3 + 1 - 44*h**2 - 2 - 10*h**3 = 0.
-7, -1, 1
Let s = -21 + 24. Let r be ((-4)/5)/((-24)/60). Factor 0*d + 1/4*d**5 + 1/4*d**4 - 1/2*d**s + 0 + 0*d**r.
d**3*(d - 1)*(d + 2)/4
Let c(j) be the third derivative of -j**6/90 + j**5/45 + 2*j**4/3 - 4*j**2 + 4*j. Factor c(z).
-4*z*(z - 4)*(z + 3)/3
Factor -364/3*d + 1/3*d**2 + 33124/3.
(d - 182)**2/3
Let z(s) = 15*s**4 + 37*s**3 + 63*s**2 + 30*s - 1. Let q = 17 - 19. Let v(y) = -y**4 + y**3 - y**2 + 1. Let h(o) = q*z(o) - 10*v(o). Let h(b) = 0. Calculate b.
-2, -1, -1/5
Let j(m) be the first derivative of 3*m**4/8 - 3*m**3/2 - 3*m**2/4 + 9*m/2 + 18. Determine q, given that j(q) = 0.
-1, 1, 3
Let s = 40895/2 + -940573/46. Factor 8/23 - 2/23*x**2 + s*x.
-2*(x - 4)*(x + 1)/23
Let d(n) be the second derivative of -1/3*n**3 + 1/2*n**4 + 1/10*n**5 + 6*n - 2*n**2 + 0 - 1/15*n**6. Factor d(k).
-2*(k - 2)*(k - 1)*(k + 1)**2
Suppose 6*y + 15 = 7*y. What is k in y*k**3 - 12*k**3 - 12 - 12*k**2 - 9*k + 66 = 0?
-2, 3
Let b be ((-54)/(-15))/9 - -1. Let w(n) be the second derivative of 1/21*n**7 - 2/5*n**6 - 2*n**2 + 3*n**3 + 6*n + 0 + b*n**5 - 8/3*n**4. Factor w(i).
2*(i - 2)*(i - 1)**4
Suppose 0 = -125*m - 1369 + 1744. Let 1/4*a**2 - 3/2*a + 0 + 1/4*a**m = 0. Calculate a.
-3, 0, 2
Let h(d) be the second derivative of -1/5*d**5 + 0 - 9*d + 0*d**3 + 0*d**2 + 2*d**4. Suppose h(m) = 0. What is m?
0, 6
Suppose 4*k + 4 - 8 = 0. Let t be (-1)/(k - 10/8). Factor 0*a**3 + 2*a**3 + 2*a**5 - t*a**5 + 0*a**5.
-2*a**3*(a - 1)*(a + 1)
Suppose 2*l = -2*n + 76, 0*l + n = -3*l + 110. Let u be (-48)/l*6/(-10). Factor u*f**4 + 0*f - 2/5*f**3 + 0 + 0*f**2 - 2/5*f**5.
-2*f**3*(f - 1)**2/5
Factor 2/7*c**2 + 0*c + 0.
2*c**2/7
Let d(u) be the second derivative of 2/3*u**4 - 1/5*u**5 + 0 + 0*u**2 - 3*u + 0*u**3. Determine b so that d(b) = 0.
0, 2
Suppose -4*n + 8*n = 8. Find v such that -20*v**5 + 2*v**2 - 3*v**3 - 15*v**4 - 2*v**n + 8*v**5 = 0.
-1, -1/4, 0
Let d(x) be the first derivative of 1/2*x**4 + 4/9*x**3 + 0*x**2 - 4/15*x**5 - 1/3*x**6 + 0*x + 6. Suppose d(b) = 0. What is b?
-1, -2/3, 0, 1
Suppose -35*r + 38*r - 6 = 0. Let f = -525/4 - -132. Find m such that 9/4*m + 0 - f*m**r = 0.
0, 3
Let c(a) be the third derivative of 0 - 5/6*a**3 + 5/8*a**4 + 0*a - 1/6*a**5 + 16*a**2. Factor c(w).
-5*(w - 1)*(2*w - 1)
Let l(t) be the second derivative of -t**4/15 - 22*t**3/15 - 4*t**2 + 58*t. Factor l(i).
-4*(i + 1)*(i + 10)/5
Let a(s) be the first derivative of 6*s**5/5 + 15*s**4/8 + s**3/2 + 226. Factor a(d).
3*d**2*(d + 1)*(4*d + 1)/2
Let j = 20 + -19. Suppose -j = -4*s + 7. Find r such that -s*r + 2*r**5 + 0*r - 5*r**4 + r**4 + 4*r**2 = 0.
-1, 0, 1
Let i be (-39)/(-75)*(-60)/(-40). Let g(o) be the second derivative of 1/15*o**4 + 0*o**3 + i*o**6 - 8*o + 0*o**2 - 27/70*o**7 + 0 - 2/5*o**5. Factor g(q).
-q**2*(q - 1)*(9*q - 2)**2/5
Let u = -1661 + 8321/5. Let -u*i**3 + 0 + 6/5*i**4 + 4/5*i + 6/5*i**2 = 0. What is i?
-1/3, 0, 1, 2
Let g(j) = j**3 + 4*j**2 - 3*j + 12. Let i be g(-5). Suppose -2*l**2 + i*l**2 + 4*l**2 + 4*l**3 = 0. What is l?
-1, 0
Let q(t) be the first derivative of 3*t**5/5 + 177*t**4/4 + 1197*t**3 + 27075*t**2/2 + 41154*t - 206. Factor q(g).
3*(g + 2)*(g + 19)**3
Let y(v) be the second derivative of 4*v + 0*v**5 + 0*v**4 + 1/315*v**7 + 0*v**2 + 0 + 1/225*v**6 + 0*v**3. Let y(r) = 0. What is r?
-1, 0
Let k = -12/31 + 1111/2790. Let a(t) be the third derivative of 1/450*t**5 - 6*t**2 + 0 + k*t**4 + 1/45*t**3 + 0*t. Factor a(g).
2*(g + 1)**2/15
Let i = 259 + -224. Let k be (6/i)/(21/98). Let -6/5*o**2 - 2*o**3 + 0 + k*o = 0. Calculate o.
-1, 0, 2/5
Let 11*c - c**3 - 4*c - 10*c**2 + c**2 - 15*c + 0*c**3 = 0. Calculate c.
-8, -1, 0
Let p = 16 - 14. Factor 15*r - 48*r**p + 18 + 15*r**2 + 17*r**2 + 19*r**2.
3*(r + 2)*(r + 3)
Let r(x) be the first derivative of 3*x**4/2 + 11*x**3/2 + 15*x**2/4 - 3*x + 38. Solve r(j) = 0 for j.
-2, -1, 1/4
Suppose -14 - 61 = -15*m. Let v(k) be the first derivative of -1/4*k**3 + 1/2*k**2 - 3 - 1/4*k**4 + k - 1/20*k**m. Factor v(z).
-(z - 1)*(z + 1)*(z + 2)**2/4
Suppose 0*o - 6 = -2*o. Factor -2*c + 0*c - c - 3 - o*c**2 - 3*c.
-3*(c + 1)**2
Let c(u) = u**2 - 3*u + 4. Let r be c(3). Suppose -4*i + 5*i - 5 = -4*a, 20 = 4*a - r*i. Solve -9*o**3 - 7*o**5 + 0 - 1/2*o**a + 31/2*o**4 + o = 0.
-2/7, 0, 1/2, 1
Let f(y) be the first derivative of -5*y**6/6 + y**5 + 5*y**4/4 - 5*y**3/3 - 759. Factor f(x).
-5*x**2*(x - 1)**2*(x + 1)
Let h be ((-2)/14)/(43/(-14) + 255/102). Solve -5/2 + h*f**2 - 9/4*f = 0.
-1, 10
Let b(s) be the second derivative of -s**7/112 - 7*s**6/80 - 3*s**5/20 + s**4/2 - 128*s. What is n in b(n) = 0?
-4, 0, 1
Let f be -13 + 11 + 25/45 + 5. Factor 14/9*q**3 - 8/9 - f*q - 10/9*q**2.
2*(q - 2)*(q + 1)*(7*q + 2)/9
Let x(z) = 4*z**2 - 2*z - 1. Let l be x(-1). Let q be 12/(-33)*55/(-15). Suppose -19/3*i**2 + 4/3*i - 4/3*i**3 + q + l*i**4 = 0. Calculate i.
-1, -2/5, 2/3, 1
Suppose -84 + 195 = 37*q. Let y(n) be the first derivative of 8 - 1/4*n**4 + 0*n**2 + 0*n + 0*n**q. Factor y(l).
-l**3
Let d(i) be the third derivative of -19*i**6/960 + 3*i**5/80 + i**4/192 - 106*i**2. Factor d(z).
-z*(z - 1)*(19*z + 1)/8
Let p(t) = -t**3 + 32*t**2 - 31*t + 3. Let d be p(31). Let i(z) be the first derivative of 1/2*z + 0*z**d - 1/16*z**4 + 3/8*z**2 - 4. Factor i(h).
-(h - 2)*(h + 1)**2/4
Let s(n) be the second derivative of n**9/45360 + n**8/20160 - n**7/1890 - n**6/540 - 3*n**4 - 14*n. Let p(z) be the third derivative of s(z). Factor p(i).
i*(i - 2)*(i + 1)*(i + 2)/3
Let h(w) = -w**3 - 2*w**2 - 2*w - 4. Let l be h(-2). Suppose 2*v - 4 = -l*v. Let -73*f**v - 3*f - 3*f**4 + 76*f**2 + 3*f = 0. What is f?
-1, 0, 1
Factor 41*r**3 - 26*r**4 - 33*r**5 + 60*r + 74*r**3 + 140*r**2 + 66*r**4 - 32*r**5 + 70*r**5.
5*r*(r + 1)*(r + 2)**2*(r + 3)
Suppose 2*i = -3*h - 0*h + 46, -2*h + 34 = -2*i. Factor -4*k**4 - 23*k**3 - 12 + 15*k**3 - 8*k + 16*k**3 + h*k**2.
-4*(k - 3)*(k - 1)*(k + 1)**2
Let v(x) be the first derivative of 4*x**3/3 + 126*x**2 + 488*x - 510. Suppose v(m) = 0. Calculate m.
-61, -2
Let c(r) = -6 + 9 - 8 - 2*r - 3. Let v be c(-5). Determine l so that 21*l - 5*l - 45 - 5*l**v + 14*l = 0.
3
Suppose 5*l - 15 = 2*s - 0*s, 2*s = -4*l + 12. Factor 3/2*f + s + 1/2*f**2.
f*(f + 3)/2
Let i = -938 - -945. Let k(j) be the first derivative of 8/21*j**3 + 3/7*j**2 + 1/14*j**4 + 0*j + i. Factor k(m).
2*m*(m + 1)*(m + 3)/7
Let p(c) be the second derivative of 1/27*c**4 + 9*c + 0 + 7/90*c**5 + 0*c**3 + 0*c**2. Factor p(d).
2*d**2*(7*d + 2)/9
Let a(h) = -4*h**5 + 12*h**3 - 14*h**2 - 6*h + 6. Let s be 2 - (-1)/((-3)/(-12)). Let u(m) = -m**2 - m + 1. Let j(d) = s*u(d) - a(d). Find b such that j(b) = 0.
-2, 0, 1
Let v(g) be the second derivative of g**5/70 + g**4/7 - 19*g**3/21 - 24*g**2/7 - 4*g - 7. Factor v(h).
2*(h - 3)*(h + 1)*(h + 8)/7
Let g(v) be the third derivative of v**8/14280 - v**6/3060 - 4*v**3/3 + 12*v**2. Let u(f) be the first derivative of g(f). Find s, given that u(s) = 0.
-1, 0, 1
Let p(o) be the first derivative of 29/12*o**3 + 1/20*o**5 - 44 + 9/16*o**4 + 39/8*o**2 + 9/2*o. Find y, given that p(y) = 0.
-3, -2, -1
Let u = -9/20 - -83/140. Factor 4/7 + u*k**2 - 4/7*k.
(k - 2)**2/7
Suppose 0 = -0*a - 5*a + 25. Determine i, given that -8 - 8*i**4 + 16*i**2 - 4*i - 11*i**5 + a*i**3 + 7*i**5 + 3*i**3 = 0.
-2, -1, 1
Let j(c) be the third derivative of c**9/4536 - c**8/1260 + c**7/1260 - c**3/2 + 7*c**2. Let g(m) be the first derivative of j(m). Factor g(x).
2*x**3*(x - 1)**2/3
Factor -13/5*w**2 + 0 + 11/5*w**3 + 4/5*w - 2/5*w**4.
-w*(w - 4)*(w - 1)*(2*w - 1)/5
Let d be 6 - (0 + 6/3). Let r(u) be the third derivative of 0*u**3 + 0*u + 1/270*u**5 + 0 + 3*u**2 - 1/540*u**6 + 0*u**d. Solve r(w) = 0.
0, 1
Let z(x) be the first derivative of -3*x**2 + 0*x - 1/15*x**3 + 1/40*x**4 + 11 - 1/300*x**5. Let j(c) be the second derivative of z(c). Factor j(u).
-(u - 2)*(u - 1)/5
Solve -2/11*s**2 + 2/11*s + 4/11 = 0.
-1, 2
Suppose -o = -0*o - 15. Suppose 0 = 2*l - o*l + 10*l. Factor 0*y + l + 0*y**2 + 2/3*y**4 + 0*y**3 + 1/3*y**5.
y**4*(y + 2)/3
Let s(o) be the third derivative of -o**8/420 - 4*o**7/525 + o**6/75 + 4*o**5/75 - o**4/30 - 4*o**3/15 - 3*o**2 + 16. Determine c so that s(c) = 0.
-2, -1, 1
Let d(b) be the third derivative of 0 + 0*b - 1/5*b**5 - 1/3*b**4 + 3/28*b**8 + 0*b**3 - 9*b**2 + 7/10*b**6 - 10/21*b**7. Let d(