(w + 7)(w - 2)
(w² + 5w + 6) / (w² - w - 12)= [(w + 2)(w + 3)] / [(w - 4)(w + 3)]= (w + 2) / (w - 4)
It is either a linear equation in a variable ww or a quadratic equation in a variable w, (with ww denoting w2).
Area of triangle = 0.5 * width * height So 27 = 0.5 * w * (w-3) or 54 = w2 - 3w ie w2 - 3w - 54 = 0 w2 - 9w + 6w - 54 = 0 w(w - 9) + 6(w - 9) = 0 ie (w - 9)(w + 6) = 0 So w = 9 or w = -6 But since w is a width, it must be positive and so w = 9 cm.
The length of the diagonal is not enough to determine the dimensions of the rectangle. Take any length W such that 0<W<sqrt(132/2) that is, 0<W<9.192 cm. And let L = sqrt(132 - W2) cm. Then 9.192<L<13 so that any combination of W and L is unique. There are infinitely many possible values for W and so infinitely many different combinations for W and L. That is, infinitely many rectangles whose width is W cm and length is L cm. And, since, L2 = 132 - W2, L2 + W2 = 132 so the diagonal is 13 cm.
42/6
That doesn't factor neatly. Applying the quadratic formula, we find two real solutions: 4 plus or minus 2 times the square root of 11x = 10.6332495807108x = -2.6332495807108
(w - 12)(w - 2)
(w + 7)(w - 2)
(w² + 5w + 6) / (w² - w - 12)= [(w + 2)(w + 3)] / [(w - 4)(w + 3)]= (w + 2) / (w - 4)
w2+18w+77 = (w+7)(w+11) when factored
you do 2 sets of parenthesis and check it. for example: w2(w squared)-7w-8 (w+1) (w-8) *if you add 1w and -8w you will get -7w, which is what they want you to get. and w & w multiply to get w2(w squared), which is also what the factoring wants. another example: 3w2 (3w squared)+2-8 (3w-4) (w+2) *same thing applies with 3w x w = 3w2, and -4 +2=2, which is the answer. use this theory in all of them, unless there is a greatest common factor (GCF).
The answer is -12
(w + 9)(w + 9)
If by w2 you mean "w squared", then it cannot be done. BECAUSE w2 + 49 = 0 w2 +49 - 49 = 0 - 49 w2 = -49 w2 means a number multiplied by itself. Any number multplied by itself will result in a POSITIVE number. positive x positive = positive negative x negative = negatve
The grouping of the factors of w^2 + 30w + 81 (a perfect square) is (w + 27) and (w + 3)3 is a prime factor of 27, 30 and 81 but without two terms to compare, there won't be a GCF (not gfc)
There is a formula for the "difference of squares." In this case, the answer is (6v + w)(6v - w)