 = 0.
0, 2
Let w(p) be the third derivative of 2*p**2 + 1/8*p**4 + 0*p + 0 - 1/70*p**7 + 1/30*p**5 + 1/6*p**3 - 1/60*p**6 - 1/336*p**8. Suppose w(c) = 0. Calculate c.
-1, 1
Let v = -43/40 + 6/5. Let n(r) be the first derivative of 1/4*r**2 - 2 - v*r**4 - 1/6*r**3 + 1/2*r. Suppose n(l) = 0. Calculate l.
-1, 1
Suppose a - o = -4*a + 10, -a + 2*o = 7. Factor 5*k + 2*k - 5*k**2 - 3 - a + 4.
-(k - 1)*(5*k - 2)
Let z(n) = 7*n - 1. Let f be z(2). Suppose -3*r + 28 = -4*w, 5*w = -2*r - 2 + f. Let -6*p**2 + r*p**2 + p**4 + 4*p**3 + p**4 = 0. Calculate p.
-1, 0
Let q(d) be the third derivative of d**5/390 - d**4/39 - 21*d**2. Factor q(n).
2*n*(n - 4)/13
Let p(w) = -w**3 + 11*w**2 - 9*w - 8. Let j be p(10). Factor 5*r + 0 + r**j + r + 1 - 8*r.
(r - 1)**2
Suppose 9*t + 16 = 43. Let h(a) be the third derivative of -3*a**2 - 3/8*a**4 + 0 + 3/5*a**5 + 0*a - 7/40*a**6 - a**t. Factor h(v).
-3*(v - 1)**2*(7*v + 2)
Determine h so that 0*h - 6*h**4 - h**2 + 5/2*h**5 + 9/2*h**3 + 0 = 0.
0, 2/5, 1
Let p(h) be the first derivative of 1/9*h**3 - 5 - 1/6*h**2 + 0*h. Suppose p(q) = 0. What is q?
0, 1
Let j = -138 + 138. Factor 1/4*g**2 + j + 1/4*g.
g*(g + 1)/4
Factor 0 + 0*b + 0*b**2 - 1/2*b**4 - 1/2*b**3.
-b**3*(b + 1)/2
Factor 3/5*c - 3/5*c**3 + 0 + 0*c**2.
-3*c*(c - 1)*(c + 1)/5
Let o be ((-8)/14)/(16/56). Let l be (-13)/52 + o/(-4). Factor -l*c**2 - 1 - c.
-(c + 2)**2/4
Suppose -2 - 10*z**3 + 2 + 3*z**2 + 12*z**4 - 5*z**3 = 0. Calculate z.
0, 1/4, 1
Let y(z) be the third derivative of -z**7/945 + 2*z**5/135 + 7*z**2. Find o, given that y(o) = 0.
-2, 0, 2
Let 0 - 1/3*h**5 + 1/3*h**3 + 0*h + 1/3*h**4 - 1/3*h**2 = 0. Calculate h.
-1, 0, 1
Let i(s) be the first derivative of -35*s**6/24 - 3*s**5 + 55*s**4/16 + 5*s**3 - 5*s**2/2 + 12. Solve i(b) = 0.
-2, -1, 0, 2/7, 1
Let q be (-9)/(-36)*12/15. Let n(d) be the third derivative of 0 + 4/25*d**5 - q*d**4 - 3*d**2 + 1/10*d**3 + 0*d. Find p, given that n(p) = 0.
1/4
Let x = -1 + 3. Suppose 23 = 5*y - x*u, 0*u = -y + 5*u. Solve -f + 46*f**3 - 4*f - 9*f + 2 - 16*f**4 + 14*f**2 - 32*f**y = 0 for f.
-1, 1/4, 1
Factor 0 + 0*g**3 - 1/3*g**2 + 0*g + 1/3*g**4.
g**2*(g - 1)*(g + 1)/3
Let b(q) = 2*q**4 - 14*q**3 + 14*q**2 + 6*q. Suppose 0 = 2*s - s - 5. Let y(k) = k**4 - 9*k**3 + 9*k**2 + 4*k. Let x(v) = s*b(v) - 8*y(v). Factor x(p).
2*p*(p - 1)*(p + 1)**2
Let u(g) be the first derivative of 0*g**3 - 2 + 1/18*g**4 - 1/45*g**6 - 3*g + 0*g**5 + 0*g**2. Let o(z) be the first derivative of u(z). Factor o(h).
-2*h**2*(h - 1)*(h + 1)/3
Let j(i) be the first derivative of -i**6/39 - 12*i**5/65 - i**4/2 - 8*i**3/13 - 4*i**2/13 - 18. Factor j(b).
-2*b*(b + 1)**2*(b + 2)**2/13
Suppose 0 = 31*c - 38*c + 14. Find r, given that -3*r**c - 9/2*r - 3/2 = 0.
-1, -1/2
Suppose r + 14*r = 75. Solve -1/4*s - 1/2*s**4 + 0 + 0*s**3 + 1/2*s**2 + 1/4*s**r = 0 for s.
-1, 0, 1
Suppose 2*o + 2 = 6. What is l in 2/7 + 0*l**o + 4/7*l - 2/7*l**4 - 4/7*l**3 = 0?
-1, 1
Suppose -4*i**2 + 4*i**4 - 1 + 13*i - 21*i + 8*i**3 + 1 = 0. What is i?
-2, -1, 0, 1
Suppose -2 = 3*c - 8. Suppose -c*y + 4*l + 6 = 0, 3 = -y - 4*l - 0. Factor 0 - 3*q**3 + 3*q**5 - 1 + y.
3*q**3*(q - 1)*(q + 1)
Let o be -3 + (-37)/(-10) + (-2)/10. Solve 3/2*x - 1/2 + o*x**3 - 3/2*x**2 = 0 for x.
1
Let d(i) = i**5 + 5*i**4 - 7*i**3 - 19*i**2 - i. Let s(h) = -2*h**4 + 2*h**3 + 6*h**2. Let x(b) = -2*d(b) - 7*s(b). Find a, given that x(a) = 0.
-1, 0, 1
Let u = -4 - 1. Let h(i) = 6*i - 5*i**2 - 16*i**2 - 24*i**3 + 3*i**2. Let d(y) = -16*y**3 - 12*y**2 + 4*y. Let r(b) = u*h(b) + 7*d(b). Factor r(q).
2*q*(q + 1)*(4*q - 1)
Let g(z) = 6*z**2 - 29*z - 91. Let n(y) = y**2 - 6*y - 18. Let d(r) = -4*g(r) + 22*n(r). Suppose d(v) = 0. What is v?
-4
Let b(m) be the second derivative of -m**4/42 + 2*m**3/21 - m**2/7 - 14*m. Suppose b(t) = 0. Calculate t.
1
Let h(j) be the first derivative of -1/25*j**5 - 1/10*j**2 + 1/5*j**3 - 2/5*j + 1/20*j**4 - 4. Let h(z) = 0. Calculate z.
-1, 1, 2
Solve 8/9 - 35/9*a**2 - 4/9*a**3 - 23/9*a = 0.
-8, -1, 1/4
Let u(l) = -l**2 - 8*l + 8. Let d be (2/6)/((-1)/3). Let z(h) = 3*h**2 - h - 1. Let r be z(d). Let b(m) = -m**2. Let w(x) = r*b(x) - u(x). Solve w(o) = 0.
2
Let i = 13 + -8. Suppose i - 1 = 2*x. Solve -9*j + j - 2 + x*j**2 + 10 = 0.
2
Factor -384/7*l + 48/7*l**2 - 2/7*l**3 + 1024/7.
-2*(l - 8)**3/7
Let i(x) be the second derivative of 1/105*x**7 + 0*x**3 - 2*x + 0 + 0*x**2 - 1/50*x**5 + 1/75*x**6 - 1/30*x**4. Factor i(d).
2*d**2*(d - 1)*(d + 1)**2/5
Let j(k) be the third derivative of 0*k + 1/4*k**4 + 0*k**6 + 3/20*k**5 + 0 - 1/70*k**7 + 0*k**3 + 4*k**2. Factor j(x).
-3*x*(x - 2)*(x + 1)**2
Let o(t) be the first derivative of t**4/2 + 8*t**3 + 48*t**2 + 128*t + 13. Determine l so that o(l) = 0.
-4
Let o(d) be the third derivative of 5*d**8/504 - 19*d**7/315 + 139*d**6/900 - 97*d**5/450 + 8*d**4/45 - 4*d**3/45 - 14*d**2. Solve o(r) = 0 for r.
2/5, 1
Let k be (-12)/8*(-16)/6. Let o(z) = -4*z**2 + 0*z**2 + 3*z + z**2. Let m(p) = -16*p**2 + 16*p. Let l(g) = k*m(g) - 22*o(g). Suppose l(v) = 0. What is v?
0, 1
Factor 10/3*s - 4/3 - 8/3*s**2 + 2/3*s**3.
2*(s - 2)*(s - 1)**2/3
Let c(v) be the third derivative of 2*v**7/105 - v**6/10 + v**5/5 - v**4/6 - 18*v**2. Suppose c(d) = 0. Calculate d.
0, 1
Factor 4*k**5 + 4*k**5 - 5*k**4 - 3*k**5.
5*k**4*(k - 1)
Let v(j) be the second derivative of -j**5/60 + j**4/18 + j**3/18 - j**2/3 - 6*j. Factor v(y).
-(y - 2)*(y - 1)*(y + 1)/3
Let h(q) be the second derivative of 0*q**2 + 0*q**5 + 1/42*q**7 - 1/30*q**6 + 0*q**4 + 0 + 6*q + 0*q**3. What is o in h(o) = 0?
0, 1
Let m = 1/14 + 5/28. Let r = 29 + -25. Determine t so that 0*t + m*t**r + 1/2*t**2 + 0 + 3/4*t**3 = 0.
-2, -1, 0
Suppose -24 = -5*v - 3*a, -5*v + 4*v = 3*a - 12. Solve 27*x**2 - 21*x + 2 + 1 + v*x**4 - 6*x**3 + 3 - 9*x**3 = 0.
1, 2
Let w be (-13)/(-4) + 6/(-24). Factor -7*q + 2*q - 3*q + 6*q**w - 12*q**2 + 0*q + 3*q**5 + 11*q**4.
q*(q - 1)*(q + 2)**2*(3*q + 2)
Let h(w) = -30*w**2 - w - 1. Let r be h(-1). Let p be (-20)/15*r/4. Find g, given that -2*g**2 - 3*g**5 - 7*g**3 + 10*g - 8*g**4 - p*g = 0.
-1, -2/3, 0
Factor 5*w**2 - 13*w**2 - 4*w - 2*w**2 - 6*w**2.
-4*w*(4*w + 1)
Let f be ((-95)/(-57))/(10/4). Factor 0 + 2/3*l**2 + f*l**3 + 0*l.
2*l**2*(l + 1)/3
Let b(g) = 5*g**4 + 2*g**3 - 5*g**2 + 2*g + 2. Let r(w) = 11*w**4 + 5*w**3 - 11*w**2 + 5*w + 5. Let s(y) = -5*b(y) + 2*r(y). What is q in s(q) = 0?
-1, 0, 1
Let r(y) be the third derivative of -y**5/420 - y**4/56 + 5*y**2. Factor r(k).
-k*(k + 3)/7
Let z(t) = -6*t + 7. Let v(k) = -5*k + 6. Let b(m) = 5*v(m) - 4*z(m). Let r be b(0). Factor 0 + 0*u + 3/5*u**3 + 3/5*u**4 + 1/5*u**5 + 1/5*u**r.
u**2*(u + 1)**3/5
Let l(x) be the first derivative of 3/5*x - 3/20*x**4 + 3/5*x**3 + 4 - 9/10*x**2. Find f, given that l(f) = 0.
1
Let s(r) be the second derivative of -r**4/18 - 2*r**3/9 - 18*r. Factor s(i).
-2*i*(i + 2)/3
Factor 0*i + 16/3*i**2 + 0*i**3 + 0 - 4*i**4 + 4/3*i**5.
4*i**2*(i - 2)**2*(i + 1)/3
Let v = -107/6 + 37/2. Factor -v*j**3 + 0 - 1/6*j**4 + 0*j - 2/3*j**2.
-j**2*(j + 2)**2/6
Let v(r) be the second derivative of -1331*r**6/150 + 121*r**5/20 + 99*r**4/10 + 62*r**3/15 + 4*r**2/5 - 6*r. Factor v(k).
-(k - 1)*(11*k + 2)**3/5
Let u(f) = f**3 + 2*f**2 - 1. Let z be u(1). Let 4*v - z*v**2 - v - v = 0. What is v?
0, 1
Let q be 6/(-24) - 17/(-4). Determine t so that 2*t**5 - 15 + 12 + 16*t**q - 31*t**3 + 56*t**2 + 34*t + 11 + 75*t**3 = 0.
-4, -1
Let o(j) be the second derivative of -37/20*j**5 + 7/30*j**6 + 0 + 4*j**2 + 11/2*j**4 + 4*j - 22/3*j**3. Factor o(l).
(l - 2)**2*(l - 1)*(7*l - 2)
Let q(t) = t**3 - t**2 - 4*t. Let o be q(3). Suppose 0 + 4/3*s + 8*s**3 + o*s**2 + 10/3*s**4 = 0. What is s?
-1, -2/5, 0
Determine w, given that 3/4*w - 3/2 + 3/4*w**2 = 0.
-2, 1
Let r(f) be the first derivative of 0*f**2 + 0*f + 1/10*f**4 + 2 + 2/15*f**3. Factor r(k).
2*k**2*(k + 1)/5
Let d(o) be the second derivative of o**5/10 - o**4/8 + o**2 + 5*o. Let r(c) be the first derivative of d(c). Factor r(g).
3*g*(2*g - 1)
Let t(v) = -v**2 - 10*v - 13. Let i be t(-8). Suppose -18/5*q - 4/5 + 6*q**i - 8/5*q**2 = 0. What is q?
-2/5, -1/3, 1
Let a(q) be the third derivative of 1/8*q**4 - 10*q**2 + 0 + 3/20*q**5 - 1/40*q**6 - 3/2*q**3 + 0*q. Find b such that a(b) = 0.
-1, 1, 3
Let a(d) be the second derivative of d**6/45 - d**5/10 + d**4/6 - d**3/9 + 2*d. L