 + 27/2*d**2 + 81/4 - a*d**c - 27*d.
(d - 3)**4/4
Let c(m) be the second derivative of -m**5/5 + 2*m**3/3 + 17*m. Factor c(r).
-4*r*(r - 1)*(r + 1)
Let 4/3 - 4/3*p + 1/3*p**2 = 0. Calculate p.
2
Let a(b) be the third derivative of -b**7/1470 + b**5/420 - 3*b**2. Solve a(t) = 0.
-1, 0, 1
Suppose k - 16 = -12. Let g(c) be the second derivative of -1/120*c**6 - 1/80*c**5 + 0*c**2 + 0 + 1/48*c**k + 1/24*c**3 + 2*c. Determine h, given that g(h) = 0.
-1, 0, 1
Suppose 2*t - 6 = 6. Let a(d) be the first derivative of -1/20*d**5 + 0*d - 2 + 0*d**3 + 0*d**2 + 0*d**4 - 1/24*d**t. Factor a(j).
-j**4*(j + 1)/4
Let n(h) be the second derivative of -h**5/10 + 8*h**4/9 - h**3/3 - 10*h**2/3 - 24*h. Let n(y) = 0. Calculate y.
-2/3, 1, 5
Suppose 0 = -5*a + 3*r + 12, 3*a - 2*r + 0*r = 7. Let 0*i**2 + 0*i - 1/4*i**5 + 0*i**a + 1/4*i**4 + 0 = 0. What is i?
0, 1
Let a(g) be the second derivative of g**4/12 - g**3/2 - 3*g**2 - 2*g. Let f be a(6). Factor 12 - 8*v**2 - 2*v - f.
-2*v*(4*v + 1)
Let i(r) = -r**4 + r + 1. Let s(m) = 8*m**4 - 2*m**3 - 6*m**2 - 4*m - 2. Suppose 60 = -12*u + 17*u. Let n(w) = u*i(w) + 2*s(w). Factor n(p).
4*(p - 2)*(p - 1)*(p + 1)**2
Let k(i) be the first derivative of -3*i**4/4 + 9*i**2/2 - 6*i + 25. Factor k(d).
-3*(d - 1)**2*(d + 2)
Let q be 12/5*60/24. Let j(m) be the third derivative of 0*m**4 + 0*m - m**2 + 1/6*m**3 + 1/480*m**q + 0 - 1/80*m**5. Solve j(r) = 0 for r.
-1, 2
Let w(p) be the third derivative of -p**7/210 - p**6/40 - p**5/60 + p**4/8 + p**3/3 - 8*p**2 - 3. Suppose w(u) = 0. What is u?
-2, -1, 1
Let b(z) be the third derivative of z**5/180 - z**4/9 + 8*z**3/9 + 4*z**2. Solve b(t) = 0 for t.
4
Suppose 4/5 + 16/5*v**2 + 14/5*v - 2/5*v**5 - 4/5*v**4 + 4/5*v**3 = 0. Calculate v.
-1, 2
Find u such that 3*u**2 - u**2 + 288 + 430*u - 478*u = 0.
12
Suppose -3 + 31 = 4*c - 4*f, -4*c + 13 = -f. Factor 0 + 0*a - 2/5*a**3 - 2/5*a**c.
-2*a**2*(a + 1)/5
Let i = 321 - 3525/11. Factor -i*y - 4/11 + 4/11*y**2.
2*(y - 2)*(2*y + 1)/11
Let s = -1634/5 - -328. Suppose -237*k - 2 = -238*k. Let -s*m + 4/5 + 2/5*m**k = 0. What is m?
1, 2
Let z(k) = -k**3 - 4*k**2 - 2*k - 6. Let f be z(-4). Let v = -111 - -563/5. What is j in v*j**2 + 2/5 - f*j = 0?
1/4, 1
Find v such that -3*v**3 + 1/2*v + 4*v**4 + 0 + 0*v**2 - 3/2*v**5 = 0.
-1/3, 0, 1
Let i(o) = -2*o + 1. Let y be i(-10). Let k = y + -15. Factor -27*u**2 - 10 - k*u - 36*u**3 - 15*u**4 + 10.
-3*u*(u + 1)**2*(5*u + 2)
Let f = 715 + -2123/3. Factor 4/3 + f*x + 8*x**2.
2*(3*x + 2)*(4*x + 1)/3
Suppose q = -3*o - 2*q - 27, q + 1 = 0. Let j be ((-30)/o - 3)*4. Find w such that -4/11*w**2 + 0*w + 0 + 6/11*w**j - 2/11*w**4 = 0.
0, 1, 2
Let s be (-12*3/(-6))/2. Factor 0 + 0 + 2*j**2 + 1 - s*j**2.
-(j - 1)*(j + 1)
Let h be 4 - 0 - (-26 + 26). Let t(f) be the second derivative of 0 + 0*f**3 - 1/12*f**4 + h*f + 0*f**2. Factor t(n).
-n**2
Let 4*w**2 - 3*w**3 + w**3 - 2*w + 2*w = 0. What is w?
0, 2
Let c(y) be the second derivative of -5*y**4/12 + 5*y**3/2 + 10*y**2 - 18*y. Factor c(i).
-5*(i - 4)*(i + 1)
Let n(g) = 2*g. Let l be n(2). Let k = 192/7 - 190/7. Factor 0*p**2 + 0*p**l - 2/7*p**5 + 4/7*p**3 + 0 - k*p.
-2*p*(p - 1)**2*(p + 1)**2/7
Let f(q) be the second derivative of q**4/18 - 2*q**3/9 - q**2 - 4*q. Factor f(c).
2*(c - 3)*(c + 1)/3
Determine d, given that -1/3*d**2 - 1/3 + 2/3*d = 0.
1
Let w be -1 + (-2 - -2 - -3). Let c(i) be the third derivative of -1/48*i**4 + 0*i + 1/120*i**5 + 0*i**3 + 0 - w*i**2. Factor c(q).
q*(q - 1)/2
Solve -1/2*l**2 - 1/4*l**4 + 0*l + 3/4*l**3 + 0 = 0.
0, 1, 2
Let p(n) = 2*n**3 + n**2 - 2*n - 1. Let f(d) = 5*d**3 + 3*d**2 - 5*d - 3. Let w(m) = 3*f(m) - 8*p(m). Find o, given that w(o) = 0.
-1, 1
Let 5/4*w**3 + 1/2 - 5/4*w - 5/4*w**2 + 3/4*w**4 = 0. What is w?
-2, -1, 1/3, 1
Let x(h) be the second derivative of 0*h**2 + 2/9*h**3 - 7*h + 0 - 1/18*h**4 - 1/30*h**5. Factor x(n).
-2*n*(n - 1)*(n + 2)/3
Let i(g) = 7*g**3 - 20*g**2 - 23*g + 2. Let n(s) = -50*s**3 + 140*s**2 + 160*s - 15. Let y(q) = -15*i(q) - 2*n(q). Find z, given that y(z) = 0.
-1, 0, 5
Let i be (-52)/(-96) - (-4)/32. Find k, given that -2/3*k**3 + 0*k**2 + i*k + 1/3 - 1/3*k**4 = 0.
-1, 1
Determine o so that -46*o**2 - 2*o - 2 + 45*o**2 + 0*o + 5*o = 0.
1, 2
Let p(u) be the first derivative of -32/9*u - 112/27*u**3 + 16/9*u**4 + 1/27*u**6 + 16/3*u**2 - 2/5*u**5 + 2. Factor p(q).
2*(q - 2)**4*(q - 1)/9
Factor -4/9*q - 2/9 - 2/9*q**2.
-2*(q + 1)**2/9
Let g(j) be the first derivative of j**5/10 + j**4/3 + j**3/3 - 6*j - 5. Let f(u) be the first derivative of g(u). Find c, given that f(c) = 0.
-1, 0
Let o be (-1)/(-4 + (-21)/(-6)). Find t such that -4/5*t + 4/5 + 1/5*t**o = 0.
2
Let m = 10 + -5. Let l = m + -2. Factor -1/3*g + 0 + 1/3*g**2 - 1/3*g**4 + 1/3*g**l.
-g*(g - 1)**2*(g + 1)/3
Let b be (-23)/(-7) - 4/14. Suppose -l - 1 = -b. Solve -l*c**2 + 2*c**3 - 2 - 6*c - 4*c**3 - 4*c**2 = 0.
-1
Let f(s) be the second derivative of s**6/165 - s**5/55 + s**4/66 - 8*s. Factor f(q).
2*q**2*(q - 1)**2/11
Let m be 4*(3 + (1914/(-60))/11). Determine w so that m*w**3 - 4/5*w + 2/5*w**2 + 0 = 0.
-2, 0, 1
Let h be ((-4)/(-9))/((-1)/(12/(-16))). Factor -1/3*z**2 + 0 - h*z.
-z*(z + 1)/3
Let l(q) be the third derivative of -q**7/840 - q**6/240 - q**5/240 + 4*q**2. Suppose l(j) = 0. Calculate j.
-1, 0
Let k(o) = 14*o**2 - 2*o + 1. Let b be k(1). Let r(s) = s**2 - 12*s - 11. Let w be r(b). Factor -2/11*f**3 - 8/11 + 0*f + 6/11*f**w.
-2*(f - 2)**2*(f + 1)/11
Determine h so that 3*h**4 - 3*h**2 + 2*h + 6*h**3 + 3*h + 0*h**4 - 11*h = 0.
-2, -1, 0, 1
Let r = 197 - 197. Factor r*m**3 + 1/3*m + 2/3*m**2 - 2/3*m**4 + 0 - 1/3*m**5.
-m*(m - 1)*(m + 1)**3/3
Let z = 66/1229 - 3259770/8603. Let c = z - -380. Suppose 0 - 2*j**4 + 2/7*j**2 - c*j**5 + 0*j - 4/7*j**3 = 0. Calculate j.
-1, 0, 1/4
Let n(x) be the first derivative of 2*x**4 - 32*x**3/3 + 21*x**2 - 18*x - 34. Solve n(f) = 0.
1, 3/2
Suppose 0 = -5*w + 169 + 6. Let b be (-2)/3 + w/30. Factor -1/4*i**3 + 0*i - b*i**2 + 0.
-i**2*(i + 2)/4
Let u(r) = r**2 + 8*r - 20. Let b be u(-10). Factor -o + b + o**3 + 5/2*o**4 - 5/2*o**2.
o*(o - 1)*(o + 1)*(5*o + 2)/2
Let p(f) be the first derivative of -f**6/42 + 6*f**5/35 - f**4/2 + 16*f**3/21 - 9*f**2/14 + 2*f/7 - 14. What is n in p(n) = 0?
1, 2
Let a = -318 - -2228/7. Factor 6/7*f - 18/7 + 10/7*f**2 + a*f**3.
2*(f - 1)*(f + 3)**2/7
Suppose 3*p + 3 = 5*v + 15, -3*v = -4*p + 16. Factor 0 + 0*m**3 + 0*m + m**p - 1/2*m**5 + 0*m**2.
-m**4*(m - 2)/2
Factor -10*r**2 - 5*r + 122*r**4 + 5*r**3 + 114*r**4 - 226*r**4.
5*r*(r - 1)*(r + 1)*(2*r + 1)
Let z(q) be the second derivative of 1/24*q**3 + 0 + 1/48*q**4 - 1/4*q**2 - 7*q. Find w, given that z(w) = 0.
-2, 1
Let n(f) be the second derivative of -f**4/3 - 2*f**3/5 + 4*f**2/5 + 13*f. Factor n(m).
-4*(m + 1)*(5*m - 2)/5
Let z = 12/13 - 82/117. Solve z*u + 2/9*u**5 + 0*u**4 - 4/9*u**3 + 0*u**2 + 0 = 0 for u.
-1, 0, 1
Suppose -96/7*n**2 - 2/7*n**4 + 0 + 24/7*n**3 + 128/7*n = 0. Calculate n.
0, 4
Let u = -24/11 + 26/11. Determine q so that -8/11*q - u*q**2 - 8/11 = 0.
-2
Let s(g) be the third derivative of -g**8/9240 - g**7/4620 + g**6/1980 + g**5/660 + g**3/6 + g**2. Let x(t) be the first derivative of s(t). Factor x(k).
-2*k*(k - 1)*(k + 1)**2/11
Determine r so that 20*r + 21*r**3 - 40*r**4 + 4*r**3 + 40*r**2 + 45*r**4 = 0.
-2, -1, 0
Let m(r) be the second derivative of -r**10/15120 - r**9/3780 - r**8/3360 - r**4/4 + 2*r. Let d(q) be the third derivative of m(q). Factor d(h).
-2*h**3*(h + 1)**2
Suppose 5*t - 7 = 13. Let z(l) be the first derivative of 2 - 1/4*l**2 + 0*l**3 + 1/4*l + 1/8*l**t - 1/20*l**5. Find q such that z(q) = 0.
-1, 1
Suppose 7/3*q**4 - 19/3*q**3 + 25/3*q**2 - 16/3*q + 4/3 - 1/3*q**5 = 0. What is q?
1, 2
Suppose -5*v = -25, -3*v + 17 = -3*b + 4*b. Determine k so that 8*k + 4 - 4*k - 2*k - 2*k**b + 0*k**2 = 0.
-1, 2
Let d(x) = -x + 20. Let c be d(18). Suppose 3*t - 9 = 5*f, -2*t = 3*t + 5*f - 15. Factor -1/3*v + 0 + 4/3*v**t + v**c.
v*(v + 1)*(4*v - 1)/3
Suppose 2*v + 6 = 0, 0*v + 2*v + 8 = r. Suppose 0 = 5*i + a - 5, 4 + 6 = -i + r*a. Find j, given that 2/9*j**2 + 0*j + i = 0.
0
Suppose 4*p - 16 + 8 = 0. Factor 0*i - 2/7*i**p + 2/7.
-2*(i - 1)*(i + 1)/7
Factor 9/4*z**2 - 1/2*z - 5/2*z**3 + 0 + 3/4*z**4.
z*(z - 2)*(z - 1)*(3*z - 1)/4
Let 0 - 4/7*y - 2/7*y**2 = 0. What is y?
-2, 0
Let g = 1426