
Constant term in X × Coefficient of a2 term in Y = 8 × 5 = 40.
So the coefficient of a2 in X × Y is (–30) + 27 + 40 = 37.
To get the coefficient of a term:
Coefficient of a term in X × Constant term in Y = –9 ×5 = –45.
Constant term in X × Coefficient of term in Y = 8 × –3 = –24.
So the coefficient of a term in X × Y is (–45) + (–24) = – 69.
Algebra 2 Review Example problem: 2
Find the coefficients of a4, a3, a2 and a terms in the product of a3 – a2 – a + 1 and a2 – a + 1 without doing actual multiplication.
Solution: To get the coefficient of a4:
Coefficient of a4 term in X × Constant term in Y = 0 × 1 = 0.
Coefficient of a3 term in X × Coefficient of a term in Y = 1 × – 1 = –1.
Coefficient of a2 term in X × Coefficient of a2 term in Y = – 1 × 1 = –1.
Coefficient of a term in X × Coefficient of a3 term in Y = – 1 × 0 = 0.
Constant term in X × Coefficient of a4 term in Y = 1 × 0 = 0.
So the coefficient of a4 in the product of X × Y is 0 + (–1) + (–1) + 0 + 0 = –2.
To get the coefficient of a3:
Coefficient of a3 term in X × Constant term in Y = 1 × 1 = 1.
Coefficient of a2 term in X × Coefficient of a term in Y = – 1 × – 1 = 1.
Coefficient of a term in X × Coefficient of a2 term in Y = – 1 × 1 = –1.
Constant term in X × Coefficient of a3 term in Y = 1 × 0 = 0.
So the coefficient of a3 in X × Y is 1 + 1 + (– 1) + 0 = 8.
To get the coefficient of a2:
Coefficient of a2 term in X × Constant term in Y = – 1 × 1 = –1.
Coefficient of a term in X × Coefficient of a term in Y = –1 × –1 = 1.
Constant term in X × Coefficient of a2 term in Y = 1 × 1 = 1.
So the coefficient of a2 in X × Y is (–1) + 1 + 1 = 1.
To get the coefficient of a term:
Coefficient of a term in X × Constant term in Y = –1 × 1 = –1.
Constant term in X × Coefficient of term in Y = 1 × –1 = –1.
So the coefficient of a term in X × Y is (–1) + (–1) = – 2.
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics (Source: Wikipedia) in this topic we discussed about algebra 2 review introduction and algebra 2 review examples.
Algebra 2 Review Example problem: 1
Find the coefficients of a4, a3, a2 and a terms in the product of 7a3 – 6a2 – 9a + 8 and 5a2 – 3a + 5 without doing actual multiplication.
Solution: To get the coefficient of a4:
Coefficient of a4 term in X × Constant term in Y = 0 × 5 = 0.
Coefficient of a3 term in X × Coefficient of a term in Y = 7 × – 3 = –21.
Coefficient of a2 term in X × Coefficient of a2 term in Y = – 6 × 5 = –30.
Coefficient of a term in X × Coefficient of a3 term in Y = – 9 × 0 = 0.
Constant term in X × Coefficient of a4 term in Y = 8 × 0 = 0.
So the coefficient of a4 in the product of X × Y is 0 + (–21) + (–30) + 0 + 0 = –51.
To get the coefficient of a3:
Coefficient of a3 term in X × Constant term in Y = 7 × 5 = 35.
Coefficient of a2 term in X × Coefficient of a term in Y = – 6 × – 3 = 18.
Coefficient of a term in X × Coefficient of a2 term in Y = – 9 × 5 = –45.
Constant term in X × Coefficient of a3 term in Y = 8 × 0 = 0.
So the coefficient of a3 in X × Y is 35 + 18 + (– 45) + 0 = 8.
To get the coefficient of a2:
Coefficient of a2 term in X × Constant term in Y = – 6 × 5 = –30.
Coefficient of a term in X × Coefficient of a term in Y = –9 × –3 = 27.
Constant term in X × Coefficient of a2 term in Y = 8 × 5 = 40.
So the coefficient of a2 in X × Y is (–30) + 27 + 40 = 37.
To get the coefficient of a term:
Coefficient of a term in X × Constant term in Y = –9 ×5 = –45.
Constant term in X × Coefficient of term in Y = 8 × –3 = –24.
So the coefficient of a term in X × Y is (–45) + (–24) = – 69.
Algebra 2 Review Example problem: 2
Find the coefficients of a4, a3, a2 and a terms in the product of a3 – a2 – a + 1 and a2 – a + 1 without doing actual multiplication.
Solution: To get the coefficient of a4:
Coefficient of a4 term in X × Constant term in Y = 0 × 1 = 0.
Coefficient of a3 term in X × Coefficient of a term in Y = 1 × – 1 = –1.
Coefficient of a2 term in X × Coefficient of a2 term in Y = – 1 × 1 = –1.
Coefficient of a term in X × Coefficient of a3 term in Y = – 1 × 0 = 0.
Constant term in X × Coefficient of a4 term in Y = 1 × 0 = 0.
So the coefficient of a4 in the product of X × Y is 0 + (–1) + (–1) + 0 + 0 = –2.
To get the coefficient of a3:
Coefficient of a3 term in X × Constant term in Y = 1 × 1 = 1.
Coefficient of a2 term in X × Coefficient of a term in Y = – 1 × – 1 = 1.
Coefficient of a term in X × Coefficient of a2 term in Y = – 1 × 1 = –1.
Constant term in X × Coefficient of a3 term in Y = 1 × 0 = 0.
So the coefficient of a3 in X × Y is 1 + 1 + (– 1) + 0 = 8.
To get the coefficient of a2:
Coefficient of a2 term in X × Constant term in Y = – 1 × 1 = –1.
Coefficient of a term in X × Coefficient of a term in Y = –1 × –1 = 1.
Constant term in X × Coefficient of a2 term in Y = 1 × 1 = 1.
So the coefficient of a2 in X × Y is (–1) + 1 + 1 = 1.
To get the coefficient of a term:
Coefficient of a term in X × Constant term in Y = –1 × 1 = –1.
Constant term in X × Coefficient of term in Y = 1 × –1 = –1.
So the coefficient of a term in X × Y is (–1) + (–1) = – 2.