*h**4 + 1/70*h**5. Find l, given that g(l) = 0.
0, 1
Let s(m) = 9*m**5 + 7*m**4 - 12*m**3 - m**2 - 3. Let d(f) = -80*f**5 - 64*f**4 + 108*f**3 + 8*f**2 + 28. Let t(j) = -3*d(j) - 28*s(j). Let t(w) = 0. What is w?
-1, -1/3, 0, 1
Let q(h) be the first derivative of 3*h**2/2 - 63*h + 40. Let b be q(22). Suppose 2/7*s + 0 + 0*s**2 - 2/7*s**b = 0. Calculate s.
-1, 0, 1
Suppose -11*v = 17*v - 56. Let b(t) be the third derivative of 0 + v*t**2 + 0*t**3 + 0*t - 1/84*t**4 + 1/210*t**5. Factor b(a).
2*a*(a - 1)/7
Let r(f) = -5*f**3 + 35*f**2 - 10*f - 5. Let c(n) = -7 - n + 8 + n**2 - 2*n**2. Let d(a) = -15*c(a) - r(a). Factor d(v).
5*(v - 2)*(v - 1)**2
Let x = -203 + 751. Let x*r - 6*r**3 + 3*r**2 + 6*r**5 - 548*r - 3*r**4 = 0. Calculate r.
-1, 0, 1/2, 1
Let u(a) be the second derivative of 17*a**6/15 + 9*a**5/5 - 598*a. Factor u(h).
2*h**3*(17*h + 18)
Factor 2/23*i**2 - 772/23*i + 74498/23.
2*(i - 193)**2/23
Let j(g) be the second derivative of -g**4/6 - 179*g**3/6 - 89*g**2/2 - 394*g. Factor j(p).
-(p + 89)*(2*p + 1)
Let i(y) be the second derivative of -17*y**5/60 + 5*y**4/12 + y**3/9 - 217*y. Suppose i(g) = 0. Calculate g.
-2/17, 0, 1
Let x be (8/10)/(7/175*5). Suppose d - x*q = 0, 6 = 2*d - 2*q - 0. Suppose 0*m**3 + 2/3*m + 4/3*m**2 - 4/3*m**d - 2/3*m**5 + 0 = 0. Calculate m.
-1, 0, 1
Let y be (-474)/(-2212)*35/45. Factor y*v**2 - 5/6*v + 1/6*v**3 + 1/2.
(v - 1)**2*(v + 3)/6
Suppose -k + 0*k - 4*x = -17, -2*k - 6 = -2*x. Let c = k - 0. Solve 3/2*f**2 + 3/2*f**4 - 7/2*f**3 + 3/2*f - c = 0 for f.
-2/3, 1
Suppose 3*g + 1 + 11 = p, -5*g - 20 = 0. Let x(q) be the second derivative of 1/6*q**3 + 0 - 1/6*q**4 + p*q**2 + q + 1/20*q**5. Find s, given that x(s) = 0.
0, 1
Factor 1093*w**2 + 6241/6 - 80/3*w**3 - 6320/3*w + 1/6*w**4.
(w - 79)**2*(w - 1)**2/6
Let p(v) be the second derivative of 353*v**4/3 - 4*v**3/3 + 450*v. Let p(l) = 0. What is l?
0, 2/353
Suppose -92*g = 56*g - 47*g. Suppose -2/3*k - 2/3*k**2 + g = 0. Calculate k.
-1, 0
Let -4/9*d**5 - 100/9 + 266/9*d**2 - 202/9*d**3 + 50/9*d**4 - 10/9*d = 0. What is d?
-1/2, 1, 2, 5
Let d(m) be the first derivative of m**4/4 - 35*m**3 + 2703*m**2/2 + 2809*m - 179. Let d(q) = 0. What is q?
-1, 53
Factor k**3 + 3*k**3 - 3*k**3 - 2*k**3 + 3*k - 2.
-(k - 1)**2*(k + 2)
Find j, given that 14/11*j**3 + 4/11*j**4 + 2/11*j**2 - 6/11 - 14/11*j = 0.
-3, -1, -1/2, 1
Let w(u) be the first derivative of 4*u**5/5 + 8*u**4 + 20*u**3 - 8*u**2 - 80*u - 53. Factor w(v).
4*(v - 1)*(v + 2)**2*(v + 5)
Let p(x) = x**3 + 8*x**2 - 12*x + 3. Let d be p(-9). Suppose -55 - 24 - 3*l**2 + 4 - d*l = 0. What is l?
-5
Let t(p) be the first derivative of -p**4/32 + p**3/6 - 3*p**2/16 + 40. Find z such that t(z) = 0.
0, 1, 3
Let a = -215 + 218. Suppose x - 3*u = -a*x + 26, 0 = x + u - 3. Factor -1/6*f**3 + 1/6*f**2 - 1/6*f**4 + 0*f + 1/6*f**x + 0.
f**2*(f - 1)**2*(f + 1)/6
Let o(n) be the third derivative of n**5/15 + 2*n**4/3 - 10*n**3/3 - 203*n**2. Find q such that o(q) = 0.
-5, 1
Let k(z) be the third derivative of z**6/40 + 77*z**5/20 + 1443*z**4/8 - 1521*z**3/2 - 2*z**2 - 41*z. Solve k(v) = 0.
-39, 1
Let w be (-50)/(-180)*(27/6 - 3). Let x(g) be the second derivative of -w*g**3 - 1/40*g**5 + 8*g - 1/2*g**2 - 1/6*g**4 + 0. Factor x(q).
-(q + 1)**2*(q + 2)/2
Let a = -28416 - -28418. Solve -2/5*z + 8/5 - 8/5*z**a + 2/5*z**3 = 0.
-1, 1, 4
Suppose -5*p + 5*h = -624 + 169, p = -3*h + 95. Determine i so that -p + 12*i - 7*i**2 + 0*i**2 + 3*i**2 + 84 = 0.
1, 2
Let a(f) = 3*f**2 + 59*f + 101. Let n(b) = -b**2 - b + 3. Let p(y) = -a(y) - 5*n(y). Find g such that p(g) = 0.
-2, 29
Let s = 1615 + -1610. Let y(n) be the second derivative of 13/12*n**3 - 23/24*n**4 + 0 + 4*n + 3/20*n**6 + 3/40*n**s - 1/2*n**2. Factor y(r).
(r - 1)*(r + 2)*(3*r - 1)**2/2
Let r = 267 - 265. Let u be -6 + 2 + 3/(9/21). Suppose 16/3*n**r + 2/3 - 11/3*n - 7/3*n**u = 0. What is n?
2/7, 1
Let v(s) be the third derivative of s**5/30 + 2*s**4/3 - s**2 + 23. Find m, given that v(m) = 0.
-8, 0
Let l(b) be the first derivative of b**6/30 + 2*b**5/25 - b**4/2 - 8*b**3/15 + 33*b**2/10 - 18*b/5 + 62. Determine o so that l(o) = 0.
-3, 1, 2
Suppose -2 = -2*q + 6. Let y(c) = -3*c**2 + 98*c - 570. Let o be y(25). Find z, given that -4/9 - 22/9*z**3 + 26/9*z**2 + 20/9*z**o - 22/9*z**q + 2/9*z = 0.
-1, -2/5, 1/2, 1
Let a(c) be the first derivative of c**5/30 - 2*c**4/9 - c**3/9 + 4*c**2/3 + 3*c - 2. Let g(s) be the first derivative of a(s). Factor g(w).
2*(w - 4)*(w - 1)*(w + 1)/3
Let w(i) be the second derivative of 0 + 5/18*i**3 - 5/36*i**4 + 4*i + 0*i**2. Factor w(j).
-5*j*(j - 1)/3
Find c such that -112*c**2 - 100 - 105*c + 37*c**2 + 34*c**2 + 36*c**2 = 0.
-20, -1
Let u(w) be the second derivative of w**5/60 + w**4/8 - w**2 - 3*w. Let y(k) be the first derivative of u(k). Let y(f) = 0. Calculate f.
-3, 0
Let -1/3*a**2 + 0 - 10/3*a = 0. Calculate a.
-10, 0
Factor -1/3*h**2 - 22*h - 363.
-(h + 33)**2/3
Let i(x) = 7*x**3 - 4*x**2 - 6*x - 9. Let y be i(6). Let g = y + -9237/7. Let g*p + 36/7 + 4/7*p**2 = 0. Calculate p.
-3
Let c(i) be the first derivative of -9/5*i**2 - 1/30*i**4 - 4 - 4*i + 2/5*i**3. Let b(w) be the first derivative of c(w). Suppose b(k) = 0. What is k?
3
Let v(a) = a + 1. Let w(b) = b**4 + 9*b**3 - 11*b**2 - 13*b + 6. Let q(u) = -12*v(u) - 3*w(u). Suppose q(x) = 0. Calculate x.
-10, -1, 1
Let x be (0 - 18/4)*(3781 - 3782). Determine z so that -x*z**2 - 3/2*z + 6*z**3 + 0 = 0.
-1/4, 0, 1
Let y(r) be the second derivative of -1/48*r**4 + 0*r**3 + 1/2*r**2 - 21*r + 0. Suppose y(a) = 0. Calculate a.
-2, 2
Let f be (-8 + 9)/(-3 - (-16)/5). Let w(u) be the first derivative of -7 - 4/3*u + 6/5*u**f + 14/3*u**3 - 25/6*u**4 - u**2. Factor w(p).
2*(p - 1)**3*(9*p + 2)/3
Suppose 3 = y, 4 + 1 = 5*h - 5*y. Suppose -77 + 14*j**5 - 25*j + 8*j**3 + 73 + 32*j**h - 28*j**2 + 3*j = 0. What is j?
-1, -2/7, 1
Suppose -r - y + 3 = 0, 2*r - 5*y + 1 + 0 = 0. Let v(x) be the first derivative of 3 + 1/3*x + 1/9*x**3 + 1/3*x**r. Factor v(l).
(l + 1)**2/3
Let l(d) = 8*d**5 + 36*d**4 + 20*d**3 - 48*d**2 + 4*d. Let t(q) = 9*q**5 + 39*q**4 + 20*q**3 - 48*q**2 + 5*q. Let n(x) = 5*l(x) - 4*t(x). What is s in n(s) = 0?
-4, -3, 0, 1
Let w = -367 - -370. Let a(f) be the second derivative of -1/21*f**7 + 0 + 9*f**2 + 5/3*f**4 + 2*f - 7*f**w + 3/5*f**5 - 1/5*f**6. Solve a(z) = 0.
-3, 1
Let m(g) be the first derivative of 16 - 16/7*g**3 + 0*g**2 - 2/21*g**6 - 16/7*g**4 + 0*g - 4/5*g**5. Factor m(h).
-4*h**2*(h + 2)**2*(h + 3)/7
Factor 14*s**3 + 14*s**2 + 144 + 14*s + s**4 + 0*s**4 + 59*s**2 + 154*s.
(s + 3)**2*(s + 4)**2
Let p(y) = -2*y - 11. Let l be p(-7). Factor 11 + 95*i**2 - 3*i**3 + 1 - 64*i - 22*i**l.
-(i - 3)*(5*i - 2)**2
Let p(v) be the first derivative of -v**6/2340 + 7*v**5/195 - 49*v**4/39 + v**3/3 + 5*v**2 + 40. Let g(q) be the third derivative of p(q). Factor g(h).
-2*(h - 14)**2/13
Suppose -3*y + 15 = 2*y. Factor y - v**2 - v + 9*v - 5*v + 1.
-(v - 4)*(v + 1)
Suppose 7*c - 6*c = -3*k, 4*k = 2*c. Let h(n) be the first derivative of -7*n**3 + 4 + c*n + 3*n**2 + 9/2*n**4. Solve h(m) = 0 for m.
0, 1/2, 2/3
Let m = -1171226227/272 + 4305984. Let j = 93/16 - m. Suppose j*h - 2/17*h**2 - 8/17 = 0. Calculate h.
1, 4
Let y be ((-30)/(-36) + -1)*(4 + 71)*-1. Let 0 - 2*u - 5/2*u**3 + 8*u**2 - y*u**4 = 0. What is u?
-1, 0, 2/5
Let z be 5/(-30) - 203/(-210). Factor 8/15*b + 8/15*b**3 + 2/15 + z*b**2 + 2/15*b**4.
2*(b + 1)**4/15
Let m(c) be the third derivative of -c**6/2160 + c**5/720 - 2*c**3 + 13*c**2. Let g(z) be the first derivative of m(z). Let g(y) = 0. What is y?
0, 1
Let x(q) = 4*q**2 + 2*q - 12. Let v(i) = i**2 + i - 2. Let g(o) = 5*v(o) - x(o). What is s in g(s) = 0?
-2, -1
Let k(s) = -s**3 - s - 1. Let u(j) = -6*j**3 + 4*j - 1. Let d(z) = -k(z) + u(z). Let d(o) = 0. Calculate o.
-1, 0, 1
Factor -2/9*j**2 - 3042 + 52*j.
-2*(j - 117)**2/9
Let j(b) be the first derivative of 3*b**5/20 - b**4/4 - 2*b**3 + 6*b**2 - b + 5. Let m(u) be the first derivative of j(u). Determine i so that m(i) = 0.
-2, 1, 2
Let q(t) = 8*t**3 + 51*t**2 - 7*t + 7. Let j(b) = 5*b**3 + 27*b**2 - 4*b + 4. Let l(r) = -7*j(r) + 4*q(r). Solve l(m) = 0.
0, 5
Let o(c) be the first derivative of -4*c**5/5 + 4*c**3 + 4*c**2 + 58. Factor o(u).
-4*u*(u - 2)*(u + 1)**2
Suppose a - 12 = -2*k, -a = 7*k - 4*k - 17. Factor -a*z - 2*z + 