0 - d**2/10 - 12*d/5 + 140. Let p(w) = 0. What is w?
-4, 6
Let w = 25 - 25. Suppose 3*n + n + 2*y = 10, -5*n - y + 11 = w. Suppose 16*x - 9 - n*x**2 - 2*x**2 - 7 = 0. What is x?
2
Let a(d) = d**3 + 11*d**2 + 31*d + 24. Let q be a(-7). Let s be (2 + -1)*(-10 + 10). Suppose s*f - 1/2*f**q + 0 - 1/6*f**4 - 1/3*f**2 = 0. What is f?
-2, -1, 0
Suppose -3*r + 12 = -3*a, -r - 12*a = -15*a - 8. Factor -2/5*k**r + 0 - 4/5*k.
-2*k*(k + 2)/5
Let g = 17174/13 - 1320. Factor 2/13*x + 0 + g*x**2.
2*x*(7*x + 1)/13
Suppose 2*g + 6 = 22. Suppose -2*k = g, 12 + 15 = 3*s - 3*k. Factor p**5 - s + p**4 + p**3 + 5 + p**4.
p**3*(p + 1)**2
Let z be -1 + 4 + (-1)/(-1). Suppose 10 = g + z*g. Factor 0*m - 2*m + 0*m**g + m**2 + m**3.
m*(m - 1)*(m + 2)
Let f(r) be the first derivative of r**7/210 + r**6/30 + r**5/20 - r**4/6 - 2*r**3/3 - r**2 - 7. Let v(y) be the second derivative of f(y). Factor v(m).
(m - 1)*(m + 1)*(m + 2)**2
Factor 8*d**3 + 72527*d**2 - 8*d**4 - 72527*d**2 + 2*d**5.
2*d**3*(d - 2)**2
Let b = 71 + -67. Let f be 7/(-1) + (-828)/(-84). Factor b*x - f*x**2 - 8/7.
-4*(x - 1)*(5*x - 2)/7
Let l(q) be the first derivative of -2*q**3/21 - 72*q**2/7 - 2592*q/7 - 120. Suppose l(f) = 0. Calculate f.
-36
Let s(l) be the second derivative of 0 + 0*l**2 + 0*l**4 - 30*l + 1/6*l**3 - 3/20*l**6 - 5/168*l**7 - 17/80*l**5. Find c, given that s(c) = 0.
-2, -1, 0, 2/5
Let k(l) be the second derivative of 5*l**4/12 - 20*l**3/3 + 40*l**2 + 349*l. Suppose k(r) = 0. Calculate r.
4
Let r be 876/357 - (-29 + (-9820)/(-340)). Let 8/7 + 2/7*n**3 + 12/7*n**2 + r*n = 0. What is n?
-4, -1
Let z(j) be the first derivative of j**4/12 + 5*j**3/9 + 7*j**2/6 + j - 40. Suppose z(g) = 0. Calculate g.
-3, -1
Let g(i) be the third derivative of -i**8/168 + 4*i**7/35 - 13*i**6/15 + 16*i**5/5 - 16*i**4/3 + 11*i**2 - 7. Find y such that g(y) = 0.
0, 2, 4
Factor 1 - 1/6*k - 1/6*k**2.
-(k - 2)*(k + 3)/6
Let a(w) be the first derivative of -8/9*w**3 + 7/9*w**6 - 13 + 4/3*w**4 + 38/15*w**5 + 0*w + 0*w**2. Let a(c) = 0. What is c?
-2, -1, 0, 2/7
Let z(y) be the third derivative of 0*y + 0*y**7 + 0*y**4 - 3/80*y**6 + 0 - 5*y**2 + 0*y**3 + 1/224*y**8 + 1/20*y**5. Determine u, given that z(u) = 0.
-2, 0, 1
Find p, given that 210*p + 56*p - 400 + 14*p - 49*p**2 = 0.
20/7
Let z = -19 + 27. Let o = z + 11. Find p such that 2*p**2 + 2*p**5 + p**4 - 5*p**3 + 8 + o*p**3 - 11*p**4 - 16*p = 0.
-1, 1, 2
Let v(b) be the first derivative of 2/3*b**5 + 1/9*b**4 - 46/27*b**3 + 16/9*b + 39 - 2/9*b**2. Find o such that v(o) = 0.
-1, -4/5, 2/3, 1
Let n be -8 + (-816)/(-104) + (-296)/(-572). Factor 0*f + 0 + n*f**3 + 0*f**2 + 2/11*f**4.
2*f**3*(f + 2)/11
Suppose -x + 8 = 4*f + 4, 0 = -4*x + 2*f - 2. Let c(j) = -j**2 + 5*j + 2. Let a be c(5). Factor -1/3*r**a + x*r + 4/3.
-(r - 2)*(r + 2)/3
Let m(l) be the second derivative of l**4/16 + 5*l**3/4 + 75*l**2/8 - 21*l - 1. Factor m(u).
3*(u + 5)**2/4
Let y(s) = 69*s**2 - 39*s. Let z(b) = -17*b**2 + 10*b. Suppose 5*u - 4 = 6*u. Let x(w) = u*y(w) - 15*z(w). Factor x(h).
-3*h*(7*h - 2)
Suppose 0 = -5*x - 4*n - 272, x = 4*x + 3*n + 165. Let g be (0 - 3)/(78/x). Factor 3/4*c**4 + 0 - 3/4*c**g + 0*c - 3/4*c**5 + 3/4*c**3.
-3*c**2*(c - 1)**2*(c + 1)/4
Let x(k) be the third derivative of -1/16*k**4 + 0*k + 0 - 3/8*k**5 - 1/20*k**7 - 17*k**2 + 1/2*k**3 - 19/80*k**6. Factor x(v).
-3*(v + 1)**3*(7*v - 2)/2
Find n such that -22*n**4 - 4 - 26*n + 18*n**4 + 19*n + 6 - 12*n**5 + 17*n**3 = 0.
-1, 1/2, 2/3
Let c(p) be the second derivative of 2*p**7/35 - 9*p**6/40 + p**5/10 + 21*p**2 - 37*p. Let l(f) be the first derivative of c(f). Factor l(h).
3*h**2*(h - 2)*(4*h - 1)
Solve -186*i**2 + 3*i**3 + 146*i**2 - 30 + 26*i + 2*i**3 + 39*i = 0 for i.
1, 6
Let w(h) be the second derivative of -15*h - 1/45*h**6 - 1/15*h**5 + 0 + 1/126*h**7 + 1/6*h**3 + 1/18*h**4 + 0*h**2. Find o such that w(o) = 0.
-1, 0, 1, 3
Let o(j) be the second derivative of 7*j**4/8 + 45*j**3 - 39*j**2 + 171*j. Factor o(f).
3*(f + 26)*(7*f - 2)/2
Let i(l) be the third derivative of l**7/504 - l**6/144 - l**5/12 - l**4/6 + 5*l**2. Let m(x) be the second derivative of i(x). Factor m(f).
5*(f - 2)*(f + 1)
Let r = -1185/52 + 93/4. Let l = r - 35/104. Factor 1/8*m**3 - 1/8*m**2 + 1/8*m**4 + 0 + 0*m - l*m**5.
-m**2*(m - 1)**2*(m + 1)/8
Let b(p) be the second derivative of -15*p**7/7 - 37*p**6/10 + 27*p**5 + 51*p**4/4 - 20*p**3 - 18*p**2 - 2*p + 12. Determine x so that b(x) = 0.
-3, -2/5, -1/3, 1/2, 2
Let h be ((-1)/(-3) + 8/6)*9. Factor 7 + 12*k**2 - 4 - 3 + h*k**3.
3*k**2*(5*k + 4)
Factor 1464*t + 26*t**2 + 213459 - 23*t**2 - 34851.
3*(t + 244)**2
Let s be 1 + 6/(-2) + 4. Let u be (1 - 0)*s + 2. Find f such that -u*f**2 - 3 + 3*f**2 - 5*f**2 + 3*f**2 + 6*f = 0.
1
Suppose -4*l + 13 = -15. Factor 6 - 16*w**2 + l*w + 2*w + w.
-2*(w - 1)*(8*w + 3)
Let f(b) be the second derivative of -b**8/1344 + b**6/120 + b**5/120 - b**4/32 - b**3/12 + 6*b**2 - 6*b. Let h(g) be the first derivative of f(g). Factor h(j).
-(j - 2)*(j - 1)*(j + 1)**3/4
Let z(r) be the first derivative of -r**7/630 + r**6/360 + r**5/60 - 5*r**4/72 + r**3/9 + r**2 + 3. Let k(t) be the second derivative of z(t). Factor k(g).
-(g - 1)**3*(g + 2)/3
Let t be 4*(2 + 5/(-4)). Suppose 1 = t*i - m - 5, -m + 6 = 3*i. What is c in -4*c**3 + c**3 - c**2 - 1 + 2 + i*c**3 + c = 0?
-1, 1
What is m in m**3 + 600 - 4*m**3 - 387*m + 54*m**2 + 72*m + 0*m = 0?
5, 8
Let a = -799/2 - -6403/16. Let x(y) be the third derivative of 1/20*y**6 - 1/2*y**3 + 0 - 13/40*y**5 + 0*y - 4*y**2 + a*y**4. Factor x(c).
3*(c - 2)*(c - 1)*(4*c - 1)/2
Factor -16/5*z**2 - 14/5 + 1/5*z**3 + 29/5*z.
(z - 14)*(z - 1)**2/5
Let k(o) = 15*o**3 + 0 + 12 + 6*o**2 - 39*o + 3*o. Let x(g) be the second derivative of -g**4/12 + g. Let t(q) = -k(q) + 3*x(q). Determine p so that t(p) = 0.
-2, 2/5, 1
Let a(b) be the second derivative of -43*b + 0*b**2 + 8/33*b**4 - 26/55*b**5 + 1/33*b**7 + 0*b**3 + 0 - 16/165*b**6. Suppose a(q) = 0. Calculate q.
-2, 0, 2/7, 4
Suppose -17 = -4*v + n, 0 = -3*v - v - 5*n - 13. Suppose -x = -v + 1. Factor x*b**4 - 8*b + 2*b**3 + 8*b.
2*b**3*(b + 1)
Suppose -5*d - 5*n = -25, -5*d - 4*n = -3*d - 16. Let t(y) be the first derivative of 1/4*y**4 + 0*y**3 + 0*y + 0*y**2 - d. Find b such that t(b) = 0.
0
Let b(t) = t**4 - t**3. Let m be 0/(-3 - -1) - 2. Let q(s) = -8*s**5 - 33*s**4 - 91*s**3 - 74*s**2 - 30*s - 4. Let j(d) = m*q(d) + 18*b(d). Solve j(h) = 0.
-2, -1, -1/4
Suppose 5*r = -5*w + 30, 9 = 4*w - 4*r - 15. Suppose 0 = -2*n - 2*q - w, 5*n + 13 - 28 = 5*q. Factor 36/5*o**4 + 0 - 48/5*o**3 + 16/5*o**2 + n*o.
4*o**2*(3*o - 2)**2/5
Let k(r) be the second derivative of 7*r**4/4 - 20*r**3 - 18*r**2 + 14*r - 4. Factor k(g).
3*(g - 6)*(7*g + 2)
Suppose -4*z - 5*x = -0*z, 2*z + 2*x + x = 0. Factor 8/3*g**4 + 14/3*g**3 + z*g - 4/3*g**2 + 0.
2*g**2*(g + 2)*(4*g - 1)/3
Suppose -5*n - 2*a + 4 = 0, a = 6*n - 2*n + 2. Let w(g) be the first derivative of 2/15*g**3 + 1 + 1/5*g**2 + n*g - 1/10*g**4 - 2/25*g**5. Factor w(t).
-2*t*(t - 1)*(t + 1)**2/5
Let y(i) be the third derivative of -i**6/8 - 3*i**5/35 + 29*i**4/56 + 3*i**3/7 + 2*i**2 - 59*i. What is z in y(z) = 0?
-1, -1/5, 6/7
Let l be -54 + 0 - (6 + 6 + -11). Let b = l + 57. Suppose 2/9 - 2/9*s + 2/9*s**3 - 2/9*s**b = 0. Calculate s.
-1, 1
Let d(b) be the third derivative of b**4/24 + b**3/6 + b**2. Let l be d(8). Let -p**3 - 13*p**3 - 6*p**2 - 6*p**4 - 3*p + l*p + 0 + 4 = 0. Calculate p.
-1, 2/3
Factor -9*y + 9*y - 3*y**3 - y**3 - 8*y**4 + 12*y**4 - 8*y**2.
4*y**2*(y - 2)*(y + 1)
Let p(x) be the third derivative of 1/70*x**7 - 3/8*x**4 - 1/8*x**6 + 20*x**2 + 7/20*x**5 + 0*x**3 + 0 + 0*x. Let p(k) = 0. Calculate k.
0, 1, 3
Let u = 125/86 + 2/43. Factor 3/2*f**2 + 0 - u*f.
3*f*(f - 1)/2
Let f(r) be the first derivative of r**4/16 + r**3/12 - 3*r**2/4 - 31. Find d such that f(d) = 0.
-3, 0, 2
Suppose -14 - 10 = -6*n. Suppose m - n*b - 6 = 2*m, -2 = b. Factor -3 - 6*u**3 - 6*u**m + 6*u**2 + 9*u**2.
-3*(u - 1)**2*(2*u + 1)
Factor 29/6*b**3 + 0 + 2*b + 16/3*b**2 + 5/3*b**4 + 1/6*b**5.
b*(b + 1)**2*(b + 2)*(b + 6)/6
Solve -1096*g**2 + 108*g**4 - 352 - 467*g**2 + 94 - 1408*g - 864*g**3 - 62 - 453*g**2 = 0 for g.
-2/3, 10
Let p(y) = 6*y**2 - 6*y + 9. Let o(l) = 11*l**2 - 13*l + 17. Let z(g) = -3*o(g) + 5*p(g). Solve z(i) = 0 for i.
1, 2
Let w = -29/33398 - -269703