2
Suppose -22/3*i + 1/3*i**2 + 0 = 0. What is i?
0, 22
Let t(w) be the third derivative of -w**7/40 + w**6/32 + w**5/5 + w**4/8 + 2*w**2 - 33*w. Determine g so that t(g) = 0.
-1, -2/7, 0, 2
Let b(m) be the first derivative of -5*m**8/336 - m**7/21 + m**6/24 + m**5/6 - 5*m**2 - 2. Let k(r) be the second derivative of b(r). Solve k(d) = 0.
-2, -1, 0, 1
Let l(f) = f**3 + f**2 - 1. Let c(w) = 8*w**3 + 18*w**2 - 30*w - 206. Let m(g) = -c(g) + 6*l(g). Let m(k) = 0. Calculate k.
-5, 4
Let g(t) = t. Let b(c) = -16*c + 23*c + 2*c**2 + 5*c**2. Let a(y) = b(y) - 6*g(y). Factor a(l).
l*(7*l + 1)
Factor -18/5*j + 18/5*j**2 + 2/15*j**4 + 0 - 6/5*j**3.
2*j*(j - 3)**3/15
Suppose 2*u = -3*h - u - 33, h + 2*u = -11. Let d = 11 + h. Factor -17*b**5 - 2*b**3 + 0 + 3*b**4 + 16*b**5 + d.
-b**3*(b - 2)*(b - 1)
Let h(o) be the first derivative of o**8/252 - 8*o**7/315 + 2*o**6/45 - 9*o**2 + 18. Let v(m) be the second derivative of h(m). Factor v(f).
4*f**3*(f - 2)**2/3
Suppose i + 6 = 9. Let s be -4 - (i + (-165)/21). Factor -2/7*c - 6/7 + 2/7*c**3 + s*c**2.
2*(c - 1)*(c + 1)*(c + 3)/7
Let h(n) be the first derivative of 7/4*n**4 - 3 - 1/5*n**5 + 0*n - 8*n**2 - 8/3*n**3. Factor h(a).
-a*(a - 4)**2*(a + 1)
Let p(s) be the third derivative of -s**5/40 + 279*s**4/8 - 77841*s**3/4 - 3*s**2 + 41. Factor p(k).
-3*(k - 279)**2/2
Let t(f) be the first derivative of -f**5/10 + f**3 - 2*f**2 + 31*f - 34. Let d(o) be the first derivative of t(o). Factor d(u).
-2*(u - 1)**2*(u + 2)
Let m(n) = 2*n**2 - 263*n - 3645. Let h(i) = i**2 - 264*i - 3645. Let d(l) = -7*h(l) + 6*m(l). Factor d(y).
5*(y + 27)**2
Let q(t) be the second derivative of 2/3*t**4 + 3*t + 27/5*t**6 - 18/5*t**5 + 0*t**3 + 0*t**2 + 0. Factor q(z).
2*z**2*(9*z - 2)**2
Let u(q) = 1. Let g(k) be the second derivative of -k**5/4 + 5*k**4/12 + 5*k**3/6 + 25*k**2/2 - 9*k. Let j(a) = g(a) - 30*u(a). Let j(v) = 0. Calculate v.
-1, 1
Suppose -u + 4*q = u - 14, -10 = 2*u + 4*q. Let g = u + -1. Factor 2/15*j**2 + 2/5*j**4 + g + 0*j - 2/5*j**3 - 2/15*j**5.
-2*j**2*(j - 1)**3/15
Factor 9/2*d + 9/4 + 11/4*d**2 + 1/2*d**3.
(d + 1)*(d + 3)*(2*d + 3)/4
Let i be 0 + 14 + (7 + -5)/(-2). Let t be (i/78)/(2/4). What is k in -5/3*k**2 - 8/3*k**3 + 0 - t*k - 4/3*k**4 = 0?
-1, -1/2, 0
Let -7*s + s**2 + 1 - 18 - 9*s + 0 = 0. What is s?
-1, 17
Let n(z) be the third derivative of z**8/504 - 23*z**7/315 + 203*z**6/180 - 841*z**5/90 + 130*z**4/3 - 100*z**3 + 212*z**2. Suppose n(d) = 0. What is d?
1, 5, 6
What is z in 6/11*z**4 + 0*z - 14/11*z**2 - 2/11*z**5 + 8/11 + 2/11*z**3 = 0?
-1, 1, 2
Let g(z) be the first derivative of 3 - 1/42*z**4 + 2*z + 2/21*z**3 - 1/70*z**5 + 0*z**2. Let l(f) be the first derivative of g(f). Let l(d) = 0. What is d?
-2, 0, 1
Let b be -47 - 1/(1/4). Let w = b - -51. Factor 1/3*a**2 + w + 1/3*a.
a*(a + 1)/3
Suppose -5/2 - 1/4*q**2 - 13/8*q = 0. Calculate q.
-4, -5/2
Let k = -3862 - -3866. Factor -5/2*j**5 - 4*j**k + 0 - 1/2*j**3 + 0*j + j**2.
-j**2*(j + 1)**2*(5*j - 2)/2
Let w(f) be the third derivative of 1/28*f**6 + 0*f**3 + 1/210*f**5 + 19/735*f**7 + 0 + 1/168*f**8 + 17*f**2 + 0*f - 1/42*f**4. Let w(u) = 0. What is u?
-1, 0, 2/7
Let a(w) = -6*w**3 + 2*w**2 + 2*w - 2. Let q(s) = 1. Let t(z) = 5*z**3 - z**2 - 2*z - 5. Let r(n) = -6*q(n) - t(n). Let b(m) = 3*a(m) - 4*r(m). Factor b(i).
2*(i - 1)*(i + 1)**2
Let l(i) = -2*i**2 + 9 + 6*i - 11 + 1. Let z(v) be the third derivative of v**3/6 - v**2. Let x(h) = 2*l(h) - 6*z(h). Find w such that x(w) = 0.
1, 2
Let m(a) = -2*a**3 + 5*a**2 + 7. Let q be m(0). Let u(s) be the first derivative of -1/9*s**3 - q + 1/3*s**2 + 0*s. Factor u(f).
-f*(f - 2)/3
Let h be (4 - -3)*(-1 - -2). Let r be -6 + h + (-6)/(-2). Factor -r*y - 15*y**4 - 10*y**3 - 12*y**2 + 6*y**4 + 5*y**4 - 2*y**3.
-4*y*(y + 1)**3
Determine z, given that 1528 + 1859 + 38 - 669 - 228*z + 1576 + 3*z**2 = 0.
38
Let o(t) be the first derivative of -1/4*t**4 + 2/3*t**2 + 0*t**3 - 12 + 1/15*t**5 + 0*t. Find h such that o(h) = 0.
-1, 0, 2
Let v(t) be the third derivative of -t**5/20 + t**4/8 + t**3 + 23*t**2. Factor v(s).
-3*(s - 2)*(s + 1)
Factor 5*p**4 + 1701 - 237*p**3 - 96*p**3 + 63*p**3 + 3365*p**2 + 7560*p + 2219.
5*(p - 28)**2*(p + 1)**2
Let k = -18 + 29. Suppose -k*j - 53 + 53 = 0. Solve 0 + 2/9*q**3 + j*q - 4/9*q**2 = 0 for q.
0, 2
Suppose 4*b + z - 535 - 189 = 0, 356 = 2*b - z. Determine y, given that -2*y**3 - 8640 - b*y**2 - 3*y**3 + 3*y**3 - 2160*y - 3*y**3 = 0.
-12
Suppose 2*f - 6*f - 33 = 5*g, 2*f = -4. Let y be (-24)/(-10) + 2/g. Factor -9 + 7*u**3 + 2*u**5 - 4*u**y - 8*u**4 + 3*u**3 + 9.
2*u**2*(u - 2)*(u - 1)**2
Let h(s) be the second derivative of s**5/40 - 37*s**4/24 + 30*s**3 - 81*s**2 + 309*s. Factor h(y).
(y - 18)**2*(y - 1)/2
Let p = 7 - 9. Let i be p - (-9)/((-9)/(-2)). Factor 4*m + 0*m**2 - 2*m**2 + 0*m + i*m.
-2*m*(m - 2)
Let u be -2 + 3/90 + (-10)/(-5). Let y(h) be the second derivative of u*h**4 - 2/15*h**3 + 0 + 5*h + 0*h**2. Let y(d) = 0. Calculate d.
0, 2
Let u(i) be the second derivative of -i**4/4 - 3*i**2/2 + 13*i. Let o(p) = 2*p**2 + 3. Let v(r) = 6*o(r) + 5*u(r). Determine y so that v(y) = 0.
-1, 1
Let x(k) = k**2 - 17*k + 14. Let u be x(16). Let s be 6/(u/1) - -3. Solve -1/3*p**4 + s + 0*p - 2/3*p**2 - p**3 = 0 for p.
-2, -1, 0
Let l(q) be the first derivative of 3/4*q**4 - 6 + 9/2*q**2 + 5*q**3 - 27*q. Solve l(s) = 0 for s.
-3, 1
Determine x, given that 0*x - 3/4*x**5 + 21/4*x**4 + 108 - 48*x**2 + 3*x**3 = 0.
-2, 2, 3, 6
Let x = -4 - -8. Let j be 10/x*(3 + (-44)/20). Factor -6*t - 3*t**3 + j + 13/2*t**2 + 1/2*t**4.
(t - 2)**2*(t - 1)**2/2
Suppose -51 = -5*g + 54. Solve 27*a**5 + 63*a**4 + g*a**3 - 48*a - 17*a**2 - 52*a**2 - 12 + 18*a**2 = 0.
-1, -2/3, 1
Let -4*o**5 - 148*o + 40 - 184*o**3 + 177*o**2 + 56*o**4 + 79*o**2 - 16*o = 0. What is o?
1, 10
Let x(o) be the third derivative of -7*o**6/160 - 83*o**5/240 - 2*o**4/3 - o**3/2 + 156*o**2. Factor x(w).
-(w + 3)*(3*w + 2)*(7*w + 2)/4
Let k be (-20*1)/(-5) - 0. Factor 4*z**5 - 10*z + 8*z**4 - 8*z**2 + 27*z - k*z**3 - 17*z.
4*z**2*(z - 1)*(z + 1)*(z + 2)
Let k be 108/63 + (-4)/(-14). Let v = 5 + -2. Solve -h**k + 3 + 2*h**2 - h**2 - v*h**2 = 0 for h.
-1, 1
Let q(t) be the second derivative of -100*t**5/13 - 350*t**4/13 - 490*t**3/13 - 343*t**2/13 + 206*t. Factor q(s).
-2*(10*s + 7)**3/13
Let j(m) = m**3 - m**2 + m - 13. Let h be j(0). Let q = -113/9 - h. Factor -2/9*g**3 - 2/3*g**2 - q*g + 0.
-2*g*(g + 1)*(g + 2)/9
Let j(d) be the first derivative of d**5/5 + 11*d**4/4 + 37*d**3/3 + 45*d**2/2 + 18*d - 697. Factor j(c).
(c + 1)**2*(c + 3)*(c + 6)
Suppose -15 = -i - 13. Suppose i*s - 2*a + 3 - 19 = 0, -2*a = -3*s + 19. Factor 0 - 1/4*z + 0*z**s + 1/2*z**4 - 1/2*z**2 + 1/4*z**5.
z*(z - 1)*(z + 1)**3/4
Let w(t) = 5*t**2 - 2. Let o(x) = -x**2 + x. Let z(k) = 6*o(k) + w(k). Let a be z(5). Factor 34 + 0*f**4 + 3*f - f**5 - 33 - 3*f**4 + 2*f**2 - 2*f**a.
-(f - 1)*(f + 1)**4
Suppose -233*c = -222*c. Let q(d) be the second derivative of c - 1/2*d**4 + 2*d**3 + 12*d**2 - 3/20*d**5 - 4*d. Suppose q(z) = 0. Calculate z.
-2, 2
Let c be (0/(-3) + -1)*94. Let n = c - -98. Factor -10/3*m**n + 0 + 4*m**3 - 2/3*m**2 + 0*m.
-2*m**2*(m - 1)*(5*m - 1)/3
What is l in 128/11 - 6/11*l**3 + 98/11*l**2 - 416/11*l = 0?
1/3, 8
Let j = 640/2233 - -182/319. Factor 4/7*x**3 + j*x + 9/7*x**2 + 1/7.
(x + 1)**2*(4*x + 1)/7
Let t(y) be the first derivative of -4*y**3/3 - 28*y**2 - 96*y + 634. Suppose t(w) = 0. What is w?
-12, -2
Suppose 0 + 5/2*v**3 + 9/2*v**4 - 7/2*v**5 + v - 9/2*v**2 = 0. Calculate v.
-1, 0, 2/7, 1
Factor 2/7*z**3 - 30/7*z + 4/7*z**2 - 72/7.
2*(z - 4)*(z + 3)**2/7
Suppose 61 = -8*y + 11*y - 5*c, 0 = 3*y - 2*c - 64. Suppose 25*p + y - 72 = 0. Suppose -2/13*k**3 + 6/13*k - 4/13 + 0*k**p = 0. What is k?
-2, 1
Suppose 12/7 - 22/7*l**2 + 26/7*l**3 - 6/7*l**4 - 10/7*l = 0. Calculate l.
-2/3, 1, 3
Let q be -5 + ((-5236)/(-55))/17. Factor -q*i**4 - 9/5*i**2 + 0 - 3*i**3 + 27/5*i.
-3*i*(i - 1)*(i + 3)**2/5
Suppose -p + 23 = 2*p + 4*v, -3*p + 11 = -2*v. Solve -3*m + p*m + 5*m + 2*m**2 + m + 8 = 0 for m.
-2
Suppose 35*l = 38*l - 81. Suppose -1 = -14*n + l. Solve 4*i**n - 3/2*i**3 - 7/2*i + 1 = 0 for i.
2/3, 1
Let d(v) be the third derivative of -v**9/12096 + v**8/4032 + 5*v**7/504 + v**6/18 - 3*v**5/10 + 44*v**2. Let m(n) be the third derivative of d(n). Fact