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Algebra comes with a whole new set of terminology to learn. One of those terminologies is that of a monomial. A monomial is a polynomial that has only one term. So what is a polynomial?
A polynomial is an expression of variables and coefficients. The variables and coefficients involve mathematical operations that include addition, subtraction, multiplication and non-negative integer-exponents.
[readmore]So, what is a variable? A variable is an alphabetic character used to represent a number that is not known. For example: x + y. The “x” and “y” are variables used in place of numeric numbers that are not known.
What is a coefficient? A coefficient is a known number that is linked to a variable. For example: 7x + 3y = 29. In this example the 7 and the 3 are coefficients because they are linked to variables. The 29 is a constant number and is not a coefficient because it is not linked to a variable.
Whenever a coefficient is linked to a variable, it is understood that the operation will be multiplied. Again looking at the above example, we know that 7 times an unknown number plus 3 times an unknown number will equal 29. When replacing a variable with a number, the number is placed within parentheses. Now let’s look at the solution to our problem as it should be written out.
7(2) + 3(5) = 29
7 x 2 = 14
3 x 5 = 15
14 + 15 = 29
x = 2
y = 5
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4(5) + 7(4) - 3 = 45
4 x 5 = 20 7 x 4 = 28 20 + 28 = 48 48 - 3 = 45 x = 5 y = 4 Answer (b) is the correct answer |
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8(8) - 2(6) = 52
8 x 8 = 64 2 x 6 = 12 64 - 12 = 52 x = 8 y = 6 Answer (c) is the correct answer |
2(4) + 9(3) + 21 = 56
2 x 4 = 8 9 x 3 = 27 8 + 27 = 35 35 + 21 = 56 x = 4 y = 3 Answer (a) is the correct answer |
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5(6) + 5(7) - 10 = 55
5 x 6 = 30 5 x 7 = 35 30 + 35 = 65 65 - 10 = 55 x = 6 y = 7 Answer (c) is the correct answer |
12(4) + 20(3) = 108
12 x 4 = 48 20 x 3 = 60 48 + 60 = 108 x = 4 y = 3 Answer (b) is the correct answer |
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9(9) - 33(1) = 48
9 x 9 = 81 33 x 1 = 33 81 - 33 = 48 x = 9 y = 1 Answer (d) is the correct answer |
6(6) + 19(4) + 26 = 138
6 x 6 = 36 19 x 4 = 76 36 + 76 = 112 112 + 26 = 138 x = 6 y = 4 Answer (b) is the correct answer |
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25(3) + 16(10) - 64 = 171
25 x 3 = 75 16 x 10 = 160 75 + 160 = 235 235 - 64 = 171 x = 3 y = 10 Answer (a) is the correct answer |
45(6) + 12(8) = 366
45 x 6 = 270 12 x 8 = 96 270 + 96 = 366 x = 6 y = 8 Answer (c) is the correct answer |
3 x 6 = 18
9 x 2 = 18
18 + 18 = 36
x = 6
y = 2
Answer (d) is the correct answer