2/83 + v. Factor 3/7*t**3 - q*t - 6/7*t**2 + 6/7.
3*(t - 2)*(t - 1)*(t + 1)/7
Suppose -66*p + 70*p = 16. Let q(k) be the first derivative of 0*k**3 + 1/13*k**2 - 7 + 0*k - 1/26*k**p. Factor q(z).
-2*z*(z - 1)*(z + 1)/13
Let a be -4 + -1 + 133/21. Let q(j) be the first derivative of 6 + 2*j + 1/2*j**4 - a*j**3 + 2/5*j**5 - 1/2*j**2 - 1/6*j**6. Suppose q(o) = 0. What is o?
-1, 1, 2
Suppose f = -32 - 24. Let x be 14/8 - 14/f. Suppose -4*i + 12*i**2 + 8*i**2 - 4*i**3 - 28*i**x = 0. Calculate i.
-1, 0
Factor 7*z - 8*z**2 - 4*z - 4*z**2 + 5*z**3 - 13*z**2 + 12*z + 45.
5*(z - 3)**2*(z + 1)
Let b(o) be the second derivative of o**6/25 + 61*o**5/100 + 8*o**4/3 + 5*o**3/6 - 59*o. Suppose b(y) = 0. Calculate y.
-5, -1/6, 0
Let k(j) be the second derivative of 2*j**6/15 - 26*j**5/5 + 75*j**4 - 432*j**3 - 207*j. Let k(m) = 0. What is m?
0, 8, 9
Let h = 5302 + -5300. Factor 0*l + 0 + 1/2*l**4 + l**h + 3/2*l**3.
l**2*(l + 1)*(l + 2)/2
Let n(x) be the second derivative of 1/48*x**4 + 0*x**2 - 1/6*x**3 + 2*x + 0. Factor n(r).
r*(r - 4)/4
Let l(d) = 8*d**2 - 12*d + 20. Let c(q) = -2*q**2 + 3*q - 1. Let y be c(0). Let o(k) = -k**2 - k - 1. Let t(h) = y*l(h) - 4*o(h). Factor t(p).
-4*(p - 2)**2
Factor -4*z - 80 + 3723*z**2 - 3719*z**2 + 0*z.
4*(z - 5)*(z + 4)
Suppose -54*o + 53*o + 2 = 0, w - 8 = -4*o. Let v(m) be the second derivative of 9*m + 1/36*m**4 + 0*m**2 + w + 1/9*m**3. Factor v(u).
u*(u + 2)/3
Let c(b) be the second derivative of b**4/42 - 90*b**3/7 + 18225*b**2/7 + 5*b - 5. Factor c(x).
2*(x - 135)**2/7
Let o(z) = z - 8 - 1 + 3 + 3*z**2 + 11*z - z**3. Let l be o(5). Factor -3/5*s**l + 3/5*s**2 + 0 - 6/5*s + 6/5*s**3.
-3*s*(s - 2)*(s - 1)*(s + 1)/5
Suppose 4*j - 4*w = 8, -2*j + 3*j - 3*w = 8. Let u be 1/j - (-42)/26. Factor 0*g + 0 + 10/13*g**4 - u*g**2 + 16/13*g**3.
2*g**2*(g + 2)*(5*g - 2)/13
Let w(q) = -59*q + 1005. Let l be w(17). Factor 2*f**l - 8/7 - 24/7*f.
2*(f - 2)*(7*f + 2)/7
Let p = 1665 - 1665. Factor 4/13*v**3 + 2/13*v**4 - 2/13*v**2 + p - 4/13*v.
2*v*(v - 1)*(v + 1)*(v + 2)/13
Let z = -22 + 22. Factor 53 - 3*c**4 + 3*c**2 + z*c**2 + 6*c - 53 - 6*c**3.
-3*c*(c - 1)*(c + 1)*(c + 2)
Let w(b) = -21*b + 2. Let j(v) = 10*v - 1. Let g(n) = 5*j(n) + 3*w(n). Let i be g(-1). Factor -f - i + 14 - 2*f**2 - f**3.
-f*(f + 1)**2
Let k = -5438 + 5442. Factor 3*c**k + 0*c + 0 - 3/2*c**3 + 0*c**2.
3*c**3*(2*c - 1)/2
Solve 10 - 9*q - 2*q**2 - 23*q + 24*q = 0.
-5, 1
Let f(h) = h**2 + h - 1. Let t(g) = 2*g**2 + 2*g - 1. Let k(s) = -6*f(s) + 2*t(s). Let u(w) = 7*w**2 + 8*w - 15. Let v(d) = 22*k(d) + 6*u(d). Factor v(z).
-2*(z - 1)**2
Suppose 416/5*s + 10609/5*s**3 - 11021/5*s**2 - 4/5 = 0. What is s?
2/103, 1
Let g(a) be the second derivative of a**4/16 + 7*a**3/8 - 27*a**2/4 - 64*a. Let g(q) = 0. Calculate q.
-9, 2
Let r(a) be the first derivative of a**7/1960 - a**6/420 - 7*a**3/3 - 11. Let c(g) be the third derivative of r(g). Factor c(q).
3*q**2*(q - 2)/7
Determine t so that 1/2*t - 1/2*t**3 + 1/4*t**2 - 1/4*t**4 + 0 = 0.
-2, -1, 0, 1
Let c(l) be the second derivative of 0 + 1/30*l**5 + 1/2*l**3 - 1/90*l**6 + 0*l**2 + 0*l**4 + 2*l. Let d(h) be the second derivative of c(h). Factor d(z).
-4*z*(z - 1)
Let x(n) be the first derivative of 4*n**3/9 + 26*n**2/3 + 88*n/3 + 82. Factor x(q).
4*(q + 2)*(q + 11)/3
Factor -4*z**3 - 4*z**3 + 42*z**2 - z**3 + 12*z**3.
3*z**2*(z + 14)
Let z(l) be the first derivative of 15 - 2*l - 4/3*l**3 + 9/2*l**2. Factor z(f).
-(f - 2)*(4*f - 1)
Let s(v) be the second derivative of -9*v**6/5 - 51*v**5/20 + v**4/4 - 159*v. Factor s(f).
-3*f**2*(f + 1)*(18*f - 1)
Let s = -11927 - -11931. Suppose 0 - 1/2*f**2 + 0*f + 3/2*f**3 - f**s = 0. What is f?
0, 1/2, 1
Let k(r) = r**2 + 19*r + 31. Let f(h) = -h + 1. Let w(d) = -2*f(d) - 2*k(d). Factor w(n).
-2*(n + 2)*(n + 16)
Suppose 0 = 4*a - 5*a + 4*f + 15, -a = 2*f - 27. Let o = a - 23. Factor -2/3*s + 1/3*s**2 + o.
s*(s - 2)/3
Solve 0*w - 2/7*w**5 + 0 + 16/7*w**4 - 2*w**3 + 0*w**2 = 0.
0, 1, 7
Suppose h - 2*k + 8 = 0, -5*h - 5 = -2*k - k. Suppose -3*z - 5*b + h*b = 0, 2*b + 15 = 3*z. Find c, given that 3*c**2 + 96*c**3 - c**2 - 4*c - 90*c**z = 0.
-1, 0, 2/3
Suppose 2*q + 8 = -3*l + 4, 5*l = 3*q + 25. Factor 0*c - 4*c**2 + l*c + 0*c + 2*c.
-4*c*(c - 1)
Suppose 0 = 2*i + 6, -4*p + 4*i = -0*p - 116. Let r(q) = -q**2 + 8*q - 3. Let o(f) = -4*f**2 + 33*f - 11. Let u(w) = p*r(w) - 6*o(w). Factor u(j).
-2*(j - 3)*(j - 2)
Let i(h) be the second derivative of h**7/21 - h**6/15 - 39*h**5/40 - 17*h**4/12 - 2*h**3/3 + 324*h. Determine q, given that i(q) = 0.
-2, -1/2, 0, 4
Let v = -51 - -62. Suppose 4*m = v + 1. Let 0 + 2/9*k**m - 4/9*k - 2/9*k**2 = 0. Calculate k.
-1, 0, 2
Let w(v) be the second derivative of -111*v**5/40 - 19*v**4/2 - 41*v**3/4 - 3*v**2/2 - 2*v - 8. Factor w(u).
-3*(u + 1)**2*(37*u + 2)/2
Let g(f) be the first derivative of -2*f**5/5 - 5*f**4/2 - 8*f**3/3 - 36. Factor g(i).
-2*i**2*(i + 1)*(i + 4)
Suppose 16*y + 5252 = 5348. Let y*j**2 + 0 - 2*j**5 - 10*j**3 - 4/3*j + 22/3*j**4 = 0. Calculate j.
0, 2/3, 1
Let i(r) be the first derivative of r**7/840 - r**6/80 + 13*r**5/240 - r**4/8 + r**3/6 - 7*r**2/2 - 13. Let x(o) be the second derivative of i(o). Factor x(a).
(a - 2)**2*(a - 1)**2/4
Let g be 6 - (-1 - (-1175)/168). Let z(x) be the second derivative of -1/24*x**3 + 0*x**5 + 1/60*x**6 + 0 - 1/24*x**4 - 4*x + g*x**7 + 0*x**2. Factor z(l).
l*(l - 1)*(l + 1)**3/4
Let 64/3 + 4/3*k**2 + 40/3*k = 0. What is k?
-8, -2
Suppose -2 = -16*l + 62. Let i be (-21)/(-6) + -2 + 2 + -2. Factor -9/2*r**2 + 3/2*r - i*r**l + 9/2*r**3 + 0.
-3*r*(r - 1)**3/2
Let 12/7*m**4 - 96/7*m**2 + 192/7 + 64/7*m - 32/7*m**3 + 4/7*m**5 = 0. Calculate m.
-3, -2, 2
Find b, given that 5/4 - 2*b**3 + 9/2*b**2 + 1/4*b**4 - 4*b = 0.
1, 5
Suppose 0 = -13*l + 14*l + 4. Let w be l/(-14) + 1112/(-168) + 8. Factor 0 - 20/3*m + w*m**2.
5*m*(m - 4)/3
Factor -19*g - 1125 - 161*g - 5*g**2 + 30*g.
-5*(g + 15)**2
Let l be 8/60 - 4/30. Let j(z) be the first derivative of 1/36*z**6 + 1/18*z**3 - 1 + 0*z**2 - 1/30*z**5 + l*z - 1/24*z**4. Factor j(y).
y**2*(y - 1)**2*(y + 1)/6
Find z such that 2904/13 - 2/13*z**3 - 82/13*z**2 - 704/13*z = 0.
-22, 3
Let -l + l**5 + 14*l**2 - l**3 - 7*l**4 + 3*l**3 - 5 - 2*l**5 - 2 = 0. What is l?
-7, -1, 1
Let h = -19 - -24. Factor -10*c**3 + 0*c**4 - 2*c**h + 4*c**5 + 5*c**4 + 3*c**5.
5*c**3*(c - 1)*(c + 2)
Suppose 1 = -3*z + 4, 0 = -4*d - 2*z + 26. Let s be (d/4)/(-1) + 42/21. Find h, given that s*h**3 + 0 + 0*h**2 - h**4 + 1/2*h**5 + 0*h = 0.
0, 1
Let v(x) be the first derivative of -x**8/2520 + x**6/270 - x**4/36 + 19*x**3/3 - 18. Let m(n) be the third derivative of v(n). Factor m(r).
-2*(r - 1)**2*(r + 1)**2/3
Let m = 42576 - 42576. Factor 0*f**2 - 2/7*f**3 + 2/7*f + m.
-2*f*(f - 1)*(f + 1)/7
Let q(u) = -2*u**2 - 36*u + 2. Let l be q(-18). Let i(t) be the first derivative of 1/2*t**l + 1/3*t**3 - 2*t + 5. Suppose i(p) = 0. What is p?
-2, 1
Let a(u) be the third derivative of -u**6/840 + u**5/140 - u**4/56 + u**3/42 - 26*u**2. Factor a(i).
-(i - 1)**3/7
Determine k so that 64*k**2 + 12 - 2 - 29*k - 25*k**3 + 5*k**4 - 6*k - 56*k**2 + 37*k**2 = 0.
1, 2
Let h(x) be the third derivative of -x**8/1176 - 11*x**7/735 - 19*x**6/210 - 26*x**5/105 - 2*x**4/7 - 36*x**2 - x. Determine v so that h(v) = 0.
-6, -2, -1, 0
Let t(q) be the third derivative of -q**6/30 + 14*q**5/15 + q**4/6 - 28*q**3/3 - 2*q**2 + 11*q. Suppose t(d) = 0. What is d?
-1, 1, 14
Let j(h) be the first derivative of -3*h**5/10 + 9*h**4/2 + h**3/2 - 9*h**2 - 93. Find l such that j(l) = 0.
-1, 0, 1, 12
Let t(x) be the first derivative of -4*x**5/5 + 27*x**4/2 - 166*x**3/3 - 63*x**2 + 98*x - 37. What is o in t(o) = 0?
-1, 1/2, 7
Let r(g) be the first derivative of -1/2*g**3 - 9/4*g**2 + 25 - 3*g. Factor r(m).
-3*(m + 1)*(m + 2)/2
Let q(t) be the second derivative of -t**7/21 + t**6/5 - t**5/5 - t**4/3 + t**3 - t**2 - 5*t + 6. Suppose q(z) = 0. What is z?
-1, 1
Let i(h) = 2*h**2 - 6. Suppose 20 = -3*n - 2*n. Let g(w) = -51 + 56 - 3*w - 2*w**2 + 3*w. Let o(p) = n*g(p) - 3*i(p). Let o(a) = 0. Calculate a.
-1, 1
Let h(p) be the first derivative of -p**6/30 + 16*p**5/25 - 22*p**4/5 + 34*p**3/3 + 5*p**2/2 - 50*p - 56. Factor h(d).
-(d - 5)**3*(d - 2)*(d + 1)/5
Let j(g) be the first derivative of -g**3/5 + 27*g**2/5 - 243*g/5 + 144. Factor j(i).
-3*(i