
Let c(z) = -z**2 + 2*z. Let b be c(1). Let g = 2 - b. Suppose -g + 4*r + 1 - 2*r**2 = 0. Calculate r.
0, 2
Let d(i) = -4*i**3 + 2*i**2 - 9. Let t(j) = -j**3 - j**2 + j. Let q(s) = d(s) - 3*t(s). Factor q(g).
-(g - 3)**2*(g + 1)
Find u such that 5*u**4 + 4*u**4 + 2*u**4 - 16*u**4 + 5*u**3 = 0.
0, 1
Factor 6/11*r**5 + 0 - 30/11*r**4 - 42/11*r**2 + 12/11*r + 54/11*r**3.
6*r*(r - 2)*(r - 1)**3/11
Let x(k) be the third derivative of k**5/30 - k**4/4 + 12*k**2. Factor x(r).
2*r*(r - 3)
Factor 1/3*y + y**2 - 1/3*y**4 - 2/3 - 1/3*y**3.
-(y - 1)**2*(y + 1)*(y + 2)/3
Let l(t) be the second derivative of t**5/70 - t**4/42 - t**3/21 + t**2/7 - 18*t. Determine y, given that l(y) = 0.
-1, 1
Let o(k) be the first derivative of -53/6*k**4 - 1 + 28/3*k**3 - 2*k + 2*k**5 - 4*k**2. Let m(p) be the first derivative of o(p). Suppose m(x) = 0. What is x?
1/4, 2/5, 2
Let l = 17 + -15. Determine g, given that -92*g - g**l + 2*g**2 + 94*g + 1 = 0.
-1
Suppose 0 = -5*y - 4*b + 22, 5*y - 6*b = -7*b + 13. Determine p, given that 2/7*p**3 + 2/7*p**y - 2/7*p - 2/7*p**4 + 0 = 0.
-1, 0, 1
Let g(x) be the third derivative of x**6/300 - x**5/50 + 3*x**2. What is c in g(c) = 0?
0, 3
Let j(q) = -18*q**2 + 28*q - 62. Let z(t) = 2*t**2 - 3*t + 7. Let d(h) = -6*j(h) - 52*z(h). Let d(w) = 0. What is w?
1, 2
Let w(k) be the second derivative of k**5/80 - k**3/6 + 3*k. Solve w(m) = 0.
-2, 0, 2
Suppose 5*x = -20, l - 13*x + 10 = -16*x. Let 1/5 - 2/5*i + 1/5*i**l = 0. What is i?
1
Determine j, given that -6 - 3 - j**2 + 0 - 6*j = 0.
-3
Let u be (-3)/(-2) + (-5)/(-10). Factor -2/3*q**4 + 0*q + 0 - 1/3*q**3 - 1/3*q**5 + 0*q**u.
-q**3*(q + 1)**2/3
Let w(c) be the third derivative of c**6/660 - 2*c**5/165 + c**4/33 + c**2. Find j such that w(j) = 0.
0, 2
Let v(t) be the third derivative of 3*t**8/28 + 5*t**7/14 + 13*t**6/40 - t**5/20 - t**4/8 - 16*t**2. Find w such that v(w) = 0.
-1, -1/3, 0, 1/4
Let i = -22 - -27. Let t(j) = -j**2 + 7*j - 10. Let z be t(i). Factor 2/5*x**4 + 2/5*x**3 + z + 0*x + 0*x**2.
2*x**3*(x + 1)/5
Let v = 27 - 23. Suppose 0 = b + v*b. Factor b + 2/3*r**2 + 2/3*r**3 + 0*r.
2*r**2*(r + 1)/3
Let -4/3*o**5 + 0*o + 0*o**2 + 0 + 5/3*o**4 - 1/3*o**3 = 0. What is o?
0, 1/4, 1
Factor 15*t + 6*t**2 - 2*t**2 + 15*t - 14*t + 12.
4*(t + 1)*(t + 3)
Let j be (-12)/8 + 1 + 15/6. Factor -2/7*u + 4/7 - 2/7*u**j.
-2*(u - 1)*(u + 2)/7
Suppose 0 = -10*w + 5*w. Let s be (-6)/7*4/(-6). Factor w*v**2 - 2/7*v**5 + 0 + 0*v**3 + 0*v - s*v**4.
-2*v**4*(v + 2)/7
Suppose -5*b - 5*c = 0, -b + c - 8 = 6*c. Let p = -129/4 + 33. Let -1/4 + p*u**3 + 5/4*u**b + 1/4*u = 0. Calculate u.
-1, 1/3
Let d = -28 - -30. Suppose 0 = d*y + y. Let y + 1/2*h**2 + h = 0. Calculate h.
-2, 0
Let k(n) be the first derivative of n**7/5880 - n**6/2520 - 5*n**3/3 - 5. Let v(p) be the third derivative of k(p). Factor v(q).
q**2*(q - 1)/7
Let m(y) be the third derivative of y**5/105 - y**4/21 - 2*y**3/7 - 6*y**2. Determine i so that m(i) = 0.
-1, 3
Let t = 0 - -4. Suppose 0 = -t*d - 3*u - u + 24, -18 = -d - 4*u. Factor 0*y - 1/2*y**d + 0 - 1/2*y**3.
-y**2*(y + 1)/2
Let v(p) be the second derivative of -1/27*p**3 - 1/90*p**5 - 9*p - 1/27*p**4 + 0*p**2 + 0. Let v(t) = 0. What is t?
-1, 0
Suppose 5*a + 4*s = 17 + 13, -3*s = a - 17. Factor 2*k**a + 4*k**2 - 4*k**2.
2*k**2
Let t(q) = q**3 - 6*q**2 - 8*q + 8. Let k be t(7). Let z be k - (1 + 8/(-12)). Factor -2/3 - z*c**2 + 4/3*c.
-2*(c - 1)**2/3
Let y(i) = i + 2. Let u be y(-2). Suppose 0 = 2*d - b - 3, -5*d - b = -u*d - 11. Suppose -2/7*v + 4/7 - 2/7*v**d = 0. Calculate v.
-2, 1
Let g(k) be the third derivative of k**6/24 - 5*k**4/24 + 7*k**2. Factor g(z).
5*z*(z - 1)*(z + 1)
Solve -1/3*v**2 + 1/3*v + 0 = 0 for v.
0, 1
Let b be (3/((-432)/3))/(3/(-4)). Let l(g) be the third derivative of 0*g + 2*g**2 + b*g**4 + 0*g**3 + 1/90*g**5 + 0. Factor l(t).
2*t*(t + 1)/3
Let m(j) = 2 + 0*j - j - 2 - 3. Let i be m(-3). Solve 2/5*z**3 + 2/5*z**2 - 2/5*z**5 + 0*z - 2/5*z**4 + i = 0.
-1, 0, 1
Let d = 7 - 3. Suppose -d*x = -7*x. Find r such that 1/4*r**5 - 1/4*r**2 - 1/4*r**3 + 1/4*r**4 + 0*r + x = 0.
-1, 0, 1
Suppose -3*z = -15, 0 = 2*y + 3*z + 2*z - 11. Let a be y/105*10/(-3). Find o, given that -2/9*o**4 - a*o**2 + 0*o - 4/9*o**3 + 0 = 0.
-1, 0
Suppose 5*i - 57 = i - 3*m, 0 = i + 5*m + 7. Factor 29 - 3*t**4 + 2*t - i*t**2 + 10*t - 32 + 12*t**3.
-3*(t - 1)**4
Let f = -2 - -2. Suppose 2*x = -f*x + 4. Suppose -2 - 5*v**x + 2*v + 3 + 6*v**2 = 0. Calculate v.
-1
Let g be (2/10)/(15/175). Let u = 3 - g. What is c in 0 + u*c + 2/3*c**2 = 0?
-1, 0
Factor 12 - 5*v**3 - v + 9*v**3 - 19*v + 4*v**2.
4*(v - 1)**2*(v + 3)
Let z(v) be the third derivative of -1/130*v**5 + 0 + 4*v**2 + 0*v - 1/156*v**4 + 0*v**3. Let z(h) = 0. What is h?
-1/3, 0
Solve 0*m - 10/9*m**3 + 0 - 2/9*m**5 + 4/9*m**2 + 8/9*m**4 = 0 for m.
0, 1, 2
Let o(v) = v**2 - 5. Let i be o(3). What is j in 7 + 2*j**2 - i*j - 5 + 0*j = 0?
1
Let g(z) = z**2 + 21*z + 40. Let s be g(-2). What is l in 2/7*l - 4/7 + 2/7*l**s = 0?
-2, 1
Determine g, given that -32/7 + 0*g + 48/7*g**2 - 32/7*g**3 + 6/7*g**4 = 0.
-2/3, 2
Factor -53*f**2 - 4*f + 44*f**2 + f + 3*f**3 + 3*f**4 + 6.
3*(f - 1)**2*(f + 1)*(f + 2)
Let i(u) be the second derivative of -11/6*u**4 - 7/15*u**6 + 4*u + 0*u**2 + 0 + 2/3*u**3 + 8/5*u**5. Determine x so that i(x) = 0.
0, 2/7, 1
Let l(z) = 8*z - 10*z**2 + 7*z**3 + z - 2*z. Let v(b) = 15*b**3 - 21*b**2 + 15*b. Let d(a) = 9*l(a) - 4*v(a). Factor d(g).
3*g*(g - 1)**2
Let x(l) = l**2 - 4. Let p be x(2). What is f in -9*f**3 + 6*f**2 + 3*f**4 + 3*f - 3*f + p*f**2 = 0?
0, 1, 2
Let q = -91/109 - -3921/9919. Let u = -2/13 - q. Solve -u*h**2 + 0 + 0*h + 2/7*h**3 = 0.
0, 1
Let t be -3*(-8)/120 + (-19)/(-5). Let c(w) be the second derivative of 0 + t*w + 1/42*w**4 + 1/7*w**2 + 2/21*w**3. Suppose c(h) = 0. Calculate h.
-1
Let z = -49 + 51. Factor 2/5*v**z + 6/5*v + 4/5.
2*(v + 1)*(v + 2)/5
Let a(q) be the third derivative of q**7/420 + q**6/72 + q**5/30 + q**4/12 - 2*q**2. Let k(d) be the second derivative of a(d). Suppose k(b) = 0. What is b?
-1, -2/3
Let c(w) be the third derivative of w**7/945 + w**6/54 + 2*w**5/15 + w**4/2 + w**3 - w**2. Factor c(a).
2*(a + 1)*(a + 3)**3/9
Let h(g) be the first derivative of -3*g**5/5 - 7*g**4/2 - 5*g**3/3 + 7*g**2 + 8*g + 10. What is o in h(o) = 0?
-4, -1, -2/3, 1
Find b, given that -1/4*b**2 - 1/4 + 1/2*b**3 + 1/8*b**5 + 1/2*b**4 - 5/8*b = 0.
-2, -1, 1
Let z(t) be the third derivative of -t**9/10584 + t**8/5880 - t**3/6 - 2*t**2. Let j(o) be the first derivative of z(o). Factor j(m).
-2*m**4*(m - 1)/7
Factor 2/3*v + 1/3*v**2 + 1/3.
(v + 1)**2/3
Suppose -3*g = -4*q - 0*q - 35, g + 5*q - 18 = 0. Suppose -3*s**2 - g*s**2 + 4 - 3*s + 5*s + 10*s**3 = 0. What is s?
-2/5, 1
Find v such that 6*v**3 - 7*v**2 - 6*v**4 + 16*v**2 - 12*v - 12 + 3*v**4 = 0.
-1, 2
Suppose 156*n = 158*n - 4. Factor 1/5*d**3 + 0 + 1/5*d**n - 2/5*d.
d*(d - 1)*(d + 2)/5
Let q be -3*(5 + 725/(-135)). Solve -4/9 + 10/9*r**3 + 4/9*r**4 - q*r + 0*r**2 = 0 for r.
-2, -1, -1/2, 1
Let l = -664 + 3304/5. Let a = -14/5 - l. Factor 0 - a*u**3 - 2/5*u - 4/5*u**2.
-2*u*(u + 1)**2/5
Let o(h) be the second derivative of 32*h**7/15 + 152*h**6/25 + 161*h**5/25 + 211*h**4/60 + 11*h**3/10 + h**2/5 + h. Find f such that o(f) = 0.
-1, -2/7, -1/4
Let d(n) be the third derivative of n**8/112 - 3*n**6/40 - n**5/10 + 13*n**2. Factor d(t).
3*t**2*(t - 2)*(t + 1)**2
Let b(d) be the first derivative of d**6/660 - d**5/110 + d**4/44 - d**3/33 + 2*d**2 + 1. Let i(z) be the second derivative of b(z). Factor i(c).
2*(c - 1)**3/11
Find r, given that -165*r**2 + 480*r - 1624*r**3 - 81*r**5 + 693*r**4 + 11 + 633*r**2 + 53 = 0.
-2/9, 1, 4
Let f(c) = 9*c**4 + 11*c**3 + 9*c**2 + 7*c + 7. Let m(r) = 5*r**4 + 6*r**3 + 5*r**2 + 4*r + 4. Let y = -13 - -9. Let d(v) = y*f(v) + 7*m(v). Factor d(j).
-j**2*(j + 1)**2
Suppose 4*j - 2*q + 6 - 22 = 0, 0 = 4*j - 3*q - 20. Let u be 4/6 + (-2)/9. Factor 14/9*g + 10/9*g**3 - u - 2/9*g**4 - j*g**2.
-2*(g - 2)*(g - 1)**3/9
Let s be 2 - (2 + -3 + 2). Suppose s = -5*g + 11. Factor -27/5*x**g + 6/5*x**3 - 12/5 + 36/5*x.
3*(x - 2)**2*(2*x - 1)/5
Suppose 0 = -4*c - 13 + 25. Suppose 0 = -14*k + 11*k + c. Factor 1/2*s**4 - 5/2*s - 3/2*s**2 + 1/2*s**3 - k.
(s - 2)*(s + 1)**3/2
Let i(d) be the second derivative of d**6/50 - 3*d**5/100 + 6*d. Factor 