t u(l) be the third derivative of l**7/1680 + l**6/960 - l**5/160 - 5*l**4/192 - l**3/24 - 15*l**2. Factor u(q).
(q - 2)*(q + 1)**3/8
Let f be 3 - (79/30 + (-8)/60). Suppose 0*w + 1/2*w**3 - f*w**2 + 0 = 0. What is w?
0, 1
Let s(j) be the first derivative of 125*j**4/4 + 300*j**3 - 390*j**2 + 160*j - 6. What is z in s(z) = 0?
-8, 2/5
Let z(l) be the first derivative of -l**3/2 - 3*l**2 - 9*l/2 + 33. Suppose z(y) = 0. Calculate y.
-3, -1
Let r be 5 - (0 + 55/15)*1. Find h, given that -8/3 + 4/3*h**2 + 4*h + r*h**4 - 4*h**3 = 0.
-1, 1, 2
Let q(j) be the third derivative of 0*j + 0 - 1/6*j**3 - 2*j**2 + 0*j**4 + 1/60*j**5. Factor q(l).
(l - 1)*(l + 1)
Suppose 3*x - 10 = -2*p, 2*p + 6*x = 7*x + 2. Solve 0 - 1/3*b**p - 1/3*b = 0.
-1, 0
Let j(q) = q + 12. Let a be j(-5). Suppose 12*i - 20 = a*i. Let 2/7*d**3 + 0 - 2/7*d + 4/7*d**i - 4/7*d**2 = 0. Calculate d.
-1, -1/2, 0, 1
Let y = -2/703 + 5630/2109. Suppose 10/9*r**3 + 2*r + 4/9 + y*r**2 = 0. What is r?
-1, -2/5
Let n be 16/60 - 2/(-5). Let l(o) be the first derivative of 4*o**2 - 3 + n*o**3 + 8*o. Factor l(t).
2*(t + 2)**2
Factor 2 + 2/9*m**2 + 4/3*m.
2*(m + 3)**2/9
Let c be (-3)/(-5) - 11/(385/21). Let -5/2*p**2 + 9/2*p**4 - 3/2*p**3 - 1/2*p + c = 0. What is p?
-1/3, 0, 1
Factor 1/4*o**4 - 1/4*o**2 + 1/4*o**3 - 1/4*o**5 + 0*o + 0.
-o**2*(o - 1)**2*(o + 1)/4
Suppose 2*w + 0*w + 5*g - 11 = 0, 5*g + 37 = 4*w. Let n be 76/18 + w/(-36). Suppose -3*b**3 + 2*b**n - 2*b**2 - b**3 + 4*b**2 = 0. What is b?
0, 1
Let v be (-520)/(-286) + 4/22. Factor -1/2*l + 1/2*l**v + 0.
l*(l - 1)/2
Determine y so that 2/7*y**4 - 4/7 - 6/7*y**3 + 2/7*y**2 + 6/7*y = 0.
-1, 1, 2
Suppose 0 = -4*w + 5*w - 2. Determine b so that -1/2*b - 3/4*b**w + 0*b**3 + 1/4*b**4 + 0 = 0.
-1, 0, 2
Let g = -18 + 31. Suppose -4*f + b = -13, 5*f - 6 - g = 4*b. Factor f*r + 3/2*r**2 + 2 + 1/4*r**3.
(r + 2)**3/4
Let x(y) be the first derivative of y**4/6 + y**3/3 - y + 1. Let t(v) be the first derivative of x(v). Factor t(h).
2*h*(h + 1)
Let m(p) = 28*p**2 - 83*p + 31. Let b(x) = -9*x**2 + 28*x - 10. Let n(u) = 14*b(u) + 4*m(u). Factor n(w).
-2*(w - 4)*(7*w - 2)
Let g(j) = j**3 - 4*j**2 - j - 2. Let l be g(4). Let n be (-9)/l + -1 - 0. Factor -1/2*f**5 + 0 + 2*f**4 + 2*f**2 - 3*f**3 - n*f.
-f*(f - 1)**4/2
Let h(i) = -6*i**3 - 6*i**2 + 12*i - 9. Let o(l) = -l**3 + l**2 - 1. Let g(n) = -h(n) + 9*o(n). Factor g(x).
-3*x*(x - 4)*(x - 1)
Let t be -11 + 20 - 452/52. Factor -2/13*p**2 + t*p + 0.
-2*p*(p - 2)/13
Factor -j**2 + 56*j - 2*j**2 - 12 - 63 - 26*j.
-3*(j - 5)**2
Let o be 2/((-10)/29) + -9 + 15. Let 3/5*u + o*u**2 + 2/5 = 0. Calculate u.
-2, -1
Let x(h) be the first derivative of -1/12*h**3 - 1/8*h**2 - 3 + 0*h. Factor x(c).
-c*(c + 1)/4
Let v(d) be the first derivative of -1/7*d**3 + 7 + 0*d - 3/28*d**4 + 0*d**2. Factor v(s).
-3*s**2*(s + 1)/7
Let z(h) be the second derivative of -h**7/273 + h**6/195 + h**5/65 - h**4/39 - h**3/39 + h**2/13 + 4*h. Determine w, given that z(w) = 0.
-1, 1
Let v be (15/90)/(0/(-2) - -2). Let o(k) be the second derivative of -3/10*k**6 + 0*k**2 - v*k**4 + 2/21*k**7 + 2*k + 0 + 0*k**3 + 3/10*k**5. Factor o(r).
r**2*(r - 1)**2*(4*r - 1)
Suppose -5*r + v + 5 = 0, -16 = 2*v - 6. Suppose -i = -r*i - 3. Solve -f**2 - f**2 + 3*f**i - 2*f**3 = 0 for f.
0, 2
Factor 2*c**3 - 18 - 13*c**2 - 20*c**2 + 19*c**2 + 30*c.
2*(c - 3)**2*(c - 1)
Let p(g) be the first derivative of 0*g + 1/4*g**4 - 1/6*g**6 + 3 + 0*g**2 + 0*g**3 + 0*g**5. Factor p(u).
-u**3*(u - 1)*(u + 1)
Let r(o) be the second derivative of 0 - 9/2*o**2 - 3*o - o**3 - 1/12*o**4. Suppose r(d) = 0. Calculate d.
-3
Let o(s) be the first derivative of s**3/3 + 5*s**2 + 8. Let t be o(-10). Suppose 0 - 1/3*h**2 + t*h - h**4 + 1/3*h**5 + h**3 = 0. What is h?
0, 1
Let g(h) = -6*h**3 - 19*h**2 - 20*h - 7. Let m(c) = -15*c**3 - 48*c**2 - 51*c - 18. Let j(f) = -12*g(f) + 5*m(f). Determine w so that j(w) = 0.
-2, -1
Let u be (-1 - -5) + (-2)/(-4)*2. Factor 3 - 3/4*z**4 + 6*z - 15/4*z**3 + 3/4*z**2 + 3/4*z**u.
3*(z - 2)**2*(z + 1)**3/4
Factor 3*b**5 - 5*b - 2 - 5*b**4 + 10*b**3 + 13*b**4 + 2*b**4.
(b + 1)**4*(3*b - 2)
Let l(r) be the third derivative of r**6/1080 + r**3/2 + r**2. Let d(b) be the first derivative of l(b). Determine x, given that d(x) = 0.
0
Let h = 23 + -18. Let q be (h - 3)*15/10. Factor 0*y**2 + 3/2*y**3 + 0 - q*y**4 + 0*y + 3/2*y**5.
3*y**3*(y - 1)**2/2
Let m(b) be the third derivative of b**6/2160 + b**5/180 + b**4/36 - 2*b**3/3 - 4*b**2. Let y(f) be the first derivative of m(f). What is j in y(j) = 0?
-2
Let c(x) be the first derivative of -x**5/5 - x**4/4 + x**3/3 + x**2/2 - 26. Factor c(j).
-j*(j - 1)*(j + 1)**2
Let g be ((24/(-124))/3)/(-1). Let s = g - -27/62. Factor -2 - s*w**2 - 2*w.
-(w + 2)**2/2
Let k(w) = -w**2 - 10*w + 77. Let n be k(5). Solve 0*p + 0 - 2/3*p**3 + 1/3*p**n + 1/3*p**4 = 0.
0, 1
Solve -24/7*n**2 + 16/7*n + 0 + 150/7*n**4 - 100/7*n**3 = 0 for n.
-2/5, 0, 2/5, 2/3
Suppose l - 76 = 756. Let n be 6/14*l/24. Find q, given that -10*q**5 + n*q + 172/7*q**2 - 34/7*q**3 - 188/7*q**4 + 16/7 = 0.
-2, -1, -2/5, -2/7, 1
Let t(i) be the second derivative of 1/30*i**3 + 0 - 1/100*i**5 + 1/10*i**2 - 1/60*i**4 + 3*i. Factor t(o).
-(o - 1)*(o + 1)**2/5
Let q = -176 + 119. Let n = q + 286/5. Factor -2/5*l**2 + 0 - n*l - 1/5*l**3.
-l*(l + 1)**2/5
Let g(v) be the third derivative of 1/42*v**5 + 0*v**3 + 1/42*v**4 - 5*v**2 - 11/420*v**6 + 4/735*v**7 + 0*v + 0. Suppose g(o) = 0. What is o?
-1/4, 0, 1, 2
Let n(m) be the third derivative of m**6/40 - m**5/20 - m**4/4 - 2*m**2. Find y, given that n(y) = 0.
-1, 0, 2
Let -9/2*x**3 - 15/2*x + 3/2*x**4 + 0 - 27/2*x**2 = 0. Calculate x.
-1, 0, 5
Let i be -34*(0 - (-4)/(-8)). Suppose i - 5 = 6*k. Determine n, given that -1/3*n**k - 4/3 - 4/3*n = 0.
-2
Let h be (-90)/60*(-3 - -1). Suppose -9/2*r - 1/2*r**3 + 0 - h*r**2 = 0. Calculate r.
-3, 0
Suppose 3*b - h - 12 = 0, -3 - 12 = -4*b + h. Let l be (-2)/b - (-14)/21. Factor 0*q**4 + 1/4*q**3 + 0 + l*q + 0*q**2 - 1/4*q**5.
-q**3*(q - 1)*(q + 1)/4
Let t be -6 + 5 - (-1 + -3). Let d(x) be the second derivative of -1/2*x**t - 2*x + 1/2*x**2 + 1/6*x**4 + 0. Let d(u) = 0. Calculate u.
1/2, 1
Factor 0 - 5/11*j**3 + 0*j + 1/11*j**5 + 3/11*j**2 + 1/11*j**4.
j**2*(j - 1)**2*(j + 3)/11
Let 13/6*m**2 - m**3 + 2/3 + 1/6*m**4 - 2*m = 0. What is m?
1, 2
Let d be (176/(-56) + 2)*7/(-2). Find g such that 1/2*g + 0 - 3/2*g**2 + 3/2*g**3 - 1/2*g**d = 0.
0, 1
Let o(m) be the second derivative of -m**7/336 + m**6/60 - m**5/40 + 14*m. Solve o(d) = 0.
0, 2
Determine l so that 4/11*l**2 - 2/11*l**5 + 0*l**4 + 0*l + 6/11*l**3 + 0 = 0.
-1, 0, 2
Let q(h) be the third derivative of h**7/525 - h**6/600 - h**5/60 - h**4/60 - h**2. Determine w so that q(w) = 0.
-1, -1/2, 0, 2
Factor 12*z**3 - 6*z**2 + 8*z**4 - 10*z**4 - 6*z**3 + 2*z.
-2*z*(z - 1)**3
What is n in -16 - 66*n**2 + 61*n**2 - 50*n + 71 = 0?
-11, 1
Suppose -3*g + 3*n - 65 = -4*g, -3*n = 5*g - 265. Let m be g/(-18) - 6/(-2). Factor -8/9*v**2 + 4/3*v**3 - 8/9*v**4 + m*v + 2/9*v**5 + 0.
2*v*(v - 1)**4/9
Let x be ((-39)/9)/((-33)/9) + -1. Factor -4/11*i - 18/11*i**3 + 14/11*i**2 - x*i**5 + 0 + 10/11*i**4.
-2*i*(i - 2)*(i - 1)**3/11
Let c(y) be the third derivative of y**6/420 - y**4/28 - 2*y**3/21 + 6*y**2. Factor c(r).
2*(r - 2)*(r + 1)**2/7
Suppose 2*q + b + 1 = -4*b, 0 = q + 5*b + 3. Let i(x) be the second derivative of 0 - 1/12*x**4 - q*x + 0*x**2 + 1/40*x**5 + 1/12*x**3. Factor i(y).
y*(y - 1)**2/2
Let z(l) be the first derivative of -l**6/18 - 7*l**5/180 + 11*l**4/72 - l**3/9 + 3*l**2/2 - 3. Let v(u) be the second derivative of z(u). Factor v(b).
-(b + 1)*(4*b - 1)*(5*b - 2)/3
Let t(o) = -4*o**3 + 8*o**2 + 4*o. Let m(p) = p**3 + p**2. Let w(g) = -4*m(g) + t(g). Determine f, given that w(f) = 0.
-1/2, 0, 1
Let p(h) be the third derivative of h**7/70 - 7*h**6/120 + h**5/20 + h**4/8 - h**3/3 - 10*h**2. Suppose p(c) = 0. Calculate c.
-2/3, 1
Let h(t) be the first derivative of -t**5/120 + t**2 - 2. Let w(a) be the second derivative of h(a). Solve w(u) = 0.
0
Let g = -13 + 12. Let w be 2 + g - 2/6. Suppose w*h**3 + 0 - 2/3*h**4 + 0*h + 0*h**2 = 0. Calculate h.
0, 1
Factor -6*q**2 - 42 - 4*q + 43*q + 9*q**2.
3*(q - 1)*(q + 14)
Let i(o) be the third derivative of 0*o**4 + 0 + 0*o + 1/30*o**5 + 3*o**2 - 4/9*o**3 + 1/180*o**6. Let i(h) = 0.