t) = 0?
0, 2
Let f(d) be the first derivative of 2*d**5/85 + 3*d**4/34 - 20*d**3/51 - 24*d**2/17 + 514. Find h, given that f(h) = 0.
-4, -2, 0, 3
Let l(y) = -y**3 - 5*y**2 + 3*y + 3. Let t be l(-5). Let r = t - -14. Factor -6*z - z**2 - r*z + 3*z**2 - 8*z + 32.
2*(z - 4)**2
Let k be (12/33)/((-1580)/(-1738)). Suppose 5*x = -0*x + 10. Factor k*u**4 - 6/5*u**2 - 4/5 + 2/5*u**3 - x*u.
2*(u - 2)*(u + 1)**3/5
Let y(q) be the first derivative of -q**4/6 - 74*q**3/9 - 323*q**2/3 + 722*q/3 + 96. Factor y(z).
-2*(z - 1)*(z + 19)**2/3
Let q be 27*(-50)/(-1575)*(-7)/(-3). Solve -1/6*b**q - 3/2 - b = 0 for b.
-3
Let -4*g**3 - 120 - 253*g + 243*g + 9*g**3 + 25*g**2 = 0. Calculate g.
-4, -3, 2
Let f = 8 + -5. Suppose -5*l + 26 = 4*a, f*a - 3 = -3*l + 15. Solve 4*c**4 - 2*c**4 + c**a = 0.
0
Let s(a) = a**2 - 107*a - 1352. Let b(t) = 3*t**2 - 427*t - 5408. Let r(g) = 6*b(g) - 22*s(g). Suppose r(k) = 0. What is k?
-26
Let x(d) = -2*d**3 - 8*d**2 - 6*d - 6. Let o be x(-4). Let q be -5 - -1 - ((-261)/o - -6). Solve 3/2*y**2 - 9/2*y**3 - 3/2*y**5 + 0 + q*y**4 + 0*y = 0 for y.
0, 1
Let a(j) be the third derivative of -j**7/7560 - j**6/1080 + j**4/12 - 17*j**2. Let x(l) be the second derivative of a(l). Factor x(u).
-u*(u + 2)/3
Let v = -264 + 267. Let i(f) be the third derivative of 0 + 0*f + 0*f**v - 1/40*f**6 + 0*f**4 + 3*f**2 - 1/112*f**8 + 1/35*f**7 + 0*f**5. Factor i(d).
-3*d**3*(d - 1)**2
Let x be 19 - (18 + (-20)/5). Factor 16/3*h**x - 20*h**4 + 80/3*h**3 + 4/3 + 0*h - 40/3*h**2.
4*(h - 1)**4*(4*h + 1)/3
Let d be ((-60)/(-120))/(-1 - -5) + 20/96. Solve -12 + 16*l - 13/3*l**2 + d*l**3 = 0.
1, 6
Let p = -130063/15 + 8673. Suppose -p + 16/15*n - 2/15*n**2 = 0. What is n?
4
Suppose 3*l = 13*l - 170. Suppose -l*a + 2*a = -a. Factor 9/5*q**3 + 3/5*q + a - 3/5*q**4 - 9/5*q**2.
-3*q*(q - 1)**3/5
Let 10/9 - 28/9*t + 8/3*t**2 - 4/9*t**3 - 2/9*t**4 = 0. What is t?
-5, 1
Let c(v) be the third derivative of v**5/210 + 2*v**4/7 + 273*v**2. Factor c(b).
2*b*(b + 24)/7
Let r(h) be the first derivative of h**5 - 95*h**4/4 + 575*h**3/3 - 1125*h**2/2 - 58. Factor r(f).
5*f*(f - 9)*(f - 5)**2
Let n(q) be the second derivative of q**4/120 - q**3/12 - 3*q**2/10 + 223*q. Factor n(a).
(a - 6)*(a + 1)/10
Let p(d) be the first derivative of -d**6/600 + d**5/200 + 2*d**3 + 13. Let q(j) be the third derivative of p(j). What is n in q(n) = 0?
0, 1
Let m(v) be the second derivative of 0 + 2/7*v**2 + 1/42*v**4 + 11*v - 1/7*v**3. Solve m(t) = 0 for t.
1, 2
Let d(c) be the first derivative of -c**8/7560 - c**7/945 - c**6/324 - c**5/270 - 2*c**3/3 + 2. Let g(v) be the third derivative of d(v). Factor g(i).
-2*i*(i + 1)**2*(i + 2)/9
Suppose -11*c + 15*c = 72. Factor -9*l - 49*l**3 + c*l - 9*l + 14*l**4 - l**5.
-l**3*(l - 7)**2
Let u = -14393 - -14396. Factor 1/2*x**u + 0*x + 0 + 3/2*x**2.
x**2*(x + 3)/2
Let d(j) be the second derivative of 0 + 8*j**2 - 43*j + 53/3*j**4 + 20*j**3 - 3/2*j**5 - 9/5*j**6. Find z such that d(z) = 0.
-2, -1/3, -2/9, 2
Let v(z) = -670*z - 4020. Let q be v(-6). Suppose -x**2 + 0 - 1/3*x**4 - 4/3*x**3 + q*x = 0. What is x?
-3, -1, 0
Suppose 0 = -g, -30 = -4*a + 3*g + 2. Let w(p) be the first derivative of -1/6*p**3 - 6 + 2*p**2 - a*p. Factor w(o).
-(o - 4)**2/2
Suppose 5 = 4*p - 11. Factor -3*a**5 + a**5 + 3*a**3 - a**3 - 2*a**2 - 2*a**4 + 4*a**p.
-2*a**2*(a - 1)**2*(a + 1)
Let 30089*c - 2186*c**4 + 93058*c**2 + 17*c**5 - 2560*c**4 + 53614*c**3 - 3*c**5 + 5000 + 9511*c + 84*c**5 = 0. What is c?
-1, -2/7, 25
Let o(u) = -6*u**3 - 3*u - 2. Let t(k) = k**3. Suppose 3*b + 35 = 140. Let h(p) = b*t(p) + 5*o(p). Find n, given that h(n) = 0.
-1, 2
Let i(t) be the third derivative of t**7/35 + 17*t**6/80 + t**5/2 + t**4/4 - 85*t**2. Let i(j) = 0. What is j?
-2, -1/4, 0
Solve 12*f**2 - f - 80 - 9*f - 235 - 7*f**2 = 0.
-7, 9
Let z be -1*6/14*-7. Suppose g + 13 - 41 = -3*s, -s = -z*g - 26. Factor 8*l - 8*l**3 + 8 + 0*l - s*l**4 + 9*l**4 - 6*l**2.
-2*(l - 1)*(l + 1)*(l + 2)**2
Let i be ((-20 - -44)/(-3))/(8/(-1)). Factor -25/4*j**3 + 4*j - i - 5/4*j**2.
-(j + 1)*(5*j - 2)**2/4
Let y(p) be the third derivative of 0*p + 0*p**3 + 1/90*p**5 + 5*p**2 + 0 + 1/36*p**4. Factor y(f).
2*f*(f + 1)/3
Let o = -25 - -28. Factor o*j + j**2 - j + 0*j**2.
j*(j + 2)
Let t(n) be the first derivative of n**6/225 + 3*n**5/50 - n**4/6 - 7*n**3 + 42. Let u(d) be the third derivative of t(d). Factor u(b).
4*(b + 5)*(2*b - 1)/5
Solve 4*s**2 - 1/2*s**4 + 0 + s**3 + 0*s = 0.
-2, 0, 4
Suppose -8*a - 5*a - 4*a = 0. Let d(r) be the second derivative of 0*r**5 + 0*r**4 + 0*r**2 + 1/15*r**6 + a*r**3 + 3*r + 1/21*r**7 + 0. Factor d(y).
2*y**4*(y + 1)
Let k be -11 + (-3 - -7) - 2. Let n be -2 + k/(-1) + -4. Determine u so that 3/4*u**2 - 3/2*u + 3/2*u**n - 3/4*u**4 + 0 = 0.
-1, 0, 1, 2
Let c(d) be the second derivative of -d**9/7560 + d**7/1260 - 11*d**4/12 - 12*d. Let h(w) be the third derivative of c(w). What is q in h(q) = 0?
-1, 0, 1
Suppose 4*j - 2 = 14. Suppose j*o - 1 = 7. Factor 6/5*i**2 + 4/5 - 2/5*i**3 - 2/5*i**4 + o*i.
-2*(i - 2)*(i + 1)**3/5
Find w such that 287496*w**3 + 80 + 1185921*w**4 + 16*w + 1040*w - 64 + 26136*w**2 = 0.
-2/33
Let o be 0/(-4)*(0 - 6/12). Let g(v) be the third derivative of -v**4 + 1/4*v**5 + o + 0*v + 2*v**3 - 1/40*v**6 + v**2. Factor g(r).
-3*(r - 2)**2*(r - 1)
Let x(d) be the first derivative of d**3/12 + d**2 + 15*d/4 + 23. Determine t, given that x(t) = 0.
-5, -3
Let u be (-40)/12*(-1 + -2). Let z(b) = b**2 - 10*b + 2. Let o be z(u). Find g, given that 3*g**2 + 3*g + g**o + 5*g = 0.
-2, 0
Let g(v) be the second derivative of -v**7/3 - 4*v**6/5 + 11*v**5/10 + 2*v**4 - 4*v**3/3 + 2*v - 26. Determine m, given that g(m) = 0.
-2, -1, 0, 2/7, 1
Let h(f) be the second derivative of -3*f**5/20 - 3*f**4/8 + 11*f**3/4 + 9*f**2/2 - 2*f - 2. Factor h(s).
-3*(s - 2)*(s + 3)*(2*s + 1)/2
What is p in -40/19*p + 0 + 2/19*p**3 - 2/19*p**2 = 0?
-4, 0, 5
Let y(d) = 4*d**2 + 19*d - 10. Let g(i) = -i**2 - 10*i + 4. Let j(p) = -5*g(p) - 2*y(p). Factor j(k).
-3*k*(k - 4)
Let a(c) = -56*c + 13*c**2 + 24 - 6 + 22 + 40. Let w(p) = -6*p**2 + 28*p - 40. Let m(o) = 2*a(o) + 5*w(o). Factor m(f).
-4*(f - 5)*(f - 2)
Let v(n) = -6*n - 44. Let t be v(-5). Let m(p) = 4*p + 56. Let x be m(t). Determine b, given that 4/7*b**2 + x + 0*b - 2/7*b**3 = 0.
0, 2
Solve 36*a**3 - 551*a**4 - 2 - 126*a**2 + 30*a**2 + 2 + 547*a**4 + 64*a = 0.
0, 1, 4
Let o(c) be the first derivative of 7*c**6/2 + 204*c**5/5 - 225*c**4 + 10*c**3 + 879*c**2/2 - 234*c + 396. Solve o(l) = 0.
-13, -1, 2/7, 1, 3
Let w be (1359/99)/(21 - 0). Let r = w - -1/77. Factor -r*t**2 - 2/3*t + 0.
-2*t*(t + 1)/3
Let g(i) be the second derivative of i**4/60 + 11*i**3/15 - 23*i**2/10 + 111*i - 4. Factor g(u).
(u - 1)*(u + 23)/5
Let g(p) be the second derivative of 1/4*p**3 + 11*p + 1/4*p**4 + 0*p**2 + 0. Factor g(h).
3*h*(2*h + 1)/2
Determine z, given that -15/2*z - 3/2*z**5 + 3*z**4 + 9*z**3 - 12*z**2 + 9 = 0.
-2, -1, 1, 3
Let p(c) be the second derivative of -1/48*c**4 + 0*c**2 + 1/8*c**3 + 17*c + 0. Factor p(n).
-n*(n - 3)/4
Let d(a) be the first derivative of 36*a**5 + 345*a**4 + 2405*a**3/3 - 460*a**2 + 80*a - 46. Factor d(b).
5*(b + 4)**2*(6*b - 1)**2
Let o be 4 - 1 - (-1 + -3). Factor o*f**3 + f**2 + f**2 - f**2 + 12*f**4.
f**2*(3*f + 1)*(4*f + 1)
Let x(v) be the third derivative of 1/2184*v**8 + 0 + 0*v - 1/260*v**6 + 0*v**5 + 2/1365*v**7 + 0*v**4 - 6*v**2 + 0*v**3. Factor x(b).
2*b**3*(b - 1)*(b + 3)/13
Factor -10*z - 2/5*z**2 + 52/5.
-2*(z - 1)*(z + 26)/5
Let u = -8 + 12. Suppose 0 = u*z + 3 - 15. Determine l, given that -l**3 + 3*l**3 - 5*l**z - 8*l**4 + 5*l**4 + 6*l**2 = 0.
-2, 0, 1
Let t = -16 + 26. Determine k so that 25*k**3 - 25*k - k**4 - 9*k**4 + 10 - 10*k**2 + t*k**2 = 0.
-1, 1/2, 1, 2
Let s be (-12*9/(-270))/(3/10). Factor s*h**3 + 4/3*h - 1/3 - 1/3*h**4 - 2*h**2.
-(h - 1)**4/3
Suppose 0 = -3*h + 13 + 17. Suppose -4 = -g - n, g + 0*g = -4*n + h. Factor 2/11 + 4/11*v**3 - 4/11*v**g - 2/11*v - 2/11*v**5 + 2/11*v**4.
-2*(v - 1)**3*(v + 1)**2/11
Suppose 6*q + 7 - 31 = 0. Suppose -2 - 10 = -q*s. Factor 76*o**3 + o + o**4 - 74*o**s + 2*o - 5*o - 1.
(o - 1)*(o + 1)**3
Let b be 616/330 - (-6)/(-5). Determine d, given that b*d**2 - 1/9 - 5/9*d = 0.
-1/6, 1
Let x(m) = -m + 1. Let u(y) = -y**2 + 4*y + 2. Let n be u(5). Let z(b) = b**2 - 17*b +