Let l(j) be the third derivative of j**6/540 + j**5/30 + 2*j**4/9 + 16*j**3/27 - 43*j**2. Factor l(x).
2*(x + 1)*(x + 4)**2/9
Suppose 4/3*u**2 + 16/3 + 16/3*u = 0. Calculate u.
-2
Let p(k) be the first derivative of k**4/22 + 24*k**3/11 + 432*k**2/11 + 3456*k/11 - 25. Factor p(o).
2*(o + 12)**3/11
Let r(y) be the third derivative of -y**8/84 - 2*y**7/35 - y**6/10 - y**5/15 - 3*y**2. Factor r(j).
-4*j**2*(j + 1)**3
Let u(a) be the second derivative of a - 1/18*a**4 + 0*a**2 - 1/15*a**6 + 0*a**3 + 0 + 1/10*a**5 + 1/63*a**7. Let u(g) = 0. Calculate g.
0, 1
Let y(x) be the first derivative of -2*x**3/3 + x**2 + 12*x - 22. Factor y(r).
-2*(r - 3)*(r + 2)
Let z be (-3 - (-66)/21)/((-3)/(-6)). Determine b so that -8/7*b**2 - 10/7*b - z*b**3 - 4/7 = 0.
-2, -1
Suppose -5*h + 21 = x, -5*x + 8 = 5*h + 3. Find f, given that -f**5 - 6*f**4 - f**3 + 3*f**h + 7*f**4 = 0.
-1, 0, 1/2
Let p(c) be the first derivative of -c**4/12 + 5*c**3/9 - c**2/2 - 3*c - 41. Determine g so that p(g) = 0.
-1, 3
Suppose -144 = -5*n + n. Let p be 39/n - (-2)/(-6). Factor -3/4*l**2 - p*l**3 + 3/4 + 3/4*l.
-3*(l - 1)*(l + 1)**2/4
Let b(g) be the second derivative of g**6/10 - 3*g**5/4 + 3*g**4/4 + 9*g**3/2 + 14*g. Factor b(m).
3*m*(m - 3)**2*(m + 1)
Let 8/5*l - 4/5*l**2 + 0 = 0. Calculate l.
0, 2
Solve -40*c - 50*c**4 + 56*c**3 - 16*c**5 + 44*c**2 + 14*c**4 + 4*c**2 - 12 = 0.
-3, -1, -1/4, 1
Suppose 14*l - 10*l = 12. Let w(x) be the first derivative of 1/3*x**l - 1/4*x**2 + 1/8*x**4 - x - 2. Factor w(q).
(q - 1)*(q + 1)*(q + 2)/2
Let r = 1 + 1. Factor -r*y**2 - 3*y + 3*y**2 + y + y**2.
2*y*(y - 1)
Let h = -1/81 - -47/1620. Let o(x) be the third derivative of 0*x + 1/300*x**6 + 0 + 2*x**2 - h*x**4 + 0*x**5 + 0*x**3. Suppose o(q) = 0. What is q?
-1, 0, 1
Suppose 1 + 13 - 2 - 5*w**4 - 10*w - 7 + 10*w**3 = 0. Calculate w.
-1, 1
Let j(i) be the third derivative of 1/96*i**6 - i**2 + 1/210*i**7 + 1/120*i**5 + 1/1344*i**8 + 0*i + 0 + 0*i**3 + 0*i**4. Factor j(k).
k**2*(k + 1)**2*(k + 2)/4
Let p(i) be the first derivative of i**3/7 - 3*i**2/2 + 17. Factor p(u).
3*u*(u - 7)/7
Let 4/5 - 26/5*c**2 + 22/5*c = 0. Calculate c.
-2/13, 1
Let t(j) be the third derivative of -j**6/40 - 3*j**5/20 + 7*j**2. Factor t(s).
-3*s**2*(s + 3)
Suppose 2*z - 2*x = 54, 0 = 9*z - 6*z + 5*x - 105. Determine w so that 56/3*w - 8/3 - z*w**2 = 0.
2/9, 2/5
Let q(r) be the first derivative of r**3 - 3*r**2 + 2. Determine n so that q(n) = 0.
0, 2
Let w(y) = -2*y**4 + 11*y**3 - 5*y**2 - 8*y + 5. Let c(j) = -j**4 + 5*j**3 - 2*j**2 - 4*j + 2. Let t(p) = -5*c(p) + 2*w(p). Solve t(a) = 0.
-1, 0, 2
Let b(x) = 2*x - 4. Let p be b(3). Suppose 0 = -p*n + 6 - 0. Let -2/9*r - 2/9*r**2 + 2/9*r**n + 2/9 = 0. What is r?
-1, 1
Let d(v) = -3*v**4 + 3*v**3 + 4*v**2 + 2*v + 2. Let t(o) = -o**4 + o**3 + o**2 + o + 1. Let y(l) = -5*d(l) + 10*t(l). Find q such that y(q) = 0.
-1, 0, 2
Let l(d) be the second derivative of -d + 0 + 1/135*d**6 + 1/30*d**5 - 1/9*d**3 + 1/54*d**4 - 2/9*d**2. Find c, given that l(c) = 0.
-2, -1, 1
Let b = -164 + 110. Let n be (-6)/2 + b/(-6). Factor 8/7 - 14*h**3 + n*h**2 + 48/7*h.
-2*(h - 1)*(7*h + 2)**2/7
Factor -66*b**4 - 48 + 16*b + 36*b**2 + 130*b**4 - 24*b**3 - 60*b**4.
4*(b - 3)*(b - 2)**2*(b + 1)
Let j(h) be the first derivative of -h**8/5040 + h**7/420 - h**6/90 + h**5/45 - h**3/3 + 3. Let d(w) be the third derivative of j(w). Let d(v) = 0. Calculate v.
0, 2
Let j(q) = -2*q**2 + q - 1. Let b be j(2). Let t be b/(-28) + (-5)/(-12). Suppose 2/3*r - t*r**3 - 7/3*r**4 + 7/3*r**2 + 0 = 0. Calculate r.
-1, -2/7, 0, 1
Let s(c) be the first derivative of c**6/120 + 3*c**5/40 + c**3/3 + 2. Let d(a) be the third derivative of s(a). Factor d(m).
3*m*(m + 3)
Let d be (-1)/(-2 - -4 - 1). Let t be (-68)/(-144) + d/4. Factor 0 + 0*n - t*n**2.
-2*n**2/9
Suppose -4*y + y = y. Determine o, given that 0 - 10/7*o**3 - 8/7*o**4 - 2/7*o**2 + y*o = 0.
-1, -1/4, 0
Let l(m) = 2*m**4 - 4*m. Let x(w) = 2*w - w**2 + 12*w**4 - 6*w - 10*w**4. Let a(k) = -5*l(k) + 6*x(k). Determine z so that a(z) = 0.
-1, 0, 2
What is d in -1/3 - 1/3*d**2 + 2/3*d = 0?
1
Factor -12*u**2 - 5*u**4 - 27*u**4 + 64*u**3 + 8*u + 4*u**4 - 32*u**2.
-4*u*(u - 1)**2*(7*u - 2)
Let j be (-8)/(-5)*(-8)/(-5 - 3). Determine i so that -j*i**2 + 2/5*i + 0 + 6/5*i**3 = 0.
0, 1/3, 1
Let w = -29 - -32. Let j(t) be the first derivative of 6*t**3 + w*t + 3/5*t**5 + 6*t**2 + 3*t**4 - 2. Factor j(x).
3*(x + 1)**4
Let 20/3*q + 5/2 + 25/6*q**2 = 0. Calculate q.
-1, -3/5
Let f(i) = 4*i**2 + 54*i. Let c(d) = 4*d**2 + 56*d. Let m(r) = -5*c(r) + 6*f(r). What is h in m(h) = 0?
-11, 0
Let w(z) be the third derivative of 1/16*z**4 + 0*z + 0 - 1/12*z**3 + 1/240*z**6 - 1/40*z**5 - z**2. Factor w(p).
(p - 1)**3/2
Let c be (-160)/(-96) - (0 - -1). Factor 0*m - 2/3*m**3 - 2/3*m**4 + 2/3*m**5 + 0 + c*m**2.
2*m**2*(m - 1)**2*(m + 1)/3
Suppose 4*v - 12 = -c + v, -4*v + 16 = -5*c. Let w = 4/17 - -32/153. Find h, given that c + w*h + 2/9*h**2 = 0.
-2, 0
Let r(x) be the second derivative of -7*x**6/15 + 8*x**5/5 - 11*x**4/6 + 2*x**3/3 - 11*x. Find y, given that r(y) = 0.
0, 2/7, 1
Let x be 160/(-413) - 2/(-7). Let t = 189/118 + x. Factor t + 21/4*c + 15/4*c**3 + 3/4*c**4 + 27/4*c**2.
3*(c + 1)**3*(c + 2)/4
Suppose 4*z - 20 = 0, 0 = -5*t + 4*z - 8 - 2. Solve -m**3 - 4*m + 8*m**t - 4*m - m**3 = 0 for m.
0, 2
Let a(j) = j**2 - j + 1. Suppose 4 = 5*l - l. Suppose 0*c - 24 = -4*c. Let u(d) = 2*d**3 + 2*d**2 + 16*d - 2. Let r(z) = c*a(z) + l*u(z). Solve r(p) = 0 for p.
-2, -1
Suppose -4*c - 8 = -0. Let w = 5 + c. Suppose l**3 - 2 - 2*l**2 - 4*l**w - 7*l - 6*l**2 = 0. What is l?
-1, -2/3
Let d(c) be the third derivative of 0*c + 0*c**4 - 1/480*c**6 + 0*c**3 - 1/1344*c**8 + 0 + 1/420*c**7 + 0*c**5 - c**2. Factor d(i).
-i**3*(i - 1)**2/4
Let u = 1 + 2. Let w(d) be the third derivative of 0 + 0*d + 0*d**u + 2*d**2 + 0*d**4 + 1/420*d**6 + 0*d**5. Factor w(g).
2*g**3/7
Suppose -2*p + 4 + 2 = 0. Suppose 3*t + w - 6 = -0*t, p*t + 2*w = 3. Factor 0*r + 2/3*r**t + 1/3*r**2 + 0 + 1/3*r**4.
r**2*(r + 1)**2/3
Factor 2/3*b - 2/3*b**2 + 4/3.
-2*(b - 2)*(b + 1)/3
Suppose -2*g - t + 3*t + 8 = 0, 0 = -3*t. Factor g*d - d**3 - 19*d + 6 - 2*d**3 + 12*d**2.
-3*(d - 2)*(d - 1)**2
Let n(a) be the first derivative of a**5/5 + 3*a**4/2 + 13*a**3/3 + 6*a**2 + 4*a - 3. Let n(q) = 0. Calculate q.
-2, -1
Let q(j) be the second derivative of -j**4/30 + j**3/15 + 2*j**2/5 - 10*j. Determine a so that q(a) = 0.
-1, 2
Let u(v) be the third derivative of 0*v + 1/240*v**8 + 0*v**3 - 2*v**2 + 8/525*v**7 + 11/600*v**6 + 0*v**4 + 0 + 1/150*v**5. Suppose u(k) = 0. What is k?
-1, -2/7, 0
Let p(y) be the third derivative of y**8/24 + 9*y**7/35 + 47*y**6/70 + 101*y**5/105 + 23*y**4/28 + 3*y**3/7 - 30*y**2. Factor p(x).
2*(x + 1)**3*(7*x + 3)**2/7
Suppose -15 = 6*i - i. Let p = 2 - i. Factor -1/4*q**3 - 1/4*q**p + 0*q - 1/2*q**4 + 0*q**2 + 0.
-q**3*(q + 1)**2/4
Let b(a) be the second derivative of -a**6/30 + a**5/10 + a**4/12 - a**3/3 - 10*a. Determine m, given that b(m) = 0.
-1, 0, 1, 2
Factor -8*t**2 + 4*t**2 - 2*t**2 - 3*t**3 + 6*t**3.
3*t**2*(t - 2)
Suppose -48 = -3*k - 6. Let g(r) = -r + 18. Let i be g(k). Determine w, given that 0 + 0*w**2 + 0*w**i - 1/2*w**3 + 1/4*w**5 + 1/4*w = 0.
-1, 0, 1
Let c be 0 + (-2)/7 + (-2176)/(-4284). Factor 0*h**2 + 4/9*h**3 + c*h**4 + 0 + 0*h.
2*h**3*(h + 2)/9
Let a = -772/231 + 299/63. Let u = a - 13/11. Solve 0 - u*g**4 + 2/9*g**2 - 2/9*g + 2/9*g**3 = 0 for g.
-1, 0, 1
Let y(x) be the third derivative of -x**8/224 - 3*x**7/140 - x**6/40 + x**5/20 + 3*x**4/16 + x**3/4 - 3*x**2. Solve y(b) = 0 for b.
-1, 1
Suppose 2*m + 2*m = -3*b - 40, -5*b - 3*m = 63. Let v be 2/3 - 16/b. Factor 2/5*o**v - 2/5*o - 4/5.
2*(o - 2)*(o + 1)/5
Suppose -6 = 4*t - 22. Let y be t*(-4)/(-56)*1. Let 0*m - 8/7*m**3 + 8/7*m**2 + 0 + y*m**4 = 0. Calculate m.
0, 2
Suppose k = 3*k - 4. Determine a so that -a**k + a**2 - a**5 + a**4 = 0.
0, 1
Let u(r) be the second derivative of -r**9/3024 + r**7/840 - r**3/6 + r. Let z(j) be the second derivative of u(j). Determine n, given that z(n) = 0.
-1, 0, 1
Let j(g) be the first derivative of 2/13*g**3 - 8/13*g + 4/13*g**2 - 2. Factor j(f).
2*(f + 2)*(3*f - 2)/13
Factor -5*v + 1 + 9*v + v**2 - 25 + 3*v**2.
4*(v - 2)*(v + 3)
Let i(m) be the third derivative of -1/30*m**5 + 0*m**3 + 0*m + 1/12