9*w**3 + 2/9.
2*(w - 1)**2*(w + 1)/9
Let b(n) be the first derivative of -n**6/1980 + n**5/220 - n**4/66 - 4*n**3/3 - 3. Let y(w) be the third derivative of b(w). Determine o, given that y(o) = 0.
1, 2
Suppose 18 - 27 = -3*u. Let m(n) be the second derivative of n + 0*n**u - 2/9*n**4 + 0 + 0*n**2 - 1/9*n**6 + 2/5*n**5. Suppose m(v) = 0. What is v?
0, 2/5, 2
Let r be 3 + -6*1 - -3 - -4. Factor -1/5*m + 1/5*m**3 + 1/5*m**r + 0 - 1/5*m**2.
m*(m - 1)*(m + 1)**2/5
Let f(t) be the third derivative of t**8/2520 - t**7/3780 - t**6/270 + t**5/180 - 3*t**4/8 - 5*t**2. Let i(y) be the second derivative of f(y). Factor i(g).
2*(g - 1)*(g + 1)*(4*g - 1)/3
Suppose -16 - 4 = -4*t. Suppose t*h = 2*h. Factor -1/4*b**3 - 1/2*b**2 - 1/4*b + h.
-b*(b + 1)**2/4
Let u(k) = -k - 6 - k + k. Let d be u(-10). Factor 7*m**2 + 3*m**d + 2*m**3 - 3*m + m - 10*m**4.
-m*(m - 1)*(m + 1)*(7*m - 2)
Let b(p) be the second derivative of 1/135*p**6 + 3*p + 0 - 1/27*p**4 + 1/9*p**2 + 1/189*p**7 + 1/27*p**3 - 1/45*p**5. Let b(z) = 0. What is z?
-1, 1
Let o = -28 + 34. Let a(u) be the third derivative of 0*u**3 + 0*u**5 + 1/525*u**7 + 0*u**4 + 0 + 2*u**2 + 0*u + 0*u**o. Factor a(x).
2*x**4/5
Let h(f) be the second derivative of f**4/60 - f**2/10 - 7*f. Find y such that h(y) = 0.
-1, 1
Let p(m) be the third derivative of m**5/20 + m**4/4 - 3*m**2. Factor p(g).
3*g*(g + 2)
Let n(b) be the first derivative of -5 + 0*b + 0*b**2 + 1/2*b**3 + 3/8*b**4. Find z, given that n(z) = 0.
-1, 0
Let o(l) = 45*l - 88. Let q be o(2). Find z, given that -1/5*z + 2/5 - 1/5*z**q = 0.
-2, 1
Let x be (-2 + 0 - -2)*1. Let c(h) = h**3 + h**2 + h + 3. Let b be c(x). Determine d so that 0*d + 0 - 2/3*d**b + 1/3*d**4 + 1/3*d**2 = 0.
0, 1
Let d = 311/5 - 62. Let t be -2 + (72/(-10))/(-3). Let -t*o + d*o**2 + 1/5 = 0. Calculate o.
1
Let v(x) be the second derivative of x**6/6 + 3*x**5/2 + 5*x**4/12 - 20*x**3 + 40*x**2 + 34*x. What is n in v(n) = 0?
-4, 1
Let t(m) be the first derivative of -m**6/780 - m**5/195 - m**4/156 - m**2 + 3. Let q(w) be the second derivative of t(w). Determine l so that q(l) = 0.
-1, 0
Let t be 54/(-132)*(-16)/3. Let k = t - -71/33. Factor 0 + 2*b**2 + 1/3*b + k*b**3 + 4*b**4 + 4/3*b**5.
b*(b + 1)**2*(2*b + 1)**2/3
Let n(p) = p - 6. Let x be n(11). Suppose 11 = x*z - 4. Factor -6/11*r**z + 0 + 2/11*r**2 - 2/11*r**5 + 0*r + 6/11*r**4.
-2*r**2*(r - 1)**3/11
Let x(d) be the second derivative of 1/66*d**4 + 0*d**3 + 0*d**2 + 0*d**5 + 5*d + 0 - 1/165*d**6. What is n in x(n) = 0?
-1, 0, 1
Suppose -32 = 4*o + y + y, -o + 2*y + 2 = 0. Let h = o + 6. Factor 1/2*v**2 - 1/2*v**3 + 0 + h*v.
-v**2*(v - 1)/2
Let q(h) be the first derivative of 2*h**3/33 + 2*h**2/11 + 2*h/11 - 12. Solve q(y) = 0.
-1
Let r(g) be the third derivative of -g**7/1155 - g**6/165 - g**5/66 - g**4/66 - 46*g**2. Factor r(a).
-2*a*(a + 1)**2*(a + 2)/11
Let f = -646/7 - -69775/756. Let o(c) be the third derivative of 0*c - 1/270*c**5 + 0*c**3 - f*c**4 + 2*c**2 + 0. Find y, given that o(y) = 0.
-1, 0
Suppose -5*l + l - 16 = 0. Let k(y) = -3*y - 6. Let w be k(l). Let w*q**5 + 2*q**2 - 12*q**3 - 4 + 6*q - 4*q**4 + 5*q**2 + q**2 = 0. What is q?
-1, 2/3, 1
Let s(a) be the third derivative of -1/1260*a**7 + 0 - 9*a**2 + 0*a - 1/36*a**3 - 1/180*a**6 - 1/60*a**5 - 1/36*a**4. Factor s(q).
-(q + 1)**4/6
Find u, given that 3/4*u**2 + 1/4*u**3 + 1/2*u + 0 = 0.
-2, -1, 0
Let a = -6 - -11. Suppose -6*n = -n. What is b in -2*b**5 + 3*b**a - b**4 + n*b**5 = 0?
0, 1
Let z = -41 + 64. Let c = -19 + z. Determine b so that 0 + 3/2*b**3 + 1/4*b - b**2 - b**c + 1/4*b**5 = 0.
0, 1
Let o(f) be the first derivative of f**3/12 - f/4 + 6. Determine d so that o(d) = 0.
-1, 1
Suppose -a - a = 32. Let y be (-6)/9 - a/6. Find f, given that -f - f**2 + 2*f + 2*f**y = 0.
-1, 0
Let g(z) be the third derivative of 1/60*z**5 + 1/3*z**3 + 5/24*z**4 + 0*z - 1/70*z**7 - 5*z**2 - 1/24*z**6 + 0. Factor g(h).
-(h - 1)*(h + 1)**2*(3*h + 2)
Let p be (5/5)/(2/(-4)). Let f = p - -4. Factor -d**5 + d**3 - 15*d**2 + 15*d**f.
-d**3*(d - 1)*(d + 1)
Let i = 1735/2607 + 1/869. Find z, given that i - 2*z - 8/3*z**2 = 0.
-1, 1/4
Let u(s) be the second derivative of 1/12*s**4 + 3*s + 1/6*s**2 - 2/9*s**3 + 0. Suppose u(v) = 0. Calculate v.
1/3, 1
Let g(n) = 2*n**2 - 22 + 3*n + 6*n**2 + 6*n - 7*n**2. Let d be g(-11). Factor 2/5*s**4 + d - 2/5*s**2 + 0*s + 0*s**3.
2*s**2*(s - 1)*(s + 1)/5
Suppose 6 = 4*c - 2. Let p(w) be the second derivative of c*w + 1/165*w**6 + 2/55*w**5 + 0*w**2 + 0 + 2/33*w**3 + 5/66*w**4. Determine b so that p(b) = 0.
-2, -1, 0
Let d(q) be the first derivative of -q**4/22 + 2*q**3/33 + 2*q**2/11 + 10. Factor d(x).
-2*x*(x - 2)*(x + 1)/11
Let g = 365/273 - 1/273. Find b, given that g*b**2 + 1/3 - 8*b**3 + 13/6*b = 0.
-1/4, 2/3
Let m(p) be the third derivative of 1/96*p**4 + 0*p**3 + 0 + 1/240*p**5 + 2*p**2 + 0*p. Let m(r) = 0. What is r?
-1, 0
Let v(u) be the second derivative of u**4/6 - 5*u**3/3 + 4*u**2 + 4*u. Factor v(a).
2*(a - 4)*(a - 1)
Let n(s) = 2*s - 5. Let o be n(4). Factor -2*r + 0*r + r**2 - r**3 + 3*r**o - 2*r**4 + r**2.
-2*r*(r - 1)**2*(r + 1)
Let p be (-4 + 1)/(-1) - 26. Let x = p - -25. Find w such that 0 + 2/3*w**x + 0*w - 2*w**3 = 0.
0, 1/3
Let l = 0 - 2. Let n = -1 - l. Suppose 4 - y**3 + n - 4 - y**2 + y = 0. What is y?
-1, 1
Factor -2*n**3 - 10*n**3 - 8*n**3 + 30*n**2 - 24*n + 5 + 4*n + 5*n**4.
5*(n - 1)**4
Let i(f) = f**2 - f - 6. Let z be i(3). Determine d so that 3/4*d - 1/4*d**3 + z*d**2 - 1/2 = 0.
-2, 1
Let p be ((-9)/(-6))/(4/8). Suppose -w = p*w. Determine j so that 0 - 2/5*j**2 + 2/5*j**3 + w*j = 0.
0, 1
Let z(i) be the third derivative of -i**8/168 - i**7/35 + 2*i**5/15 + 58*i**2. Factor z(l).
-2*l**2*(l - 1)*(l + 2)**2
Find n, given that 18/7*n**3 - 3/7*n**4 + 36/7*n - 39/7*n**2 - 12/7 = 0.
1, 2
Solve -2/11*t**2 - 2/11 - 4/11*t = 0 for t.
-1
Factor -4/7*i**2 - 2/7*i + 0 - 2/7*i**3.
-2*i*(i + 1)**2/7
Suppose -5*c = -4*c + 4. Let v(h) = -3*h**5 + 2*h**3 + 4*h**2 - 3*h. Let m(w) = -4*w**5 + 3*w**3 + 5*w**2 - 4*w. Let s(t) = c*m(t) + 5*v(t). Factor s(i).
i*(i - 1)**2*(i + 1)**2
Let j = -3 + 5. Suppose -2*y - 2*w + 8 = 0, -w - 8 = -3*y - j*y. Find f such that f**2 - f**4 - 3*f**3 - f**y - f - 3*f**2 = 0.
-1, 0
Let j = -5 - -12. Let q = j + -5. Let -4*p**2 + 2*p + 6*p - 8*p**3 - q + 6*p**2 = 0. Calculate p.
-1, 1/4, 1
Suppose 119 = -4*b + 15. Let k be (-2)/8 + b/(-8). Factor 0*f**2 - 2/7*f**k + 0 + 2/7*f.
-2*f*(f - 1)*(f + 1)/7
Let j be (24 + -30)*(-3)/8. Determine d, given that 0 - d**3 - j*d**2 - 1/2*d = 0.
-2, -1/4, 0
Let a(p) = 3*p - 6. Let u be a(5). Suppose -q - u = -t - 4, -t - 5*q - 13 = 0. Determine j, given that -2*j**t - 1 - 2 - 4*j + 1 = 0.
-1
Let x(z) be the third derivative of -z**10/7560 - z**9/1890 - z**8/1680 + z**4/24 - z**2. Let w(h) be the second derivative of x(h). Factor w(p).
-4*p**3*(p + 1)**2
Let f be (2*3)/(-2 - -1). Let a be (2/(-6))/(f/4). Factor 0 - a*c**2 - 2/9*c.
-2*c*(c + 1)/9
Suppose -25 = -8*t + 3*t. Let k(b) be the third derivative of 0*b + 0 + 1/6*b**3 + 3*b**2 + 1/12*b**4 + 1/60*b**t. Factor k(f).
(f + 1)**2
Let y = 1853/384 + -29/6. Let r = 253/384 - y. Factor 4/3 - r*b**2 - 2/3*b.
-2*(b - 1)*(b + 2)/3
Let q(p) be the third derivative of 0 - 2*p**2 - 1/70*p**5 - 1/420*p**6 + 0*p + 0*p**4 + 4/21*p**3. Factor q(w).
-2*(w - 1)*(w + 2)**2/7
Suppose -4*h + 2*h = 0. Let z(t) be the second derivative of -t - 1/36*t**4 + 0 + h*t**2 + 1/18*t**3. Suppose z(v) = 0. Calculate v.
0, 1
Let i(c) be the third derivative of 0*c - 1/480*c**6 - 1/96*c**4 - 4*c**2 + 1/120*c**5 + 0 + 0*c**3. Factor i(w).
-w*(w - 1)**2/4
Let z(n) be the third derivative of n**7/6300 - n**5/300 - n**4/24 - 3*n**2. Let v(a) be the second derivative of z(a). Determine p so that v(p) = 0.
-1, 1
Let a = -6 - -21. Suppose -a = -4*z - 3. Factor -3*l**4 + 3*l**4 + 2*l**4 + 2*l**z.
2*l**3*(l + 1)
Let d be (8 - 2)/((-6)/(-4)). Suppose q = -3*q + 12. Determine i, given that 4*i**3 - i**q - 2*i - 6*i**2 + d*i + i = 0.
0, 1
Let x(u) be the third derivative of 6*u**2 - 1/480*u**6 + 0 - 1/120*u**5 + 0*u + 0*u**3 - 1/96*u**4. Factor x(t).
-t*(t + 1)**2/4
Let i be -3 - -2 - (-38)/36. Let k(g) be the third derivative of i*g**5 + 0*g - 1/9*g**3 + 1/36*g**4 + 0 + 2*g**2 + 1/60*g**6. Determine d, given that k(d) = 0.
-1, 1/3
Let k be -3 + 303/27 + -8. What