2 + 17*r**2 = 0.
1, 3
Let h(t) = -t**3 - 4*t**2 + 5*t + 3. Let b be h(-6). Suppose 3*c = 2*r + 3*r - 35, 5*c = 5*r - b. Find j such that -r - 6*j**2 + 7 - 2*j**3 + 0*j**3 + 5 = 0.
-2, 1
Let s(w) be the third derivative of -3*w**6/40 - 3*w**5/20 + w**3 - 6*w**2. Let b(f) = -26*f**3 - 26*f**2 + 17. Let v(r) = 6*b(r) - 17*s(r). Solve v(y) = 0.
-1, 0
Let w(q) be the first derivative of -1/60*q**4 + 0*q**2 - 1/100*q**5 + 1/30*q**3 + 2 + 1/150*q**6 + 2*q. Let o(a) be the first derivative of w(a). Factor o(t).
t*(t - 1)**2*(t + 1)/5
Let d = 3 - -1. Let k be (-9)/2*d/(-6). Suppose 2*u**3 - 2*u**4 - 2 + k*u - 5*u + 3*u**4 + 1 = 0. Calculate u.
-1, 1
Let n(a) be the second derivative of -a**8/3360 + a**6/360 + a**4/4 - 3*a. Let r(t) be the third derivative of n(t). Factor r(o).
-2*o*(o - 1)*(o + 1)
Factor 11*q + 38*q**2 + 10*q - 35*q**2.
3*q*(q + 7)
Let w(l) be the first derivative of 3/10*l**5 + 3/8*l**4 - 1/2*l**3 + 0*l - 3/4*l**2 - 8. Factor w(q).
3*q*(q - 1)*(q + 1)**2/2
Solve 0 + x**3 + 1/3*x**5 + 0*x - x**4 - 1/3*x**2 = 0 for x.
0, 1
Let v(h) be the third derivative of h**8/80640 + h**7/10080 + h**6/2880 + h**5/10 + 2*h**2. Let r(s) be the third derivative of v(s). Factor r(x).
(x + 1)**2/4
Let l = 190 + -190. Let u(a) be the third derivative of -1/480*a**6 + 0 - 2*a**2 + 1/240*a**5 + l*a**3 + 0*a + 0*a**4. Factor u(s).
-s**2*(s - 1)/4
Let q(s) be the third derivative of -s**8/112 - s**7/70 + s**6/20 + s**5/10 - s**4/8 - s**3/2 - 2*s**2. Let q(b) = 0. What is b?
-1, 1
Let v(l) be the first derivative of l**7/126 - l + 5. Let c(n) be the first derivative of v(n). Factor c(i).
i**5/3
Let z(p) be the first derivative of p**3/4 - 3*p/4 - 4. Solve z(u) = 0.
-1, 1
Let w(h) be the second derivative of 2*h**7/21 + 4*h**6/15 + h**5/5 + 4*h. Factor w(z).
4*z**3*(z + 1)**2
Let g(j) = -17*j**5 + 53*j**4 - 51*j**3 + 20*j**2 + j. Let o(u) = -u**5 + u**3 - u**2 - u. Let s(h) = g(h) + 3*o(h). Suppose s(b) = 0. Calculate b.
0, 1/4, 2/5, 1
Factor -1/9*g**4 + 0 + 1/9*g**5 + 1/9*g**2 - 1/3*g**3 + 2/9*g.
g*(g - 2)*(g - 1)*(g + 1)**2/9
Let s be 10/6*(-720)/(-800). Factor s*u**2 - 2 - 1/2*u**3 + 0*u.
-(u - 2)**2*(u + 1)/2
Let r(z) be the third derivative of 0 + 1/105*z**7 + 0*z**3 - 1/30*z**5 - 1/60*z**6 + 0*z + 1/12*z**4 - 4*z**2. Determine o, given that r(o) = 0.
-1, 0, 1
Let k(x) be the first derivative of x**6/240 - x**5/40 + x**4/24 - 7*x**2/2 + 1. Let l(g) be the second derivative of k(g). Let l(p) = 0. What is p?
0, 1, 2
Let w(o) be the second derivative of -5*o**4/12 + 15*o**3/2 + 25*o**2 - 2*o. Solve w(y) = 0 for y.
-1, 10
Let l(q) = -5*q**4 + 9*q**3 - 19*q**2 + 20*q - 5. Let k(d) = -d**4 + 2*d**3 - 4*d**2 + 4*d - 1. Let y(u) = -22*k(u) + 4*l(u). Suppose y(f) = 0. Calculate f.
1
Let v = -52 + 57. Let p(k) be the first derivative of -6/5*k**v - 1/2*k**6 + 3/2*k**2 + 0*k**4 + 0*k + 2*k**3 + 2. Let p(x) = 0. What is x?
-1, 0, 1
Let q(c) = -c + 1. Let a be q(1). Let u(r) be the second derivative of 1/3*r**3 - 2*r + 0 - 1/10*r**5 + 0*r**2 + a*r**4. What is s in u(s) = 0?
-1, 0, 1
Suppose -16 = -g - 3*g. Factor -3*k**3 - k**2 + 2*k**3 + 3*k**3 + 0*k**4 - k**g.
-k**2*(k - 1)**2
Factor 0*s**2 + 0 - 2/5*s**3 + 8/5*s.
-2*s*(s - 2)*(s + 2)/5
Let y(m) be the second derivative of -3*m**5/250 - 7*m**4/150 - 2*m**3/75 + 3*m - 19. Factor y(p).
-2*p*(p + 2)*(3*p + 1)/25
Let f be 1/(-3) - (-110)/42. Let r be 6/63*(15 - 0). What is n in -f*n**4 + 8/7*n**5 - 2/7*n**2 + r*n**3 + 0 + 0*n = 0?
0, 1/2, 1
Let i(v) = 7*v**2 - 7*v**2 + 4 + 2*v**3 + 0*v**3 - 2*v**2. Let n(l) = 2*l**3 - l**2 + l + 4. Let k(d) = -3*i(d) + 2*n(d). Solve k(q) = 0 for q.
-1, 1, 2
Suppose 3*w - 13 + 2 = -2*l, 3*w - 3 = 0. Factor -3*p**4 - p**2 + 1 + 4*p**l - p**2.
(p - 1)**2*(p + 1)**2
What is f in 3/2*f + 18*f**3 + 25/2*f**5 - 13*f**2 + 0 + 45*f**4 = 0?
-3, -1, 0, 1/5
Suppose 0 = 5*a - 1 - 9. Let b(t) be the second derivative of -1/12*t**4 - a*t + 0 - 1/6*t**3 + 0*t**2. What is g in b(g) = 0?
-1, 0
Let z = -6 - -8. Solve -y + 0*y + y**z - 3*y + 2*y = 0.
0, 2
Factor 21*r + r**2 - 12*r**3 - 10*r**2 - r**2 + 6 - 5*r**2.
-3*(r - 1)*(r + 2)*(4*r + 1)
Factor -8*z**2 + 3*z**2 + 20 - 15.
-5*(z - 1)*(z + 1)
Let n(b) be the first derivative of -2*b**3/15 + b**2/5 + 4*b/5 + 3. Suppose n(r) = 0. What is r?
-1, 2
Let s(b) = -2*b**2 - b. Let q(z) be the first derivative of 0*z - 2/3*z**3 - 4 - 1/2*z**2. Let d(o) = -3*q(o) + 4*s(o). Factor d(n).
-n*(2*n + 1)
Suppose 4*f - 4*n - 30 = 2*f, 0 = -4*f + 3*n + 35. Suppose 5*z - f = 10. Let 0 - 1/4*a**z - 1/4*a**4 + 0*a + 1/4*a**5 + 1/4*a**2 = 0. What is a?
-1, 0, 1
Factor 1/4*v**5 + 0*v - 5/4*v**3 + 3/4*v**2 + 0 + 1/4*v**4.
v**2*(v - 1)**2*(v + 3)/4
Suppose 0*n - 3 = -n. Let s(x) = x**2 - 10*x + 19. Let i be s(8). Suppose 1/2 - 7/2*v**4 + i*v**2 + 5/2*v - 3/2*v**5 - v**n = 0. Calculate v.
-1, -1/3, 1
Factor -2*t**2 + t**5 - 3*t**3 + 8*t**4 - 18*t**4 + 10*t**4.
t**2*(t - 2)*(t + 1)**2
Let k(a) = -a**3 + a**2 - 5*a - 1. Let p(t) = t**3 - t**2 + 4*t + 1. Let f(u) = -5*k(u) - 6*p(u). Determine z so that f(z) = 0.
-1, 1
Solve 1/5*r**3 + 0*r - 3/5*r**4 + 7/5*r**2 - 1/5*r**5 - 4/5 = 0 for r.
-2, -1, 1
Let o(v) be the first derivative of -4*v**3 - 27*v**2/2 - 6*v + 8. Suppose o(p) = 0. Calculate p.
-2, -1/4
Let v(h) = -6*h**4 - 12*h**3 - 6*h**2 + 15*h + 9. Let u(z) = 7*z**4 + 12*z**3 + 5*z**2 - 16*z - 8. Let d(l) = -3*u(l) - 4*v(l). Factor d(i).
3*(i - 1)*(i + 1)*(i + 2)**2
Let v = 49 + -46. Factor 9/2*z**3 + 3/4*z**5 + 0 + v*z**2 + 3*z**4 + 3/4*z.
3*z*(z + 1)**4/4
Suppose -3 = -3*j, -16 = 27*f - 31*f - 4*j. Factor 1/2*z - 1/8*z**4 + 1/2*z**f - 3/4*z**2 - 1/8.
-(z - 1)**4/8
Suppose 7 = -2*k + 29. Let o be (-6)/10 + k/10. Solve -o*r - 1/4*r**2 + 0 = 0.
-2, 0
Let t = 2/715 - 2161/5720. Let q = 7/8 + t. Factor 0 + 1/2*d**2 + 0*d**3 + 0*d - q*d**4.
-d**2*(d - 1)*(d + 1)/2
Let m be 304/798 - 4/(-14). Suppose 2/3*o**5 + 4/3*o**4 + 0 - m*o**3 - 4/3*o**2 + 0*o = 0. Calculate o.
-2, -1, 0, 1
Let g = 62 + -44. Solve -15*z**2 + 4*z - 17*z**2 + g*z**5 - 31*z**5 + 60*z**3 - 51*z**5 + 32*z**4 = 0 for z.
-1, 0, 1/4, 1
Factor 0*f**2 + 1/4*f**3 + 0 + 3/8*f**4 + 1/8*f**5 + 0*f.
f**3*(f + 1)*(f + 2)/8
Determine b, given that -2/7*b**2 + 0 + 2/7*b**3 - 2/7*b + 2/7*b**4 = 0.
-1, 0, 1
Suppose -r = -4*f + 20, 3*f - 10 = 3*r - 4. Factor n**2 - 4*n + 3*n**3 + f*n + 8*n**2 + 4*n.
3*n*(n + 1)*(n + 2)
Let z(m) be the second derivative of 32*m**4/9 - 16*m**3/9 + m**2/3 - 25*m. Solve z(k) = 0 for k.
1/8
Let y(o) be the first derivative of o**5/20 - o**4/8 + o**2/4 - o/4 + 38. Determine u, given that y(u) = 0.
-1, 1
Let s(w) be the second derivative of w**5/60 - w**4/12 + w**3/9 + 4*w. What is z in s(z) = 0?
0, 1, 2
Let v = -3483/5 - -711. Let -27/5*q - v*q**4 + 48/5*q**5 + 69/5*q**2 - 21/5*q**3 + 3/5 = 0. What is q?
-1, 1/4, 1
Find z, given that -2/3 + 4/3*z**2 + 4/3*z**3 - 2/3*z**4 - 2/3*z**5 - 2/3*z = 0.
-1, 1
Let y = -2/1877 - -1889/11262. Factor 1/2*n + 0 - 2/3*n**2 + y*n**3.
n*(n - 3)*(n - 1)/6
Let g(x) = -9*x**3 + 63*x**2 + 153*x + 88. Let u(s) = -3*s**3 + 21*s**2 + 51*s + 29. Let y(n) = 2*g(n) - 7*u(n). Suppose y(d) = 0. Calculate d.
-1, 9
Suppose g = -4*j + 16, 0*g - 11 = -2*g - j. Let 34*y**2 - 15*y**2 - 15*y**2 - g = 0. What is y?
-1, 1
Let m be ((-6)/(-4))/(1/2). Suppose x - m = -1. Solve 2*v**4 - 7*v**4 + 2*v**x + 3*v**4 = 0.
-1, 0, 1
Factor -1/5*n**5 + 2*n**2 + 6/5*n**4 + 0 - 12/5*n**3 - 3/5*n.
-n*(n - 3)*(n - 1)**3/5
Let a(k) be the second derivative of -k**7/16380 - k**6/4680 + k**5/390 + 5*k**4/12 - 2*k. Let u(p) be the third derivative of a(p). Factor u(o).
-2*(o - 1)*(o + 2)/13
Let b(x) be the first derivative of -x**3/21 - 3*x**2/14 - 6. Suppose b(l) = 0. What is l?
-3, 0
Suppose 0 = -6*n - n. Let n*c + 2/5*c**4 + 0*c**2 + 0 + 0*c**3 - 1/5*c**5 = 0. Calculate c.
0, 2
Let u(h) be the third derivative of -h**5/90 - h**4/36 - 7*h**2. Factor u(s).
-2*s*(s + 1)/3
Let u(i) be the second derivative of i**6/90 - i**4/18 + i**2/6 - 29*i. Factor u(b).
(b - 1)**2*(b + 1)**2/3
Suppose f = -6 - 3. Let o = 11 + f. Find d, given that -2/5*d**3 + 2/5*d + 0 + 2/5*d**4 - 2/5*d**o = 0.
-1, 0, 1
Let k(v) be the second derivative of v**8/320 - 2*v**7/105 + v**6/60 - 5*v**4/12 + 5*v. Let l(x) be the third derivative of k(x). Suppose l(t) = 0. What is t?
0, 2/7, 2
Find n such that 8/15 + 2/15*n**2 - 8/15*n = 0.
2
Let