d + 1)/9
Let d be ((-28)/12)/((-2)/(-92)). Let m = 108 + d. Solve 2/3*p**2 + m*p - 4/3 = 0.
-2, 1
Factor -1 - b**3 - 34*b - 8*b + b**2 + 43*b.
-(b - 1)**2*(b + 1)
Let a(d) = -d**3 - 3*d**2 - d. Let o be a(-3). Suppose -3*b + 14 = 5*j - 0*j, -j + o*b = -10. Factor -c**2 + 15 - 15 + 2*c**4 - c**j.
c**2*(c - 1)*(c + 1)
Let n = -340 + 238. Let q = 102 + n. What is b in -4/3*b**3 + 0 + q*b**2 - 2/3*b**4 + 0*b = 0?
-2, 0
Let w = 42 - 44. Let a be (-7 + 7)*(-3 - w). Suppose a*h**2 - 3/5*h**3 + 0*h - 3/5*h**4 + 0 = 0. Calculate h.
-1, 0
Let c(o) be the third derivative of -7/6*o**3 + 0 - 8*o**2 + 1/60*o**5 - 1/4*o**4 + 0*o. Let i(w) = 2*w**2 - 6*w - 8. Let g(h) = -5*c(h) + 4*i(h). Factor g(v).
3*(v + 1)**2
Let m(t) be the first derivative of 1/15*t**3 + 4 - 4*t + 0*t**2 + 1/10*t**4 + 1/25*t**5. Let s(k) be the first derivative of m(k). Factor s(j).
2*j*(j + 1)*(2*j + 1)/5
Suppose -3*h + 4*h = a - 22, 0 = -5*a + 2*h + 119. Suppose 0 = -n + 1, 4*r - a = -n + 4*n. Suppose -4*i**3 + 2*i**3 - r*i**2 + 8*i**2 + i**4 = 0. Calculate i.
0, 1
Suppose 2*l + 2 - 10 = 0. Let n(s) be the first derivative of -4/21*s**3 + 4/35*s**5 - 1/7*s**4 + 2/7*s**2 - l + 0*s. Factor n(f).
4*f*(f - 1)**2*(f + 1)/7
Let b(l) = -l**2 + 3*l + 4. Let h(y) = 6*y**2 - 42. Let u(p) = -3*b(p) - h(p). Factor u(j).
-3*(j - 2)*(j + 5)
Let k(b) be the first derivative of -7*b**6/4 - 57*b**5/10 + 81*b**4/8 + 43*b**3/2 - 42*b**2 + 18*b + 20. What is h in k(h) = 0?
-3, -2, 2/7, 1
Let o be 68/84 + (-1)/7. Let i = 68 + -66. Solve 0 - o*n**i - 3*n**3 + 0*n = 0.
-2/9, 0
Suppose 0 = -5*i + 40, 32 = -50*l + 52*l + 4*i. Factor l - 4/9*o**5 - 16/9*o**2 + 4/3*o**3 - 16/9*o + 8/9*o**4.
-4*o*(o - 2)**2*(o + 1)**2/9
Let 254*c**2 + 672*c + 77*c**2 + 228 - 159*c**2 - 27*c**3 + 305*c**2 = 0. What is c?
-2/3, 19
Let i(w) be the second derivative of 1/8*w**5 - 31*w + 3/8*w**4 - 1/2*w**2 - 5/12*w**3 - 7/60*w**6 + 0. Solve i(r) = 0 for r.
-1, -2/7, 1
Suppose -12 = -9*h + 3*h. Suppose -12 = -6*y + h*y. Factor 1 + 3*m**3 - 2*m**3 + 2*m - 2*m**y - m**4 - m**3.
-(m - 1)*(m + 1)**3
Let x(y) = -y**3 + 10*y**2 - 22*y + 6. Let p be x(6). Factor -p - 22 - 22*b**2 - 148*b - 6*b**2.
-4*(b + 5)*(7*b + 2)
Let s = 74/99 + -7/11. Let n(z) be the first derivative of -s*z**2 + 7 + 0*z + 0*z**3 + 1/18*z**4. Solve n(u) = 0 for u.
-1, 0, 1
Let t(n) be the third derivative of -n**5/180 + n**4/6 - 2*n**3 + 271*n**2. What is r in t(r) = 0?
6
Factor 0 + 30/7*q - 2/7*q**4 - 46/7*q**2 + 18/7*q**3.
-2*q*(q - 5)*(q - 3)*(q - 1)/7
Let k(m) be the first derivative of -m**4/11 + 74*m**3/33 - 180*m**2/11 + 162*m/11 + 79. Suppose k(g) = 0. What is g?
1/2, 9
Let x = 4455 + -4453. Factor 1/4*p**x - 3/4*p + 0.
p*(p - 3)/4
Let i be 14/28*((-4)/4 + 1). Let j(o) be the second derivative of i - 2/15*o**4 + 4/5*o**2 + 5*o + 7/25*o**5 - 14/15*o**3. Find u, given that j(u) = 0.
-1, 2/7, 1
Let b be (292/10)/(3/30). Factor 50*h**2 + 4*h + 16*h + b - 290.
2*(5*h + 1)**2
Let q(u) be the third derivative of u**8/2940 - u**7/630 + u**6/630 + u**5/210 - 35*u**4/24 - 17*u**2. Let a(r) be the second derivative of q(r). Factor a(n).
4*(n - 1)**2*(4*n + 1)/7
Let x(l) be the second derivative of 2*l**7/21 + 8*l**6/15 - 6*l**5/5 - 32*l**4/3 - 70*l**3/3 - 24*l**2 - l - 205. Factor x(z).
4*(z - 3)*(z + 1)**3*(z + 4)
Suppose h - 3*w - 138 = 0, 3*h + h - 488 = -4*w. Let n = h + -245/2. Factor n*q**3 - 9*q**2 - 1/2*q**4 + 10*q - 4.
-(q - 2)**3*(q - 1)/2
Suppose -2/17*v**4 - 8/17*v + 8/17*v**2 + 0 + 2/17*v**3 = 0. What is v?
-2, 0, 1, 2
Solve -742*d**4 - 183*d**2 + 320 + 739*d**4 - 69*d**2 - 288*d - 52*d**3 = 0 for d.
-10, -4, 2/3
Let x(u) be the first derivative of -1/20*u**4 + 1/10*u**2 - 3 - 1/25*u**5 + 0*u + 1/15*u**3. Factor x(c).
-c*(c - 1)*(c + 1)**2/5
Let r = -15007 + 15009. Solve -2/13*z**r - 36/13*z - 162/13 = 0.
-9
Let k = -2240 + 2242. Determine m, given that 4/7 - 52/7*m**k - 48/7*m = 0.
-1, 1/13
Suppose -11*i + 3*i + 40 = 0. Let -20*x**2 - 25*x + 5*x**4 - 58*x**3 + i*x + 113*x**3 - 50*x**3 = 0. What is x?
-2, -1, 0, 2
Let z(w) be the first derivative of -w**4/14 - 8*w**3/21 - 5*w**2/7 - 4*w/7 + 266. Factor z(c).
-2*(c + 1)**2*(c + 2)/7
Let x(t) be the third derivative of t**5/240 - 7*t**4/24 + 49*t**3/6 + 464*t**2. Find o, given that x(o) = 0.
14
Suppose -2/3*r**5 + 0 + 8/3*r**2 - 22/5*r**3 + 44/15*r**4 - 8/15*r = 0. What is r?
0, 2/5, 1, 2
Suppose 91*b + 2 = 92*b. Let r(g) be the second derivative of 0 + 0*g**b + g + 1/14*g**3 + 1/28*g**4. Factor r(n).
3*n*(n + 1)/7
Find d, given that 0 - 120/11*d**2 - 28/11*d**3 - 2/11*d**4 - 144/11*d = 0.
-6, -2, 0
Let n(b) be the second derivative of 0 + 6*b + 1/80*b**5 + 1/2*b**3 - 5/2*b**2 - 1/8*b**4. Let u(h) be the first derivative of n(h). Solve u(r) = 0.
2
Let x(v) be the second derivative of 121*v**4/4 - 11*v**3/2 + 3*v**2/8 + 6*v. Determine s so that x(s) = 0.
1/22
Let i(g) = -4*g + 20 + 16*g - 138*g**2 + 139*g**2. Let l be i(-10). Determine n so that 0*n + l + 1/3*n**4 - 4/3*n**3 + 4/3*n**2 = 0.
0, 2
Let p(a) be the second derivative of -4*a + 5*a**2 + 0 - 5/2*a**4 + 5/6*a**3. Suppose p(i) = 0. What is i?
-1/2, 2/3
Let r(x) be the first derivative of -2*x**2 - 8/3*x**3 - x**4 + 0*x - 7. Solve r(i) = 0 for i.
-1, 0
Let o(u) be the second derivative of u**4/132 - 5*u**3/33 + 4*u + 1. Factor o(l).
l*(l - 10)/11
Let r(o) = 8*o**3 - 13*o**2 - 29*o - 17. Let i(j) = 22*j**3 - 38*j**2 - 86*j - 50. Let t(m) = 3*i(m) - 8*r(m). Factor t(n).
2*(n - 7)*(n + 1)**2
Factor 9*l**2 - 4/3 + 7/3*l**3 + 8*l.
(l + 2)**2*(7*l - 1)/3
Let 18463*p**2 - 525*p**3 - 214375*p + 7*p**4 - 3*p**4 + p**4 - 88*p**2 = 0. What is p?
0, 35
Let a(p) be the third derivative of 32/3*p**3 - 2*p**4 - 1/120*p**6 + 0 - 38*p**2 - 1/4*p**5 + 0*p. Factor a(w).
-(w - 1)*(w + 8)**2
Suppose -u = -2*g + g - 10, -3*u = g - 10. Let 3*s**u - 25 - 21*s - 6*s**3 + 49 - 24*s**2 - 30 + 6*s**4 = 0. What is s?
-1, 2
What is w in 120/7*w**2 + 44/7*w + 4/7 = 0?
-1/5, -1/6
Let d = 31662 + -31662. Suppose d + 4*c**2 + 0*c - 2/3*c**4 - 2/3*c**3 = 0. Calculate c.
-3, 0, 2
Let u be (1 - (-6)/3) + 9. Let v = u - 8. Find d, given that 2 + d**3 + 14*d**2 + 25*d**3 + 10*d + 2*d**5 + 6*d**2 + 10*d**v - 6*d**3 = 0.
-1
Let o be -46*(-1 - 10/(-5)). Let g = o - -46. Factor 2/5*r - 4/5*r**2 + g + 2/5*r**3.
2*r*(r - 1)**2/5
Suppose 13*x - 82 = -30. Factor -9*z**4 - 3*z**4 + 12 + 9*z**x + 12*z**3 - 9*z**2 - 12*z.
-3*(z - 2)**2*(z - 1)*(z + 1)
Suppose 109*q - 380*q = 0. Solve 4*j**2 + q*j**3 + 0 - 4/7*j**4 - 24/7*j = 0.
-3, 0, 1, 2
Let g(b) = -2*b**2 - 4*b + 6. Let h(r) = r**2 + 4*r - 5. Suppose 3*m = 4*m + 5. Let x(j) = m*h(j) - 4*g(j). What is u in x(u) = 0?
1/3, 1
Let f(z) = -z**2 + 24*z - 25*z + 2*z**2. Let o(k) = 2*k**2 + 0*k**2 - k - 4 + 3*k**2. Let b(q) = 3*f(q) - o(q). Factor b(c).
-2*(c - 1)*(c + 2)
Let c(b) be the second derivative of 2/105*b**6 + 0*b**2 + 5/21*b**4 - 4/35*b**5 - 4/21*b**3 + 25*b + 0. Factor c(m).
4*m*(m - 2)*(m - 1)**2/7
Let h be 3/6*0/(-13). Factor -2/15*q**2 - 2/15*q + h.
-2*q*(q + 1)/15
Suppose 5*y + 2*b - 26 = 0, 2*y - 2*b - 4 = -2. Let s(j) = -j**3 + 3*j**2 + 3*j + 4. Let g be s(y). Factor -3 - 4*h**2 + g*h**3 + 2*h**3 + 2*h + 3.
2*h*(h - 1)**2
Let x(q) = -4*q**4 + 4*q**3 + q**2 + 2*q + 3. Let m(c) = -c**4 + c**3 + c + 1. Let p(i) = 6*m(i) - 2*x(i). Factor p(h).
2*h*(h - 1)**2*(h + 1)
Suppose -1078*c**3 - 144*c - 623*c**2 - 56*c - 16 - 15*c**2 - 174*c**2 = 0. What is c?
-2/7, -2/11
Let i be (105/(-20))/(-7) - (-3)/(-4). Let p(k) be the first derivative of i*k**2 + 1/3*k**6 + 2 - 4/5*k**5 + 0*k**3 + 1/2*k**4 + 0*k. What is g in p(g) = 0?
0, 1
Let k(p) be the third derivative of -p**8/80640 - p**7/20160 + p**6/1440 + p**5/20 + 6*p**2. Let b(o) be the third derivative of k(o). Factor b(t).
-(t - 1)*(t + 2)/4
Suppose 5*d + 3*z - 490 = 310, -3*d + 2*z + 480 = 0. Suppose -13*c - 7*c + d = 0. Factor -26/7*r - c*r**2 - 40/7*r**3 - 4/7.
-2*(2*r + 1)**2*(5*r + 2)/7
Let l(y) be the second derivative of -y**4/3 + 80*y**3/3 - 78*y**2 + 614*y. Let l(h) = 0. What is h?
1, 39
Find y, given that 879*y**3 + 879*y**3 - 1756*y**3 + 2*y**2 - 17 - 18*y - 1 = 0.
-3, -1, 3
Determine p so that 0*p**2 + 0 + 2*p - 1/2*p**3 = 0.
-2, 0, 2
Let p(h) be the second derivative of -23*h - 2/105*h**6 - 3/140*h**5 + 0*h**4 + 0*h**2 - 1/294*h**7 + 0 + 0*h**3. Let p(j) = 0. Calculate j.
-3, -1, 