*d - 3)/15
Suppose 1 = -j + 10. Let m = 13 - j. Suppose -4*r**2 - 3*r**3 + 5*r**2 - r + 4*r**3 - r**m + 0*r**3 = 0. What is r?
-1, 0, 1
Factor -3*t**2 - 114*t + 114*t - t**3.
-t**2*(t + 3)
Let u = 495 + -495. Let c(x) be the second derivative of u + 1/9*x**3 - 2/9*x**2 - 9*x - 1/54*x**4. Suppose c(i) = 0. What is i?
1, 2
Let n(h) be the second derivative of h**7/462 - h**6/66 - 2*h**5/55 + h**4/3 + 16*h**3/33 - 32*h**2/11 - h - 27. Determine w, given that n(w) = 0.
-2, 1, 4
Let g(b) be the second derivative of -b**4/18 + 5*b**3/9 + 8*b**2 - 7*b + 48. Suppose g(a) = 0. Calculate a.
-3, 8
Let b(g) be the third derivative of -g**6/30 + 3*g**5/5 - g**4 - 32*g**3/3 - 47*g**2 + g. Determine y, given that b(y) = 0.
-1, 2, 8
Let t(k) = k. Let h(n) = -n**3 + 12*n**2 - 18*n. Let c(f) = 5*h(f) + 35*t(f). Factor c(d).
-5*d*(d - 11)*(d - 1)
Let y(j) be the second derivative of 2*j**6/15 - 48*j**5/5 + 526*j**4/3 + 800*j**3 + 1250*j**2 + 177*j. Find z, given that y(z) = 0.
-1, 25
Let j(o) be the first derivative of -2/3*o**4 + 10/9*o**3 - 1 - 2/3*o**2 + 0*o + 2/15*o**5. Factor j(p).
2*p*(p - 2)*(p - 1)**2/3
Let b(n) be the second derivative of 0 - 11*n + 0*n**2 - 1/75*n**6 + 0*n**4 + 0*n**3 + 1/50*n**5. Suppose b(r) = 0. What is r?
0, 1
Let l(o) be the first derivative of o**3/3 - o**2/2 + 6*o - 12. Let t(h) = 2*h - 6. Let a(r) = -4*l(r) - 6*t(r). Factor a(z).
-4*(z - 1)*(z + 3)
Let z(n) = -n**3 + 8*n**2 + 33*n - 38. Let r(y) = -y**3 + 17*y**2 + 66*y - 77. Let q(m) = -2*r(m) + 5*z(m). Find w, given that q(w) = 0.
-3, 1, 4
Let g(u) be the second derivative of -27*u**4/16 + 3*u**3/4 - u**2/8 + 51*u. Factor g(f).
-(9*f - 1)**2/4
Let r be (-1 - -1)*8/24. Factor 1/4*i**3 - 1/4*i**5 + 1/4*i**4 + r*i + 0 - 1/4*i**2.
-i**2*(i - 1)**2*(i + 1)/4
Factor 80 - 43*p + 21*p - 28*p + 5*p**2.
5*(p - 8)*(p - 2)
Let n = -500 - -503. Let r(z) be the second derivative of 0*z**4 + 0*z**n - 3*z + 1/25*z**5 + 0 - 7/75*z**6 + 0*z**2. Factor r(m).
-2*m**3*(7*m - 2)/5
Let d = 508/11 - 2518/55. Factor 0 - 2/5*q**3 + 4/5*q**4 - d*q**5 + 0*q**2 + 0*q.
-2*q**3*(q - 1)**2/5
Let m(q) be the first derivative of -2*q**3/21 + 4*q**2/7 - 6*q/7 + 106. Factor m(u).
-2*(u - 3)*(u - 1)/7
Let v = 885/13 + -4399/65. Factor 4/5 - v*w - 2/5*w**2.
-2*(w - 1)*(w + 2)/5
Let f = 24182/7 - 3452. Factor -6/7*h**3 + 8/7*h + 0 + 16/7*h**2 - f*h**4.
-2*h*(h - 1)*(3*h + 2)**2/7
Suppose 18*d = 21*d - 45. Factor -4 - 9*y**2 - 23*y - 8*y - 8 - 5*y + d*y**3.
3*(y - 2)*(y + 1)*(5*y + 2)
Let j(v) be the third derivative of v**6/3060 + v**5/340 + 23*v**3/6 - 5*v**2. Let x(i) be the first derivative of j(i). Determine t, given that x(t) = 0.
-3, 0
Suppose -16*j = 77*j - 279. Find k such that -2/7*k**2 + 16/7*k - 8/7 - 6/7*k**j = 0.
-2, 2/3, 1
Let f be (-40)/(-100) + 18/5. Find t such that -7 - 26*t + f*t**2 + 22*t - 1 = 0.
-1, 2
Let v(f) be the third derivative of 0*f**6 - 11*f**2 + 1/1680*f**8 - 1/1050*f**7 + 0 + 0*f**3 + 0*f**4 + 0*f + 0*f**5. Suppose v(l) = 0. Calculate l.
0, 1
Let b = -163 - -73. Let l = -88 - b. Suppose -4/5*p - 1/5*p**l - 3/5 = 0. Calculate p.
-3, -1
What is i in -4/5*i**4 - 16/5*i + 68/5*i**2 + 17/5*i**3 - 64/5 - 1/5*i**5 = 0?
-4, -1, 1, 4
Suppose 0*u - 3/4*u**3 + 0 + 1/4*u**2 - u**4 = 0. Calculate u.
-1, 0, 1/4
Suppose -16*n + 12*n - 424 = 0. Let j = n - -108. Let -1/4*m**j + m - 1 = 0. Calculate m.
2
Let y(l) be the third derivative of l**5/300 + l**4/20 + 4*l**3/15 - 2*l**2 + 64. Find v, given that y(v) = 0.
-4, -2
Let d = -4/111 - -152/111. Let x(j) be the second derivative of -2*j + 0*j**2 + 0 + d*j**3 + 1/3*j**4. Determine r so that x(r) = 0.
-2, 0
Factor 191*v + 21*v + 60*v**3 + 72 + 60*v**4 - 64*v**4 + 132*v**2 + 72*v**2.
-4*(v - 18)*(v + 1)**3
Let r(o) be the second derivative of -o**7/1680 + o**6/180 - o**5/60 + 5*o**3/2 + 18*o. Let x(i) be the second derivative of r(i). Factor x(j).
-j*(j - 2)**2/2
Find p such that -20*p**3 + 39*p**2 + 5*p**4 + 5*p**5 + 17*p - 49*p**2 + 5*p**4 - 2*p = 0.
-3, -1, 0, 1
Let f = 40 - 26. Let c be 7/f + (1 - 1). Solve 1/2*r - c*r**3 - 2*r**4 + 0 + 2*r**2 = 0 for r.
-1, -1/4, 0, 1
Suppose -8*v**3 - 537*v**5 + 4*v**4 + 0*v**4 + 541*v**5 = 0. What is v?
-2, 0, 1
Let 7/3*a - 22/9*a**3 - 7/9*a**4 + 1/9*a**5 - 3 + 34/9*a**2 = 0. Calculate a.
-3, -1, 1, 9
Suppose 36 - 21 = 5*g. Find x such that 3*x**2 - g*x**2 + 18*x - 4*x**2 - 2*x = 0.
0, 4
Let y(u) be the first derivative of 4*u**3/9 - 2*u**2 - 112*u/3 - 197. Let y(w) = 0. What is w?
-4, 7
Let 12/5*n**4 + 3/5*n**5 + 0*n**2 + 0*n + 9/5*n**3 + 0 = 0. What is n?
-3, -1, 0
Let y be (-26)/(-8) - 3 - 84/(-48). Let t(h) be the first derivative of -y*h + 0*h**2 + 4 + 2/3*h**3. Let t(p) = 0. What is p?
-1, 1
Let v(f) be the third derivative of 0*f + 1/20*f**5 - 1/4*f**4 + 0 + 0*f**3 + 1/40*f**6 - 4*f**2. Solve v(l) = 0 for l.
-2, 0, 1
Suppose 5*k = 4*m - 5, -k = 3*m - m + 1. Suppose 5*a = -h + 17 - 7, 4*h - 4*a + 8 = m. Suppose -2/11*w**3 + h*w**2 + 2/11*w + 0 = 0. Calculate w.
-1, 0, 1
Let b be 0 - (3 + -3) - 0/17. Let q(v) be the first derivative of b*v**3 + 1/10*v**4 + 0*v**2 + 0*v + 6. Solve q(r) = 0 for r.
0
Determine z, given that -21/5*z**4 - 846/5*z**3 - 9417/5*z**2 - 17784/5*z - 4332/5 = 0.
-19, -2, -2/7
Let f = -702 - -702. Let q(g) be the third derivative of 0*g + 1/90*g**6 - 6*g**2 + f*g**3 + 1/18*g**4 + 0 - 2/27*g**5. Suppose q(i) = 0. What is i?
0, 1/3, 3
Let b(m) be the first derivative of -11/2*m**2 - 1/30*m**5 + 7 + 1/20*m**4 + 0*m + 2/15*m**3. Let o(v) be the second derivative of b(v). Factor o(u).
-2*(u - 1)*(5*u + 2)/5
Let d(x) be the third derivative of x**8/28 - 37*x**7/210 + 19*x**6/60 - x**5/5 - x**4/12 + x**3/6 - 27*x**2. Find t such that d(t) = 0.
-1/4, 1/3, 1
Let q(v) = -v**5 - v**4 + v**3 - 1. Let n(a) = -2*a**5 + 4*a**4 - 9*a**3 + 10*a**2 - 5*a. Let b(u) = -5*n(u) + 5*q(u). Factor b(p).
5*(p - 1)**5
Let n = 2013 - 2007. Let g(b) be the third derivative of 0*b**4 + 0 - 2/105*b**7 + 1/15*b**5 + 0*b + 1/20*b**n - 2*b**2 + 0*b**3. What is f in g(f) = 0?
-1/2, 0, 2
Let a be 3/(-9) - (-467)/(-3). Let d be (-984)/a + -4 + -2. Determine z so that 10/13*z + 32/13*z**2 + 18/13*z**3 - d = 0.
-1, 2/9
Suppose -m = 6*m - 238. Let v = m + -34. Let v + 3/4*a**4 + 9/4*a**2 + 3/4*a + 9/4*a**3 = 0. Calculate a.
-1, 0
Let a = 8/595 - -523/5355. Solve 0*d**3 + 2/9*d**4 - 2/9*d**2 - a*d + 0 + 1/9*d**5 = 0 for d.
-1, 0, 1
Let c(z) be the third derivative of 1/2*z**4 + 0 - 2/5*z**5 + 0*z**3 + 0*z - 7/40*z**6 + 16*z**2 + 1/14*z**7. Factor c(o).
3*o*(o - 2)*(o + 1)*(5*o - 2)
Let r(o) = 12*o**3 + 240*o**2 - 21*o - 222. Let b(t) = -3*t**3 - 60*t**2 + 5*t + 56. Let a(f) = -9*b(f) - 2*r(f). Find m such that a(m) = 0.
-20, -1, 1
Let a(x) be the first derivative of x**3/18 + 27*x**2/2 + 2187*x/2 - 198. Let a(r) = 0. What is r?
-81
Suppose u = 2*s - 5 - 0, 0 = 2*u - 2. Let q(l) be the first derivative of 6*l - 3/2*l**2 + 3/5*l**5 + 3/4*l**4 - s*l**3 - 2. Factor q(w).
3*(w - 1)**2*(w + 1)*(w + 2)
Factor -27*f + 21*f**4 - 419*f**2 - 453*f**2 + 75*f**3 + 899*f**2.
3*f*(f + 1)*(f + 3)*(7*f - 3)
Let k be (2/(-8))/(4/(-32)) + 0. Factor 4/9 + k*s + 14/9*s**2.
2*(s + 1)*(7*s + 2)/9
Let w(h) = 3*h**3 - 87*h**2 + 3*h - 87. Let c be w(29). Let -104/3*g**2 + 16/3*g + 52*g**3 - 40/3*g**5 + c + 26/3*g**4 = 0. Calculate g.
-2, 0, 1/4, 2/5, 2
Let w(s) = -202*s**2 - 230*s - 64. Let c(l) = 201*l**2 + 229*l + 64. Let g(j) = -6*c(j) - 5*w(j). Find d such that g(d) = 0.
-4/7
Suppose -5 = t + t - 3*k, -30 = -t - 5*k. Suppose -24 = -5*c - 2*w + t*w, -4*w = 4*c. Determine s so that 1/2*s**c + s**2 + 0*s + 0 = 0.
-2, 0
Let t(d) = 8*d**2 + 1064*d + 28. Let c(q) = q**2 + 118*q + 3. Let k(r) = 28*c(r) - 3*t(r). Suppose k(b) = 0. What is b?
-28, 0
Factor -624*s**2 + 625*s**2 - 43*s - 2*s.
s*(s - 45)
Find s such that -3/2*s**4 - 7*s**3 - 11/3*s - 1/2 - 26/3*s**2 = 0.
-3, -1, -1/3
Let q = 8329 - 24985/3. Factor 5/3*l**2 - 4/3*l**3 - q*l + 1/3*l**4 + 0.
l*(l - 2)*(l - 1)**2/3
Let s(o) be the second derivative of o**10/15120 - o**9/7560 - o**4/12 - 5*o**3/6 + 2*o + 9. Let c(d) be the third derivative of s(d). Factor c(w).
2*w**4*(w - 1)
Let w(p) be the first derivative of -16 - p**2 + 2/9*p**3 + 4/3*p. Factor w(z).
2*(z - 2)*(z - 1)/3
Suppose -5*v + 7*v - 58 = 0. Let s = v + -26. Solve 16/5*o - 8/5 - 2*o**2 + 2/5*o**s = 0.
1, 2
Let m(t) = 3*t**2 - 5*t.