15*f**2 + 3*f**h - 3 + 16 = 0.
-1, 3
Let r(k) = 2*k**3 + k**2 + k + 1. Let c(n) = 5*n**3 + n + 3. Let a(q) = c(q) - 3*r(q). Suppose a(v) = 0. Calculate v.
-2, -1, 0
Suppose -15*b + 5*b + 20 = 0. Let f be ((-80)/(-150))/(2/3). Determine t so that 12/5*t - 12/5*t**b + 4/5*t**3 - f = 0.
1
Let p(u) = -7*u**3 + 147*u**2 - 289*u + 133. Let x(n) = 6*n**3 - 147*n**2 + 288*n - 135. Let i(t) = 3*p(t) + 4*x(t). Let i(o) = 0. What is o?
1, 47
Suppose 0 = -0*w + 2*w - 6. Suppose -b - w + 9 = 0. Find h, given that 3*h**5 + 2*h**4 - 11*h + 6*h**2 + 14*h - 3 - b*h**3 - 5*h**4 = 0.
-1, 1
Let d(r) be the first derivative of -14*r**5/5 + 9*r**4/2 + 80*r**3/3 - 12*r**2 - 56. Factor d(i).
-2*i*(i - 3)*(i + 2)*(7*i - 2)
Let l(r) be the second derivative of r**6/45 - r**5/6 + r**4/2 - 7*r**3/9 + 2*r**2/3 + 89*r. Find s such that l(s) = 0.
1, 2
Let q(p) be the first derivative of 1/9*p**3 - 1/3*p**2 - p - 1. Determine o so that q(o) = 0.
-1, 3
Let j(f) be the second derivative of 40/63*f**3 - 11/18*f**4 + 15*f - 4/21*f**2 - 121/210*f**5 + 0. Factor j(x).
-2*(x + 1)*(11*x - 2)**2/21
Let c(l) be the first derivative of l**5/10 + 5*l**4/8 + 4*l**3/3 + l**2 - 22. Solve c(j) = 0 for j.
-2, -1, 0
Let u(r) = r + 13. Let x be u(3). Suppose 6 - x = -5*a. Factor 1/3*m**3 + 0 + 4/3*m**a + m.
m*(m + 1)*(m + 3)/3
Let y(j) be the first derivative of 0*j**5 + 0*j**4 - 1/90*j**6 + 0*j + 8/3*j**3 + 0*j**2 + 7. Let m(n) be the third derivative of y(n). Factor m(i).
-4*i**2
Suppose 37 - 55 = -9*b. Suppose -2*c + 8 = b*v, 2*v = 5*v + c - 4. Factor v + 2/11*j**2 + 2/11*j.
2*j*(j + 1)/11
Factor 3*k**4 + 189/2*k + 2*k**3 - 54 - 45*k**2 - 1/2*k**5.
-(k - 3)**3*(k - 1)*(k + 4)/2
Find u such that -1/4*u**2 + 10*u - 100 = 0.
20
Let d = 138539/7 + -19791. Determine w, given that -10/7*w - 12/7 + d*w**2 = 0.
-1, 6
Suppose -85 + 5*o**3 - 55*o**2 + 73*o + 15*o + 72*o - 24 - 31 = 0. Calculate o.
2, 7
Let -10/13*i + 18/13*i**2 - 6/13*i**3 + 0 - 2/13*i**4 = 0. Calculate i.
-5, 0, 1
Let q be ((-39)/9)/((-6)/18). Let u(z) = 5*z + 109 - 109 - q*z**3 + 4*z**4 + z**2. Let b(h) = 2*h**4 - 6*h**3 + 2*h. Let g(f) = -13*b(f) + 6*u(f). Factor g(y).
-2*y*(y - 2)*(y + 1)**2
Suppose 0*p - 3*p = 6, -5*v - 4*p = 8. Suppose -h - 4 = -3*h + 2*i, 10 = 5*h + 3*i. What is u in -1/2*u**3 + v*u + 1/2*u**h + 0 = 0?
0, 1
Suppose 13*h**3 - 5*h**2 - 24 + 0*h**3 + 38*h - 11*h**3 - 11*h**2 = 0. Calculate h.
1, 3, 4
Let o(k) be the third derivative of 0*k + 0 - 1/24*k**6 + 5/6*k**3 - 1/12*k**5 + 5/24*k**4 + 6*k**2. Factor o(p).
-5*(p - 1)*(p + 1)**2
Factor -25*u**3 + 60*u**2 + u**4 + 512 + 97*u**2 + 93*u**2 - 34*u**2 - 704*u.
(u - 8)**3*(u - 1)
Solve -27/2 - 149*p**3 - 189/2*p - 87/2*p**4 - 9/2*p**5 - 207*p**2 = 0 for p.
-3, -1/3
Let d be (144/(-15))/(6/16 - 3240/1600). Factor 512/11 - d*q + 2/11*q**2.
2*(q - 16)**2/11
Let o(v) be the third derivative of -v**7/420 - 41*v**6/240 + 43*v**5/40 - 131*v**4/48 + 11*v**3/3 - 340*v**2. Factor o(h).
-(h - 1)**3*(h + 44)/2
Let f = -9 - -9. Suppose -m + 2 = -f*m. Solve 2*o**4 + 2 - 4*o**m - 2*o**3 + 0*o**4 - 2*o**3 + 2*o + 2*o**5 = 0 for o.
-1, 1
What is x in -5*x + 1 + x**5 + 31/4*x**2 - 11/4*x**3 - 2*x**4 = 0?
-2, 1/2, 1, 2
Factor -22 - 7 + 59 - f**2 + 3*f - 4*f.
-(f - 5)*(f + 6)
Let o = -1593 + 1593. Let l(c) be the third derivative of 0*c**6 + 0*c**3 + 1/90*c**4 - 1/150*c**5 + o*c + 0 + 2*c**2 + 1/1575*c**7. Factor l(w).
2*w*(w - 1)**2*(w + 2)/15
Let z(a) = -5*a**2 + 10*a + 45. Let w(j) = 6*j. Let u(g) = 5*w(g) + z(g). Factor u(t).
-5*(t - 9)*(t + 1)
Let h = 21 - 20. Factor 2*t**2 - 4*t**2 + h + 1.
-2*(t - 1)*(t + 1)
Let f = -7 + 21. Let b = f + -11. Factor -5*q + 48*q**2 + 0*q - 46*q**2 - b*q.
2*q*(q - 4)
Suppose -22*x - 3*d = -21*x + 4, 16 = 3*x - 5*d. Factor 0 - 4/5*t - 2/5*t**x.
-2*t*(t + 2)/5
Let b(k) be the first derivative of -32*k**5/5 - 10*k**4 + 14*k**3 - 23*k**2/4 + k + 5. Solve b(u) = 0 for u.
-2, 1/4
Suppose 3*q + 5*a = 0, 6*a - 4*a = 0. Factor -6 + 9*h**4 - 2*h**2 - 4*h**2 + 3*h**4 + q - 12*h**3 + 15*h - 3*h**5.
-3*(h - 2)*(h - 1)**3*(h + 1)
Factor 2/11*k**4 + 2/11 - 2/11*k**5 - 4/11*k**2 + 4/11*k**3 - 2/11*k.
-2*(k - 1)**3*(k + 1)**2/11
Let b(c) be the second derivative of -3*c**5/20 + c**4 + 21*c**3/2 - 3*c + 21. Factor b(j).
-3*j*(j - 7)*(j + 3)
Let p(d) = 6 + 0 - 4*d + 2*d**2 - 3*d**2. Let l be p(-4). Find s, given that 1/2*s**3 + 4 + 3*s**2 + l*s = 0.
-2
Let f(n) = n - 1. Let r be f(4). Suppose -r = -2*c + 7. Determine o so that 5*o**c - 4*o**2 + 0*o**3 + 0*o**5 + 7*o**4 - 8*o**3 = 0.
-2, -2/5, 0, 1
Let h = 1209 + -1209. Let q(k) be the second derivative of -1/63*k**7 + h - 1/15*k**6 - 1/10*k**5 - 1/18*k**4 + 0*k**2 + 0*k**3 + 7*k. Factor q(u).
-2*u**2*(u + 1)**3/3
Let j(h) be the third derivative of 1/252*h**4 + 1/315*h**6 + 0*h**3 + 1/126*h**5 + 0*h + 0 - 14*h**2. Factor j(i).
2*i*(i + 1)*(4*i + 1)/21
Suppose -4*k = 2*x - 5968, 5*k = 2*x - 4*x + 7460. Let -3*c**4 + 3*c**3 - k + 12*c - 15*c**3 - 6*c**2 + 1501 = 0. Calculate c.
-3, -1, 1
Let p = -61 + 66. Suppose -p*k = -3*q, -k - k = 4*q. Let q*s - 2/5*s**3 - 4/15*s**2 + 0 = 0. What is s?
-2/3, 0
Let p(a) = a - 1. Let b(k) = 11*k**2 + 36*k + 4. Let w(s) = -b(s) + 3*p(s). Let d(f) = -16*f**2 - 50*f - 10. Let g(h) = 5*d(h) - 8*w(h). Factor g(l).
2*(l + 1)*(4*l + 3)
Let z(a) be the second derivative of -5*a**4/42 - 29*a**3/42 + 3*a**2/14 + 104*a. Find d, given that z(d) = 0.
-3, 1/10
Let z = -2/75 + 41/600. Let w(q) be the third derivative of 0*q - 1/64*q**4 + 0 - z*q**3 + 0*q**5 + 1/960*q**6 - 5*q**2. Factor w(o).
(o - 2)*(o + 1)**2/8
Suppose 0 = 4*o + 28, 0 = -3*p + 195*o - 191*o + 334. Solve -57*k**3 - 15*k**4 - 171/2*k - 3/2*k**5 - p*k**2 - 27 = 0 for k.
-3, -2, -1
Let k = 2328/12199 + -10/1109. Solve 6/11*x**4 + 0*x**3 + 0 + k*x**5 + 0*x - 8/11*x**2 = 0.
-2, 0, 1
Let p(j) be the second derivative of 5*j**4/4 - 235*j**3/6 + 75*j**2 + 610*j. Determine w so that p(w) = 0.
2/3, 15
Let f be (90/(-108))/(120/(-32)) - 92/(-234). Let f*i**3 + 0*i + 4/13*i**4 + 0 - 2/13*i**5 - 16/13*i**2 = 0. Calculate i.
-2, 0, 2
Let n(u) be the first derivative of -2*u**3/9 + 3*u**2 - 40*u/3 - 95. Solve n(k) = 0.
4, 5
Let n(z) be the third derivative of z**8/112 - 3*z**7/70 - z**6/10 + 4*z**5/5 - 8*z**3 + 2*z**2 + 2*z. Determine p so that n(p) = 0.
-2, -1, 2
Let q(h) be the second derivative of h**6/15 + 4*h**5/5 + 5*h**4/2 - 8*h**3/3 - 16*h**2 + 29*h. Factor q(y).
2*(y - 1)*(y + 1)*(y + 4)**2
Let q = -5285/3 - -1763. Determine n, given that q - 2/3*n**2 - 2/3*n = 0.
-2, 1
Let s(c) be the third derivative of 0*c**3 - 2 - 5/84*c**4 + 0*c - 1/140*c**5 + c**2 + 1/840*c**6. Factor s(g).
g*(g - 5)*(g + 2)/7
Let t(g) be the second derivative of -g**4/48 - g**3/8 + g**2/2 + 2*g + 41. Factor t(n).
-(n - 1)*(n + 4)/4
What is i in 30*i + 0*i**2 - 15 - 12 + 2*i**2 - 5 = 0?
-16, 1
Let f(k) be the first derivative of -1/3*k**3 + k + 2 - 1/2*k**2 + 1/4*k**4. Suppose f(d) = 0. What is d?
-1, 1
Factor 2*q**2 + 2/3*q - 2 - 2/3*q**3.
-2*(q - 3)*(q - 1)*(q + 1)/3
Let l(c) be the third derivative of -c**7/70 - c**6/20 + c**4/4 + c**3/2 + 51*c**2. Factor l(x).
-3*(x - 1)*(x + 1)**3
Factor -3*r + 14 - 27*r**2 - 39 + 21*r + 0*r**3 + r**3 + 33*r.
(r - 25)*(r - 1)**2
Let s be (-136)/1050 - 3/(-21). Let v(b) be the second derivative of -s*b**6 + 1/10*b**4 - b + 1/50*b**5 + 2/5*b**2 + 0 - 1/3*b**3. Factor v(i).
-2*(i - 1)**3*(i + 2)/5
Determine s so that -12*s**2 - 5*s**5 - 26*s**3 - 293*s**4 - 2*s + 321*s**4 + 2*s - s**5 = 0.
-1/3, 0, 2, 3
Let r(x) be the third derivative of -x**5/110 - 14*x**4/11 - 5*x**3 - x**2 - 760*x. Suppose r(p) = 0. What is p?
-55, -1
Suppose -63 = -3*x - 57. Factor 0*d**2 + d + x*d**2 + 14*d + d**2.
3*d*(d + 5)
Let l be 2 + 1*(3 + (-263)/2). Let d = l + 127. Factor 1/2*a**3 + 1 - d*a - a**2.
(a - 2)*(a - 1)*(a + 1)/2
Let h(g) = g**3 - 15*g**2 + 14*g - 14. Let m be h(14). Let w = m - -17. Factor 7*p**3 + 11*p**3 - 14*p**w - 4*p**2.
4*p**2*(p - 1)
Let j(a) be the third derivative of 0*a - 1/84*a**4 + 0 - 2*a**2 - 1/420*a**5 - 1/42*a**3. Determine y so that j(y) = 0.
-1
Let 1105*b - 2571*b - 4*b**3 - 77*b**2 - 2886*b - 4096 - 183*b**2 = 0. What is b?
-32, -1
Let c = 2/737 + 721/5896. Let p(u) be the first derivative of 2/3*u**3 - 3 + 1/4*u**2 + 0*u - 2/5*u**5 - c*u**4. Factor p(z).
-z*(z - 1)*(z + 1)*(4*z + 1)/2
Let i(v) = 3*v**4 + 6*v*