Determine y so that 4*y - 4*y**2 + 3*y + 10*y - 5*y = 0.
0, 3
Let u(t) = -t + 11. Let o be u(9). Let 9*g**2 - g**3 - 19*g**o + 11*g**2 = 0. Calculate g.
0, 1
Determine t so that -t**2 + 2*t**2 - 5*t + 3*t + t**2 = 0.
0, 1
Let a = 33 - 31. Suppose -i + 18 = -d + 5*d, -4*i = -5*d + 12. Suppose -8 + r**i - 5*r**2 - 2*r**a + 4*r**2 - 8*r = 0. What is r?
-2
Let h(x) be the first derivative of 9*x + 3*x**2 + 1/3*x**3 - 2. Let h(r) = 0. Calculate r.
-3
Determine l so that -1/3*l + 0 + 1/6*l**3 - 1/6*l**2 = 0.
-1, 0, 2
Let a(m) = -m**3 + 3*m**2 + 3. Let i be a(3). Suppose -i*n = n. Find h such that n*h**4 + 2/3*h**5 + 0 + 2/3*h - 4/3*h**3 + 0*h**2 = 0.
-1, 0, 1
Let b(d) be the third derivative of d**7/700 + d**6/225 + d**5/300 - d**3/2 + 3*d**2. Let p(v) be the first derivative of b(v). Determine h so that p(h) = 0.
-1, -1/3, 0
Let 1/12*l**3 - 1/12 - 1/12*l + 1/12*l**2 = 0. Calculate l.
-1, 1
Let g(r) be the second derivative of r**5/20 - r**4/6 - r**3/3 - r. Let a be g(3). Suppose -2*d**4 - 5 + 1 - 2*d**2 + 4 + 4*d**a = 0. What is d?
0, 1
Let y = 2/77 + 67/385. Let v(d) be the first derivative of -y*d**2 + 1 - 1/5*d**5 + 1/10*d**4 + 1/3*d**3 + 0*d. Factor v(g).
-g*(g - 1)*(g + 1)*(5*g - 2)/5
Suppose -m = -4*p - 5*m, 0 = -3*p + 4*m. Find z such that p*z - 14*z**2 + 2*z**3 + 9*z**3 + 4*z - z**3 = 0.
0, 2/5, 1
Let f(z) = -6*z**2 + 4. Let r(w) = 1 - 6*w**2 - 4*w**2 + 13*w**2 - 4*w**2. Let g be 2 + -6*(0 - -1). Let u(d) = g*r(d) + f(d). Factor u(m).
-2*m**2
Let f = 0 + 5. Suppose 3*m - c - 2*c = -6, 0 = 3*m - f*c + 14. Find o such that -8 - 2 + 8*o - m*o**2 + 2 = 0.
2
Let s(x) be the second derivative of -x**5/40 + 7*x**4/24 - 5*x**3/6 - 6*x. Let s(l) = 0. What is l?
0, 2, 5
Let w be (-20)/15*9/(-6). Factor -2/7 + 4/7*a + 6/7*a**w.
2*(a + 1)*(3*a - 1)/7
Let y(u) be the first derivative of 6 - 9/16*u**4 - 3/20*u**5 + 0*u**3 + 3/2*u**2 + 0*u. Factor y(h).
-3*h*(h - 1)*(h + 2)**2/4
Suppose -2*p = 3*y - 10, 2*p + 4 = 3*y + y. Let h = -25 + 27. Factor -h - 6*o**3 - p*o**4 + 6*o**3 + 4*o**2.
-2*(o - 1)**2*(o + 1)**2
Let i = -8 - -10. Determine y, given that -3*y**i + 2*y**2 + 5*y**2 - 5*y**2 + y = 0.
0, 1
Let t(f) be the third derivative of -1/112*f**8 - 1/2*f**3 + 1/20*f**6 - 7*f**2 + 1/10*f**5 - 1/8*f**4 - 1/70*f**7 + 0*f + 0. Let t(l) = 0. What is l?
-1, 1
Let m = 82 + 2. Let j be m/20 + 1/(-5). Determine g, given that 0*g**2 + 0 + 0*g**j - 3/5*g**5 + 3/5*g**3 + 0*g = 0.
-1, 0, 1
Let i = -1 + 4. Let w be 4*(-1 + i)/2. Solve w*v**4 - 2*v**2 - 3*v**3 - v**2 + 2*v**2 = 0 for v.
-1/4, 0, 1
Let 32*n + 17*n + 3*n**4 + 24 + 17*n + 24*n**3 + 63*n**2 = 0. Calculate n.
-4, -2, -1
Let x(z) be the third derivative of z**7/1260 - z**6/360 - z**5/360 + z**4/72 - 18*z**2. Factor x(f).
f*(f - 2)*(f - 1)*(f + 1)/6
Let j be 7/((-35)/10)*-1. Factor -1/3*n**j - n - 2/3.
-(n + 1)*(n + 2)/3
Let a be 9/6*(-14)/12. Let b = a + 85/44. Suppose 0*m**2 + 6/11*m - b*m**3 + 4/11 = 0. Calculate m.
-1, 2
Suppose 4*n + b + 61 = 0, 2*n + b + 15 = -14. Let z be n/28 - 115/(-140). Factor z*s + 1/4*s**4 + 0 + 3/4*s**3 + 3/4*s**2.
s*(s + 1)**3/4
Let i(x) = 4*x - 24. Let v be i(7). Suppose -5*l + v*l + 9*l**2 + 2 - 10*l = 0. Calculate l.
2/9, 1
Let w be 3*((3 - 1) + -1). Let z = -13 - -15. Find i such that 0*i**z + 1 + i**2 - w*i**2 + i**4 = 0.
-1, 1
Factor 3 + a**2 - 2*a - 11*a**2 + 1 + 6*a**2 + 2*a**3.
2*(a - 2)*(a - 1)*(a + 1)
Let x(h) be the second derivative of -2*h**7/15 - h**6/3 - 13*h**5/50 - h**4/15 + 3*h. What is c in x(c) = 0?
-1, -1/2, -2/7, 0
Let a(c) be the first derivative of 2*c**6/3 - 8*c**5/5 - 2*c**4 + 16*c**3/3 + 2*c**2 - 8*c + 7. Suppose a(g) = 0. What is g?
-1, 1, 2
Let j = 110/9 + -157/18. Factor 0 - 5/2*m**2 - m + j*m**3.
m*(m - 1)*(7*m + 2)/2
Let r(j) = 4*j - 9. Let c be r(4). Suppose -c*o - 7*o + 18*o + 8 - 28*o**4 - 60*o**2 + 76*o**3 = 0. What is o?
-2/7, 1
Let y(o) be the third derivative of 7*o**5/60 + o**4/8 + 5*o**2. Let j(x) = 6*x**2 + 2*x. Let p(k) = 5*j(k) - 4*y(k). Factor p(c).
2*c*(c - 1)
Suppose -40*i**2 - i + 0*i - 14*i = 0. What is i?
-3/8, 0
Let l(o) be the second derivative of -5/39*o**3 + 2/39*o**4 + 5*o - 1/130*o**5 + 2/13*o**2 + 0. Factor l(w).
-2*(w - 2)*(w - 1)**2/13
Let d = -10 - -6. Let x = d - -6. Solve x*c**3 - 2*c + 3*c + 3*c**3 - 6*c**3 = 0.
-1, 0, 1
Let 9*o**4 - 24*o**2 + 4*o**3 + 0*o**4 + 0*o**5 + 16*o - 2*o**5 - 3*o**4 = 0. What is o?
-2, 0, 1, 2
Let v(u) be the first derivative of u**6/33 + 2*u**5/55 - u**4/11 - 11. Solve v(x) = 0 for x.
-2, 0, 1
Let n be (2 + -3)*1 - 0. Let o be (24/9 + -3)*n. Factor -1/3*z**4 + o + 0*z**2 - 2/3*z**3 + 2/3*z.
-(z - 1)*(z + 1)**3/3
Let d(y) be the second derivative of y**5/210 + y**4/84 + 3*y**2/2 + 3*y. Let u(i) be the first derivative of d(i). Determine p so that u(p) = 0.
-1, 0
Suppose -1/3*d**2 + 4/3 - 1/3*d**3 + 4/3*d = 0. What is d?
-2, -1, 2
Suppose 4*d + 9*b = 4*b + 7, 0 = 5*d - b - 16. Suppose -d*c + 8 = c. Determine o, given that 16/3*o + 4*o**3 - 2/3*o**4 - 8*o**c + 0 = 0.
0, 2
Let t(d) be the second derivative of -3*d + 0 - 1/45*d**5 + 1/18*d**4 + 0*d**3 + 1/360*d**6 + d**2. Let v(b) be the first derivative of t(b). Factor v(x).
x*(x - 2)**2/3
Suppose -10 = f - 5*n, -f - 2*n = -n - 8. Let g be 14*((-4)/f + 1). Determine k, given that -18/5*k + 4/5 + g*k**2 = 0.
2/7, 1
Let h(f) = -f**2 + 6*f - 5. Let q be h(4). Let 4 - s**5 + 11*s**5 + 24*s**4 - 28*s**2 - 6*s - q*s**5 - 8*s**3 + 7*s**5 = 0. What is s?
-1, 2/7, 1
Let f(i) be the third derivative of i**6/1080 + i**5/90 + i**4/18 + i**3/2 + i**2. Let j(o) be the first derivative of f(o). Factor j(l).
(l + 2)**2/3
Determine g so that 45*g**4 - 33*g**4 + 3*g**5 - 18*g**3 - 50*g**2 + 15*g + 38*g**2 = 0.
-5, -1, 0, 1
Suppose -47 + 59 = 6*q. Factor 2/7*h**q - 2/7*h**3 + 2/7*h + 0 - 2/7*h**4.
-2*h*(h - 1)*(h + 1)**2/7
Let l(z) = -5*z**3 + 35*z**2 + 13*z - 27. Let h(t) = -2*t**3 + 18*t**2 + 6*t - 14. Let r(m) = -11*h(m) + 6*l(m). Factor r(q).
-4*(q - 2)*(q + 1)*(2*q - 1)
Suppose -13 + 3 = -2*v. Suppose 0*r = -v*r + 10. Let -4*p**r + 2*p + 3*p**3 + 0*p**2 - p**3 = 0. Calculate p.
0, 1
Let t(y) be the first derivative of y**6/720 + y**5/60 + y**4/12 - y**3 + 4. Let d(c) be the third derivative of t(c). Factor d(n).
(n + 2)**2/2
Let y(h) = h + 1. Let n be y(11). Suppose 4*q - 2*p + 8 = 0, 0 = 7*q - 3*q - 3*p + n. Let -2/7*c + 0*c**2 + q + 2/7*c**3 = 0. What is c?
-1, 0, 1
What is q in 1/4 + 1/4*q - 1/4*q**3 - 1/4*q**2 = 0?
-1, 1
Let i = -6 + 12. Factor 2*s + 6*s**3 - i*s**2 + 2*s**3 - 4*s**2.
2*s*(s - 1)*(4*s - 1)
Let g(v) = 0*v**2 + 7*v**3 - 9*v**3 - v**2 + 3*v**3 - 1. Let y(s) = -29*s**3 - 25*s**2 + 3*s + 5. Let r(k) = -2*g(k) - y(k). Suppose r(a) = 0. What is a?
-1, -1/3, 1/3
Let o be (1 + 1)*(-2 + -4). Let c be -2 - o/(4 + -2). Find s, given that 1/3*s**c + s**2 + 0 - s**3 - 1/3*s = 0.
0, 1
Suppose -q = -5*o + 37, 0 = -3*o + 4*o + 3*q - 17. Let p = 11 - o. Factor -1/4*i**p - 2*i - 1 - 5/4*i**2.
-(i + 1)*(i + 2)**2/4
Let l = 4896610/87 - 56282. Let j = l - 6/29. Determine g so that -1/3 - j*g + 0*g**2 + 2/3*g**3 + 1/3*g**4 = 0.
-1, 1
Let a(l) be the second derivative of l**6/180 + l**5/30 + 5*l**4/72 + l**3/18 + 40*l. Factor a(c).
c*(c + 1)**2*(c + 2)/6
Let f(w) = -3*w**3 + 5*w**2 - 2*w + 4. Let s(u) = -2*u**3 + 5*u**2 - 3*u + 3. Let g(d) = -3*f(d) + 4*s(d). Factor g(r).
r*(r - 1)*(r + 6)
Let g = -113/5562 + 4/103. Let n(u) be the second derivative of 0*u**3 - 2*u - g*u**4 + 0*u**5 + 0*u**2 + 0 + 1/135*u**6. Find q such that n(q) = 0.
-1, 0, 1
Suppose -6*u + 15 + 3 = 0. Let b(f) be the second derivative of 0*f**2 + 1/90*f**6 + 0 + f + 1/12*f**4 + 1/18*f**u + 1/20*f**5. Factor b(s).
s*(s + 1)**3/3
Suppose -7 = d + 2*p, 3*d - 10 - 9 = 4*p. Suppose 0 = -4*k + 3*i - d, -k + 16 = 5*i - 1. Factor 0*h**3 + 5*h**3 - 3*h**3 - k*h**2.
2*h**2*(h - 1)
Let c(o) be the second derivative of -o**5/20 - 5*o**4/12 - o**3/2 + 9*o**2/2 + 3*o. Factor c(a).
-(a - 1)*(a + 3)**2
Let a(v) be the third derivative of v**8/13440 - v**6/1440 - v**4/4 - 5*v**2. Let z(g) be the second derivative of a(g). Factor z(s).
s*(s - 1)*(s + 1)/2
Let d(y) = y**4 + 10*y**3 + 5*y**2. Let j(m) = 15*m**4 + 140*m**3 + 70*m**2. Let q(k) = -55*d(k) + 4*j(k). Factor q(v).
5*v**2*(v + 1)**2
Let b be ((-90)/10 + 8)/(-2). Find j, given that -b - 1/2*j**4 + j**2 + 0*j**3 + 0*j = 0.
-1, 1
Let j(a) be the 