= 0. Calculate r.
-1, 0, 2/5, 1
Let f(y) be the first derivative of -5/8*y**2 - 2 + 1/2*y + 1/3*y**3 - 1/16*y**4. Factor f(m).
-(m - 2)*(m - 1)**2/4
Let g(c) = -4*c**2 + 4*c + 12. Let f(n) = n. Let a(o) = 4*f(o) + g(o). Let a(q) = 0. What is q?
-1, 3
Let b(o) be the first derivative of -o**4/28 + o**3/21 + o**2/7 - 32. Factor b(a).
-a*(a - 2)*(a + 1)/7
Factor -g**2 - 20*g - 7*g**2 - 20 + 13*g**2 + 5*g**3.
5*(g - 2)*(g + 1)*(g + 2)
Let c be -2 + 7 + (4 - 6). Factor 3*r + 6/5 + 12/5*r**2 + 3/5*r**c.
3*(r + 1)**2*(r + 2)/5
Let r be 135/60 - 2/8. Factor 2/3*h**r - 4/3*h + 2/3.
2*(h - 1)**2/3
Let i(c) be the third derivative of -c**6/30 - c**5/5 - c**4/3 + 20*c**2. Factor i(w).
-4*w*(w + 1)*(w + 2)
Let v(h) be the first derivative of 2*h**3/45 + 4*h**2/15 + 8*h/15 + 39. Factor v(a).
2*(a + 2)**2/15
Let r be (114/(-56) - -2) + 0. Let o = 15/28 + r. Factor -o*b + b**2 + 0 - 1/2*b**3.
-b*(b - 1)**2/2
Let r = -428 + 431. Factor 4*l**2 - 6*l**r - 2/3*l + 0.
-2*l*(3*l - 1)**2/3
Let h(r) = -7*r**3 + 3*r**2 - 5. Suppose 12 = g + 3*g. Let b(x) = -4*x**3 + 2*x**2 - 3. Let z(d) = g*h(d) - 5*b(d). Factor z(w).
-w**2*(w + 1)
Let s(j) be the first derivative of 2*j**5/25 - 4*j**3/15 + 2*j/5 - 2. Factor s(n).
2*(n - 1)**2*(n + 1)**2/5
Let w(s) be the third derivative of s**6/200 + 11*s**5/100 + 3*s**4/5 - 18*s**3/5 + 18*s**2. Suppose w(p) = 0. Calculate p.
-6, 1
Let p = -19773/5 + 4016. Let o = -61 + p. Factor o*a**5 - 7/5*a**4 + 9/5*a**3 - a**2 + 0 + 1/5*a.
a*(a - 1)**3*(2*a - 1)/5
Find n, given that -4/5*n - 4/5*n**3 - 8/5*n**2 + 0 = 0.
-1, 0
Let p(t) be the first derivative of t**4/14 + 4*t**3/21 + 18. Factor p(y).
2*y**2*(y + 2)/7
Let f(q) be the first derivative of -q**4/8 - q**3/3 + 3*q**2/4 - 41. Find j, given that f(j) = 0.
-3, 0, 1
Suppose -3/8*o**3 + 3/8*o - 3 + 3*o**2 = 0. What is o?
-1, 1, 8
Suppose -10*s = -8*s - 2. Let a(b) be the first derivative of 0*b**2 - 1/4*b**4 + s - 1/3*b**3 + 0*b. Determine p, given that a(p) = 0.
-1, 0
Factor 9*v**5 + 20*v**3 + 2*v**2 + 25*v**4 + 3*v**2 + v**5.
5*v**2*(v + 1)**2*(2*v + 1)
Determine l, given that 23*l + 4 - 6 - 5*l - 25 - 3*l**2 = 0.
3
Let i = -1 - -5. Factor 3*m**2 + 3*m**i - 2*m**4 + 3*m**4 + 2*m - 5*m**4.
-m*(m - 2)*(m + 1)**2
Let y be (-8)/(-2) + -1 + -3. Let h = -3 + 5. Suppose y*c**4 + 2*c**4 - h*c**5 + c**5 + 3*c**5 = 0. Calculate c.
-1, 0
Let p = -27/2 - -55/4. What is t in 1/4 + p*t - 1/2*t**2 = 0?
-1/2, 1
Let g(a) be the third derivative of a**7/42 + a**6/8 + a**5/4 + 5*a**4/24 + 2*a**2 + 24. Let g(s) = 0. What is s?
-1, 0
Suppose -8*u = -13*u + 15. Factor 1/2 + 7/4*v + 3/4*v**u + 2*v**2.
(v + 1)**2*(3*v + 2)/4
Let g(c) = -8*c**2 + 20*c - 32. Let w(t) = 7*t**2 - 21*t + 33. Let d(b) = -3*g(b) - 4*w(b). Determine p so that d(p) = 0.
3
Let s = 161/603 - 3/67. Factor s*b**2 + 4/9*b + 0 - 2/9*b**3.
-2*b*(b - 2)*(b + 1)/9
Suppose -u + v + 8 = 2*v, -u + 13 = 2*v. Factor 4*i**4 - 5*i**4 - i**3 + 2*i**u + 2*i**4.
i**3*(i + 1)
Let k be ((2498/1)/2)/(-4). Let p = k - -314. Let -1 - p*h**3 + 3*h + 9/4*h**2 = 0. Calculate h.
-1, 2/7, 2
Suppose 2*g + 16 = 4*g. Suppose -4*t = -5*r - g + 32, -11 = -3*r - t. Factor 1/2*z**5 - 1/2*z**r - 1/2 + 1/2*z + z**2 - z**3.
(z - 1)**3*(z + 1)**2/2
Suppose 6*b - 4*q = 4*b - 10, 0 = 3*q - 12. Let k = -7 - -12. Solve -t**3 + 2*t**3 + 4*t**4 + 2*t**b - 5*t**k + 2*t + 3*t**4 - 7*t**2 = 0 for t.
-1, 0, 2/5, 1
Let k(o) = 2*o - 6. Let j be k(4). Factor 4*z + j*z**2 - 2 - 2 - 2*z.
2*(z - 1)*(z + 2)
Factor -2/3*v**3 + 2*v**2 - 2/3*v**4 + 4/3 + 10/3*v.
-2*(v - 2)*(v + 1)**3/3
Let a(j) be the second derivative of 6*j + 4/55*j**6 + 32/33*j**4 + 0*j**2 + 0*j**3 - 1/231*j**7 + 0 - 24/55*j**5. Let a(s) = 0. Calculate s.
0, 4
Suppose 4*d = -6 + 18. Factor -j**5 + 3 - d*j**4 + 3 + 3*j + 2*j**2 - 2*j**3 - 5.
-(j - 1)*(j + 1)**4
Let d(g) be the first derivative of g**6/24 - g**4/8 + g**2/8 + 29. Determine w, given that d(w) = 0.
-1, 0, 1
Let s(d) = -3*d**5 + 3*d**4 - d**3 - 9*d**2 - 2*d + 4. Let o(w) = -10*w**5 + 9*w**4 - 4*w**3 - 28*w**2 - 7*w + 12. Let y(m) = -2*o(m) + 7*s(m). Factor y(b).
-(b - 2)**2*(b - 1)*(b + 1)**2
Let f(l) be the second derivative of l**6/300 - l**5/50 + l**4/20 - l**3/15 - l**2 - l. Let u(q) be the first derivative of f(q). Find g such that u(g) = 0.
1
Let m be 4/38 - (-165)/(-7524). Let j(i) be the third derivative of 0*i - 3*i**2 + 0 + 2/75*i**5 - m*i**4 - 1/300*i**6 + 2/15*i**3. Solve j(o) = 0.
1, 2
Let k = 3 + -1. Let r(f) be the first derivative of -2 - 2*f**k + 3/2*f**4 + 0*f - 2/3*f**3. Solve r(s) = 0.
-2/3, 0, 1
Let y(l) = -l**2 - l + 1. Suppose -m = 3*u - 1, -4*u - 4*m - 3 = u. Let b(f) = -9*f**2 - 9*f + 12. Let q(s) = u*b(s) - 6*y(s). What is o in q(o) = 0?
-2, 1
Factor 0 + 3*r**2 - 7/3*r**3 - 2/3*r.
-r*(r - 1)*(7*r - 2)/3
Suppose 29*z - 34 = 12*z. Find o such that -1/5*o**z - 4/5 + 4/5*o = 0.
2
Let g(b) = 3*b + 50. Let j be g(-16). Find v, given that -2/11*v**j + 0 - 2/11*v = 0.
-1, 0
Let k(a) = a**4 - a**2 + a. Let n(j) = 10*j**4 + 4*j**3 - 6*j**2 + 8*j. Let f(g) = 8*k(g) - n(g). Factor f(m).
-2*m**2*(m + 1)**2
Factor 3*r**3 - r**3 - 2*r**2 - 4 + 4.
2*r**2*(r - 1)
Factor 3*d**5 + 65*d**3 + 42*d**5 + 10*d**2 + 63*d**4 + 37*d**4.
5*d**2*(d + 1)**2*(9*d + 2)
Let w(q) be the first derivative of q**4/6 - 4*q**3/9 - 21. Let w(j) = 0. What is j?
0, 2
Let t(c) be the first derivative of -1 - c - 1/8*c**4 - 3/4*c**3 - 3/2*c**2. Let a(k) be the first derivative of t(k). Factor a(i).
-3*(i + 1)*(i + 2)/2
Suppose -3*b + 18 = -6*b. Let p(t) = -t - 3. Let w be p(b). Suppose -2/3*z**w - 4/3*z**2 + 0 - 2/3*z = 0. What is z?
-1, 0
Let j be 1 - (-4 + 3 + -2). What is u in -2*u**2 + 8*u - 5 + j - 7 = 0?
2
Let g(z) be the first derivative of 0*z**2 - 2 - 1/9*z**3 - z - 1/18*z**4. Let f(q) be the first derivative of g(q). Factor f(b).
-2*b*(b + 1)/3
Let q(a) = 4*a**3 + 8*a**2 - 22*a - 26. Let p(m) = m - 1. Let r(o) = -6*p(o) - q(o). Determine h so that r(h) = 0.
-2, 2
Let k(j) be the first derivative of -5*j**3/3 + 10*j**2 + 22. Factor k(b).
-5*b*(b - 4)
Suppose 0 = 2*k - 0*k - 4. Solve o + 2 + o**2 - k*o - 2*o**2 + 2*o = 0 for o.
-1, 2
Let o(x) = -x**2 - 10*x + 15. Let n be o(-11). Let i(v) be the second derivative of 1/20*v**5 + 0 - v - 1/6*v**3 + 0*v**2 + 0*v**n. Find h, given that i(h) = 0.
-1, 0, 1
Let w be 2 + -1 - 2/8. Let n be 0*((-3)/2 + 1). Suppose 0*v + n + 0*v**2 - w*v**3 + 3/4*v**4 = 0. Calculate v.
0, 1
Let p(z) be the third derivative of -z**8/28 - 2*z**7/5 - 73*z**6/40 - 43*z**5/10 - 11*z**4/2 - 4*z**3 + 27*z**2. Factor p(o).
-3*(o + 2)**3*(2*o + 1)**2
Factor 2/3*g - 2/3*g**2 + 4/3.
-2*(g - 2)*(g + 1)/3
Let h(t) be the third derivative of -4*t**2 + 1/2*t**3 + 1/14*t**7 + 5/8*t**4 + 0 + 1/112*t**8 + 1/2*t**5 + 0*t + 1/4*t**6. What is l in h(l) = 0?
-1
Let s(q) = -4*q**2 - 4*q - 4. Let y(f) = -9*f**2 + 7*f - 9. Let b(w) = 4*w**2 - 3*w + 4. Let r(o) = 7*b(o) + 3*y(o). Let v(j) = 2*r(j) + s(j). Factor v(z).
-2*(z + 1)**2
Let r(d) be the first derivative of -d**7/7 - 7*d**6/10 - 27*d**5/20 - 5*d**4/4 - d**3/2 + 8*d - 4. Let g(a) be the first derivative of r(a). Factor g(b).
-3*b*(b + 1)**3*(2*b + 1)
Let b(l) = -2*l**3 - 4*l - 3. Let s be b(-2). Factor -2*m**2 - 4*m**2 + 21*m**3 - 6 + 15*m**4 - 3*m**2 - s*m.
3*(m - 1)*(m + 1)**2*(5*m + 2)
Factor 2/5 + 2/5*q**4 + 0*q**3 + 0*q - 4/5*q**2.
2*(q - 1)**2*(q + 1)**2/5
Let c = 8 + 1. Let t(y) = -8*y**2 - 18*y - 32. Let x(u) = 15*u**2 + 36*u + 63. Let r(m) = c*t(m) + 5*x(m). Factor r(l).
3*(l + 3)**2
Let t(s) be the first derivative of 0*s**2 - 2/3*s**3 + 2*s + 3. Factor t(d).
-2*(d - 1)*(d + 1)
Factor 8/13*s - 2/13 + 8/13*s**3 - 2/13*s**4 - 12/13*s**2.
-2*(s - 1)**4/13
Suppose -2*y + 77 = -7*f + 2*f, 2*y = -5*f - 73. Let w be (f + 25)*4/5. Factor 4*p**3 + 2/3*p**4 + w*p + 8/3 + 26/3*p**2.
2*(p + 1)**2*(p + 2)**2/3
Determine r, given that -20 - 4/5*r**2 - 8*r = 0.
-5
Determine i so that 4/17*i**2 - 6/17*i + 2/17 = 0.
1/2, 1
Suppose 4*p - 27 = -11. What is h in 212/3*h**2 - 98/3*h**5 - 196/3*h**p + 106/3*h**3 - 16/3 - 8/3*h = 0?
-2, -1, -2/7, 2/7, 1
Suppose 5*w - 10 - 5 = 2*r, 3*r - 35 = -4*w. Let y be (-7)/105 + 2/r. Suppose 1/3*a + 0*a**2 + 0 - y*a**3 = 0. What is a?
-1, 0, 1
Let c(p) be the first derivative of 1/5*p**2 + 4/15*p**3 + 0*p - 2 + 1/10*p**4. Solve c(o) = 0.
-1, 0
Let z(l) be the third derivative of l**7/315