
Let c be -14 - ((-948)/36 - -12). Factor -c*p**2 - 14/3*p - 49/3.
-(p + 7)**2/3
Factor 2/15*v**2 + 184/15 + 18/5*v.
2*(v + 4)*(v + 23)/15
Suppose b = -5*j - 2, -8 = 5*j - b + 5*b. Suppose 0*s + 0 + 0*s**4 + j*s**2 + 2/7*s**5 - 2/7*s**3 = 0. Calculate s.
-1, 0, 1
Let w be (-518)/(-630) + 6/(-27). Let i(q) be the first derivative of -3/2*q**4 - w*q**5 + 0*q**2 - q**3 + 0*q + 8. Factor i(t).
-3*t**2*(t + 1)**2
Let v(l) be the second derivative of -3*l + 0*l**2 + 0 - 1/20*l**5 + 0*l**3 - 1/6*l**4. Let v(h) = 0. What is h?
-2, 0
Solve -145 + i**5 + 240*i**4 + 9600*i**3 + 145 + 128000*i**2 + i**5 = 0 for i.
-40, 0
Let v(u) be the first derivative of -2/45*u**5 + 1 + 0*u - 1/9*u**4 + 0*u**2 + 0*u**3. What is w in v(w) = 0?
-2, 0
Let k be 720/1400 + (-4)/(-70). Suppose -8/7*n**2 - k + 2/7*n**3 + 10/7*n = 0. Calculate n.
1, 2
Suppose 3*h = -4*i - 0*h - 38, -h + 2 = 0. Let v = i + 14. Suppose 36*u**2 + 50*u**v - 5*u**3 + 15*u**4 - 12*u - 3*u**4 = 0. What is u?
-2, 0, 1/4
Let k be 6 - 3*1/(-3). Let s(m) be the second derivative of -m + 0*m**2 + 0 + 0*m**4 - 1/30*m**6 - 1/42*m**k + 0*m**3 + 1/10*m**5. Factor s(w).
-w**3*(w - 1)*(w + 2)
Let m be (-1 + 2/(-4))*96/(-36). Suppose 0 = s + x - 2 - 2, 5*x = -m*s + 18. Find o, given that 2/11*o**4 + 0*o**3 + 0*o - 2/11*o**s + 0 = 0.
-1, 0, 1
Let f(o) be the first derivative of -2*o**5/5 + 9*o**4/2 + 28*o**3/3 - 36*o**2 - 80*o + 373. Suppose f(i) = 0. Calculate i.
-2, -1, 2, 10
Let q(o) be the first derivative of o**5/25 - o**4/5 + 2*o**3/5 - 2*o**2/5 - 22*o - 16. Let b(t) be the first derivative of q(t). Let b(k) = 0. What is k?
1
Let u(j) be the first derivative of -j**5/140 - j**4/56 - 9*j**2/2 + 7. Let m(s) be the second derivative of u(s). Factor m(o).
-3*o*(o + 1)/7
Let g(t) = t - 21 - 2*t + 8 + 2. Let o be g(-15). Suppose 0*x + 0*x**3 + 1/2*x**o + 0*x**2 + 0 = 0. Calculate x.
0
Let j(q) be the third derivative of -q**7/105 - 13*q**6/120 - 2*q**5/5 - 17*q**4/24 - 2*q**3/3 + 4*q**2 - 2*q. Factor j(u).
-(u + 1)**2*(u + 4)*(2*u + 1)
Let j be -23 - (-1568)/70 - (-51)/35. Suppose -4/21 - 2/3*d + j*d**2 = 0. Calculate d.
-2/9, 1
Let t(r) be the second derivative of 1/48*r**7 + 0 + 13*r + 1/20*r**6 + 0*r**2 + 0*r**3 + 3/160*r**5 - 1/48*r**4. Solve t(j) = 0 for j.
-1, 0, 2/7
Let o be (-248)/186*(-9)/16. Factor 3/4*d**4 + 1/4*d**5 - 1/2*d**2 - 1/4 + 1/2*d**3 - o*d.
(d - 1)*(d + 1)**4/4
Let o(w) be the first derivative of -w**5/5 - w**4 + 10*w**3/3 - 7*w**2 + 5*w + 2. Let h(q) = q**3 + q**2. Let l(s) = 10*h(s) + 5*o(s). What is i in l(i) = 0?
-5, 1
Factor 4*z**4 + 291*z**3 - 3*z**4 - z**4 + 2*z**4 + 6050*z**2 - 71*z**3.
2*z**2*(z + 55)**2
Let k(w) be the third derivative of w**6/360 - w**5/180 + 31*w**2. Suppose k(i) = 0. What is i?
0, 1
Suppose -2*y + 1 = -29. Let -6*t**3 + y - 10 - 9 + 6*t + 4*t**3 = 0. What is t?
-2, 1
Suppose 1/5*g**2 + 19/5*g + 84/5 = 0. Calculate g.
-12, -7
Factor -27/2*w + 3/4*w**4 - 27/4 + 3/2*w**3 - 6*w**2.
3*(w - 3)*(w + 1)**2*(w + 3)/4
Let g(o) be the first derivative of -3/16*o**4 - 5/12*o**3 - 7 - 1/4*o**2 + 0*o. Factor g(s).
-s*(s + 1)*(3*s + 2)/4
Let z(g) be the second derivative of -g**4/24 - 17*g**3/6 - 289*g**2/4 - 2*g + 30. Find w such that z(w) = 0.
-17
Let x(g) be the third derivative of g**8/336 + g**7/210 - g**6/120 - g**5/60 + 58*g**2 + 2. Determine a so that x(a) = 0.
-1, 0, 1
Let g(y) be the first derivative of y**4/4 - y**3/3 - y**2/2 + 6. Let b(x) = -4*x**3 + 7*x**2 + 5*x. Let f(l) = 3*b(l) + 15*g(l). Factor f(s).
3*s**2*(s + 2)
Let p(v) be the second derivative of -v**8/33600 + v**7/6300 + v**4/2 - 4*v. Let n(y) be the third derivative of p(y). Factor n(w).
-w**2*(w - 2)/5
Let t(w) be the first derivative of -w**3/2 - 61*w**2/4 + 21*w + 1. Suppose t(p) = 0. What is p?
-21, 2/3
Let d(j) be the first derivative of 3*j**5/4 - 29*j**4/16 + 11*j**3/12 + 5*j**2/8 - j/2 - 456. Determine a, given that d(a) = 0.
-2/5, 1/3, 1
Let n = 13010/9753 + -2/3251. Factor 10/3*s**2 - n*s + 0 + 2/3*s**4 - 8/3*s**3.
2*s*(s - 2)*(s - 1)**2/3
Let v(z) be the second derivative of -z**7/42 + z**6/15 + 3*z**5/20 - 2*z**4/3 + 2*z**3/3 + 181*z. Solve v(b) = 0.
-2, 0, 1, 2
Let d be (-174)/4*(1 - -1). Let a = d - -263/3. What is t in 0*t + a - 1/6*t**2 = 0?
-2, 2
Let c(a) be the second derivative of -a**6/6 - 8*a**5 - 425*a**4/4 + 80*a**3/3 + 640*a**2 + 37*a - 1. Factor c(f).
-5*(f - 1)*(f + 1)*(f + 16)**2
Let b be 14/8 + ((-1105)/52)/(-17). Factor -6/5 + 8/5*c + 4/5*c**2 - 8/5*c**b + 2/5*c**4.
2*(c - 3)*(c - 1)**2*(c + 1)/5
Let h(p) be the first derivative of -2*p**6/3 - 28*p**5/5 - 16*p**4 - 32*p**3/3 + 32*p**2 + 64*p + 48. Determine d, given that h(d) = 0.
-2, 1
Let n = -413 + 422. Let p(g) be the third derivative of -n*g**2 + 1/15*g**3 + 1/40*g**4 + 1/300*g**5 + 0 + 0*g. Factor p(v).
(v + 1)*(v + 2)/5
Factor 1/3*t**3 + 2 + 11/3*t + 2*t**2.
(t + 1)*(t + 2)*(t + 3)/3
Let t = -2/4875 + 2927/4875. Factor t*n**2 - 9/5*n - 12/5.
3*(n - 4)*(n + 1)/5
Let y(s) be the first derivative of -3 - 3/4*s**4 + 0*s**3 + 3/2*s**2 + 0*s. Determine v so that y(v) = 0.
-1, 0, 1
Determine s so that 0 + 0*s**4 - 8/3*s**2 - 2/3*s**5 + 6*s**3 - 8*s = 0.
-3, -1, 0, 2
Let y(f) = f - 1. Let u be y(4). Suppose 0 = -u*w + 10 - 1. Suppose -38 + 12*b**w + 6*b + 15*b**2 + 38 + 3*b**4 = 0. What is b?
-2, -1, 0
Let n(u) = -2*u**3 + 31*u**2 + 51*u + 3. Let m be n(17). Suppose 1/3 + 2/3*o**m + 7/3*o + 14/3*o**2 - 3*o**5 - 5*o**4 = 0. What is o?
-1, -1/3, 1
Factor 68*w - 20*w**4 + 20*w**2 + 28*w - w**5 + 4*w - 99*w**3.
-w*(w - 1)*(w + 1)*(w + 10)**2
Let c(x) be the second derivative of -x**5/60 + 5*x**4/12 + x**3/18 - 5*x**2/2 - 8*x + 1. Solve c(r) = 0.
-1, 1, 15
Let k = 14155 + -14155. Factor 6*o**2 - 3/2*o**4 - 12*o + k + 3*o**3.
-3*o*(o - 2)**2*(o + 2)/2
Let f(k) be the second derivative of -k**4/4 + 171*k**3 - 87723*k**2/2 + 30*k - 2. Factor f(u).
-3*(u - 171)**2
Let t(j) be the second derivative of 1/8*j**3 + 2*j + 0*j**2 - 17 - 1/48*j**4. Determine o so that t(o) = 0.
0, 3
Let t(w) = w**3 + 4*w**2 - 5*w - 7. Let k be t(-5). Let z(j) = j + 7. Let d be z(k). Factor 3/4*i**5 - 3/4*i + d + 0*i**3 - 3/2*i**4 + 3/2*i**2.
3*i*(i - 1)**3*(i + 1)/4
Let v be ((-43)/3 - -1)*187/(-1496). Factor -v*j**2 + 7/3*j - 2/3.
-(j - 1)*(5*j - 2)/3
Let o be (-120)/(-308) - 32/(-176). Factor -10/7*f**4 + o - 26/7*f**3 - 18/7*f**2 + 2/7*f.
-2*(f + 1)**3*(5*f - 2)/7
Let w(i) be the second derivative of i**7/2520 - i**6/360 - i**5/360 + i**4/24 - 19*i**3/6 - 52*i. Let z(m) be the second derivative of w(m). Solve z(c) = 0.
-1, 1, 3
Factor 70*a**2 + 5 - 5*a**3 - 165 - 40*a**2.
-5*(a - 4)**2*(a + 2)
Let z = 8 + 4. Let x(y) = -60*y**4 - 164*y**3 - 96*y**2 - 4*y. Let d(f) = f. Let c(t) = z*d(t) - x(t). Solve c(l) = 0 for l.
-2, -2/5, -1/3, 0
Let u be ((-112)/6)/(-4) - (-6)/(-9). Suppose -15 = -3*i + 4*f, -i + 1 = -5*f - u. Factor 1/3*o**i + o**4 - 1/3 + 2/3*o**3 - o - 2/3*o**2.
(o - 1)*(o + 1)**4/3
Let y = 179/6 + -689/24. Solve -y*k + 0 - 3/8*k**2 = 0 for k.
-3, 0
Factor -2974*w**2 + 4*w**3 + 2974*w**2 - 4*w**5.
-4*w**3*(w - 1)*(w + 1)
Let l(h) be the second derivative of -h**4/20 - 3*h**3/5 + 24*h**2/5 + 119*h - 3. Let l(a) = 0. What is a?
-8, 2
Let a = 13 + -17. Let w = 6 + a. Factor -y + y**2 + 4*y**2 - 6*y**w.
-y*(y + 1)
Suppose 99/7 - 3/7*p**3 + 75/7*p - 27/7*p**2 = 0. What is p?
-11, -1, 3
Let k(f) be the second derivative of f**6/72 - f**5/12 - 2*f**3/3 - 12*f. Let o(x) be the second derivative of k(x). Factor o(n).
5*n*(n - 2)
Let t(s) be the third derivative of s**9/13608 + s**8/2520 + s**7/1260 + s**6/1620 - 5*s**3/6 - 15*s**2. Let b(g) be the first derivative of t(g). Factor b(p).
2*p**2*(p + 1)**3/9
Let o(a) be the third derivative of -a**7/70 - 3*a**6/8 + 13*a**5/5 - 9*a**4/2 + a**2 + 7*a. Factor o(l).
-3*l*(l - 2)*(l - 1)*(l + 18)
Let b(k) be the second derivative of -k**4/84 - 3*k**3/14 + 11*k**2/7 + k + 477. Factor b(y).
-(y - 2)*(y + 11)/7
Let b(u) be the third derivative of -u**5/45 + u**4/2 - 4*u**3 + 24*u**2. Determine n so that b(n) = 0.
3, 6
Let t be (-21)/(-18) - ((-44)/24 - -3). Factor -j - 1/3*j**3 + t + 4/3*j**2.
-j*(j - 3)*(j - 1)/3
Let v be ((-4)/(-6))/((360/81)/10). Let a(m) be the first derivative of -v*m + 7/16*m**4 + 4/3*m**3 - 3 - 17/8*m**2. Solve a(x) = 0 for x.
-3, -2/7, 1
Let n(k) be the third derivative of -k**5/210 - 9