 Find w such that h(w) = 0.
-5, -1, 1
Let h(q) be the third derivative of -q**5/20 - 3*q**4 - 72*q**3 - 2*q**2 - 2*q. Find y such that h(y) = 0.
-12
What is d in -2/15*d**4 - 14/15*d**2 - 22/15*d**3 + 16/15 + 4/3*d + 2/15*d**5 = 0?
-2, -1, 1, 4
Let g(z) be the third derivative of z**5/30 - 5*z**4/8 + 11*z**3/6 + 21*z**2. Let y(b) = b - 1. Let u(l) = 2*g(l) + 22*y(l). Factor u(t).
4*t*(t - 2)
Let k be (0 + (-12)/(-3))*(-4)/(-14). Let x = -387 + 2725/7. Find b, given that 1/7*b**2 + k*b + x = 0.
-4
Let c = -2/579 + 589/2895. Let p(i) be the second derivative of 0 - 1/4*i**4 + i**3 - c*i**6 + 0*i**2 - 2*i - 3/4*i**5. Factor p(r).
-3*r*(r + 1)*(r + 2)*(2*r - 1)
Let o(k) = 18*k**4 - 37*k**3 - 8*k**2 + 37*k - 5. Let y(c) = -10*c**4 + 19*c**3 + 4*c**2 - 19*c + 3. Let x(g) = -3*o(g) - 5*y(g). Factor x(z).
-4*z*(z - 4)*(z - 1)*(z + 1)
Let d(w) = -w**2 - 2*w + 8. Let c(y) = 2*y - 1. Let m(i) = 3*c(i) + d(i). Determine v so that m(v) = 0.
-1, 5
Let m(u) = 88*u + 2. Let q be m(1). Factor -4*p + 88*p**2 - q*p**2 - p**3 + 3*p**3.
2*p*(p - 2)*(p + 1)
Suppose 8*y**3 + 2*y**4 - 120*y + 53 + 1 - 28*y**3 + 18 + 74*y**2 + 0 = 0. Calculate y.
2, 3
Suppose -7*l + 1 = -13. Let x(t) be the third derivative of 0 - t**l + 0*t - 2/33*t**3 + 7/132*t**4 - 1/66*t**5. Factor x(z).
-2*(z - 1)*(5*z - 2)/11
Let y be (1/14)/((-54)/(-567)). Find q such that 0 + 3/4*q + y*q**3 - 3/2*q**2 = 0.
0, 1
Factor 11/3*n - n**2 - 2 + 1/3*n**4 - n**3.
(n - 3)*(n - 1)**2*(n + 2)/3
Let y = -71 - -76. Solve -2*k**4 + 1 + y*k + 2*k**2 + 0 - k**4 - k - 4*k**3 = 0.
-1, -1/3, 1
Let d(c) be the second derivative of 3*c**5/10 - 4*c**4/3 + 4*c**3/3 - 24*c. Find g such that d(g) = 0.
0, 2/3, 2
Let a(y) = 68*y**2 + 608*y + 1088. Let r(o) = 14*o**2 + 122*o + 218. Let i(t) = -5*a(t) + 24*r(t). Suppose i(p) = 0. What is p?
-26, -2
Suppose -56 - 232 = -8*j. Factor 5*r**3 + 6*r**2 - j*r**4 + 2*r**3 + 21*r**5 + 2*r**3.
3*r**2*(r - 1)**2*(7*r + 2)
Solve -1/4*p**2 + 1/4*p + 1/2 = 0 for p.
-1, 2
Let a(s) = -128*s - 510. Let b be a(-4). Factor 80/7*r**4 - 2/7*r + 0 - 66/7*r**3 + 20/7*r**b - 32/7*r**5.
-2*r*(r - 1)**2*(4*r - 1)**2/7
Let o(a) = -a + 8. Suppose -17*p = -13*p - 20. Let b be o(p). Suppose -1/6*h**4 + 0 - 4/3*h**2 - 2/3*h - 5/6*h**b = 0. What is h?
-2, -1, 0
Let k(b) be the first derivative of -b**4/4 + 41*b**3 - 5043*b**2/2 + 68921*b - 1. Determine r, given that k(r) = 0.
41
Let u(k) be the second derivative of -k**8/1680 - k**7/210 - k**6/90 - 7*k**4/6 - 21*k. Let i(s) be the third derivative of u(s). Factor i(f).
-4*f*(f + 1)*(f + 2)
Let v(t) be the second derivative of -3/2*t**3 + 36 - t + 0*t**2 + 5/4*t**4 - 1/10*t**6 - 3/20*t**5. Factor v(h).
-3*h*(h - 1)**2*(h + 3)
Suppose 5*r = 4 + 6. Factor 2 + 3*c**2 - 4*c**2 + 3*c**r - 4*c.
2*(c - 1)**2
Let x(n) be the third derivative of n**9/15120 + n**8/6720 - n**7/2520 - n**6/720 - n**4/2 + 12*n**2. Let a(f) be the second derivative of x(f). Factor a(r).
r*(r - 1)*(r + 1)**2
Let g(o) = -15*o**2 + 45*o - 40. Let r = 6 - 8. Let q(k) = -7*k**2 + 22*k - 20. Let j(b) = r*g(b) + 5*q(b). Determine t, given that j(t) = 0.
2
What is n in -3/7*n**3 + 0 + 1/7*n**4 + 2/7*n**2 + 0*n = 0?
0, 1, 2
Let v(m) be the third derivative of 0 + 0*m + 25/2*m**5 - 9*m**2 + 20/3*m**3 - 125/24*m**6 - 25/2*m**4. Suppose v(s) = 0. Calculate s.
2/5
Factor -16/3*m + 0 - 2/3*m**2.
-2*m*(m + 8)/3
Let l(n) be the third derivative of 1/8*n**4 + 2/15*n**5 - 19*n**2 + 0*n**3 + 0 + 1/20*n**6 + 0*n - 1/336*n**8 + 0*n**7. Factor l(a).
-a*(a - 3)*(a + 1)**3
Let k be (-44)/(-33) + 0/(-2). Let a(v) be the first derivative of v**2 - 10/9*v**3 - 2 + k*v. Let a(u) = 0. Calculate u.
-2/5, 1
Let j = 482 + -2406/5. Factor 0*y**2 + 2/5*y**5 - j*y**3 + 0 + 0*y**4 + 2/5*y.
2*y*(y - 1)**2*(y + 1)**2/5
Suppose 9 = 4*h - 11. Factor 2*k**2 + k + h*k + 4 - 12*k.
2*(k - 2)*(k - 1)
Factor -156*u + 170*u + 13 + 2*u**2 - 2 + 13.
2*(u + 3)*(u + 4)
Let q(m) be the second derivative of 6*m - 2/9*m**3 + 1/6*m**2 + 0 + 1/12*m**4. Factor q(h).
(h - 1)*(3*h - 1)/3
Let i(r) be the first derivative of r**5/60 - r**3/18 + 39*r - 34. Let s(d) be the first derivative of i(d). Let s(g) = 0. What is g?
-1, 0, 1
Factor 192/5 + 12*b**2 - 3/5*b**3 - 204/5*b.
-3*(b - 16)*(b - 2)**2/5
Suppose -2 = 2*v - 26. Let m = 15 - v. Factor -3*k**m + 7*k + 2*k - 4*k - 2*k.
-3*k*(k - 1)*(k + 1)
Let c(q) = -q**3. Let x(g) = -7*g**3 + 14*g**2 + g - 14. Let u(v) = 6*c(v) - x(v). Suppose u(i) = 0. Calculate i.
-1, 1, 14
Let c(k) be the third derivative of -1/32*k**4 + 0 - 3/80*k**5 + 0*k + 0*k**3 + 10*k**2 + 1/40*k**6. Determine u, given that c(u) = 0.
-1/4, 0, 1
Let u(l) = -l**5 + l**4 - l**3 + l. Let d(q) = 8*q**5 - 12*q**4 + 16*q**3 - 12*q. Let y(t) = d(t) + 12*u(t). Factor y(o).
-4*o**3*(o - 1)*(o + 1)
Let c = -177/11 - -1604/99. Let o(x) be the second derivative of 1/18*x**4 + c*x**3 + 1/9*x**2 + 0 + 1/90*x**5 - 8*x. Let o(g) = 0. What is g?
-1
Suppose 2*o - 26 = 14. Factor -11*p + 12*p**2 + 4*p**3 - 4*p - 21*p + o.
4*(p - 1)**2*(p + 5)
Let k(g) be the second derivative of -g**7/27720 + g**5/1320 - g**4/6 + 11*g. Let t(z) be the third derivative of k(z). Factor t(w).
-(w - 1)*(w + 1)/11
Let n = -581/30 + 39/2. Let d(i) be the first derivative of 0*i**2 + 0*i - 4 - n*i**5 - 1/27*i**6 - 2/27*i**3 - 1/6*i**4. Factor d(q).
-2*q**2*(q + 1)**3/9
Suppose 14 = -3*k + 4*k + 4*t, -k = -t - 9. Let d(b) be the first derivative of -4/3*b**3 + 4/5*b**5 - 1/3*b**6 + 0*b + 0*b**4 + b**2 - k. Factor d(r).
-2*r*(r - 1)**3*(r + 1)
Let v(w) = -32*w + 34. Let r be v(1). Factor 8*y**4 + 7/2*y**5 + 2*y**3 - 11/2*y - 1 - 7*y**r.
(y - 1)*(y + 1)**3*(7*y + 2)/2
Suppose -6*v + 4*v + 4 = 0. Solve -6*r**4 + r**3 + r**3 - r**3 + 3*r**2 + v*r**3 = 0 for r.
-1/2, 0, 1
Let m(k) = 3*k**3 + 6*k**2 + 3*k. Let d(q) = 3*q**3 + 5*q**2 + 2*q. Suppose 0 = 3*y - 3 - 6. Let l(b) = y*m(b) - 4*d(b). Find n such that l(n) = 0.
-1, 0, 1/3
Factor -20 + s**2 + 4 - 8*s + 7.
(s - 9)*(s + 1)
Suppose -5*j + 5*k = -25, 4 = -2*k - 0. Let c(m) be the third derivative of -1/5*m**5 - 2/3*m**j + 0 - 1/2*m**4 - m**2 + 0*m - 1/30*m**6. Factor c(r).
-4*(r + 1)**3
Let d(s) be the first derivative of s**6/720 + s**5/90 + s**4/48 - 13*s**2/2 + 17. Let p(x) be the second derivative of d(x). Solve p(q) = 0.
-3, -1, 0
Suppose 2*j + 5*z + 1 = -0, z + 3 = j. Factor -3 + 2*c**j - 3*c**2 + 4*c**2.
3*(c - 1)*(c + 1)
Determine a so that -5/4*a**3 + 0 + 1/2*a - 1/2*a**4 - 1/4*a**2 = 0.
-2, -1, 0, 1/2
Let p(t) be the third derivative of 5*t**8/168 + t**7/42 - 27*t**2. Suppose p(j) = 0. What is j?
-1/2, 0
Let s be (2/24)/((-267)/(-1424)). Determine v so that s*v**3 - 4/9*v - 2/9*v**4 + 2/9 + 0*v**2 = 0.
-1, 1
Let c(t) be the first derivative of -6/7*t - 2/7*t**2 - 1 + 2/21*t**3. Let c(g) = 0. Calculate g.
-1, 3
Let q(s) be the first derivative of 4/5*s - 7/5*s**2 + 2/3*s**3 - 7. Suppose q(c) = 0. What is c?
2/5, 1
Let f(o) be the third derivative of o**9/70560 + o**8/70560 - 13*o**5/20 - o**2 - o. Let j(a) be the third derivative of f(a). Let j(w) = 0. What is w?
-1/3, 0
Let h be -1 + -1 + (-6)/(-372)*112. Let w = 43/62 + h. Suppose 3/2*p**2 - w - p**3 + 0*p = 0. What is p?
-1/2, 1
Factor -3/8*x**3 - 165*x + 129/8*x**2 - 363/2.
-3*(x - 22)**2*(x + 1)/8
Let 1/2*c - 43 + 43*c**2 - 1/2*c**3 = 0. Calculate c.
-1, 1, 86
Let u be (-12)/((-384)/80) - 29/18. Solve -10/9*j**3 + 2/9*j - 2/3*j**2 + 0 + 2/3*j**4 + u*j**5 = 0.
-1, 0, 1/4, 1
Let v(l) = -l**2 - l. Let q(b) = 5*b**4 + 60*b**3 + 114*b**2 - 416*b + 245. Let w(i) = q(i) + 4*v(i). Factor w(g).
5*(g - 1)**2*(g + 7)**2
Let g(x) = 5*x**5 - 25*x**4 - 8*x**3 + 7*x**2 + 12*x. Let d(u) = -u**5 + 6*u**4 + 2*u**3 - 2*u**2 - 3*u. Let i(c) = 18*d(c) + 4*g(c). Find v such that i(v) = 0.
-3, -1, 0, 1
Let h(b) be the third derivative of b**6/600 - b**5/75 - 7*b**4/120 + b**3/3 - 62*b**2. Factor h(q).
(q - 5)*(q - 1)*(q + 2)/5
Let m(a) be the first derivative of -16*a - 4/3*a**3 + 8*a**2 + 27. Factor m(n).
-4*(n - 2)**2
Let i = 2778/7 - 33329/84. Factor -1/6*l - 1/4 + 1/3*l**2 - i*l**4 + 1/6*l**3.
-(l - 3)*(l - 1)*(l + 1)**2/12
Let h = 9091 - 209087/23. Determine q so that 0*q - 6/23*q**5 + 0 + h*q**3 + 2/23*q**4 - 2/23*q**2 = 0.
-1, 0, 1/3, 1
Let c(m) be the third derivative of 1/30*m**6 + 14*m**2 + 1/168*m**8 + 0*m + 0*m**4 - 1/60*m**5 + 0*m**3 + 0 - 1/42*m**7. Find x, given tha