1
Let y be 25/(-15)*1 + 2. Suppose 0*t - 8 = -4*t - 5*f, t - f - 2 = 0. Solve y*k - 1/3*k**3 + k**t - 1/3*k**4 - 2/3 = 0 for k.
-2, -1, 1
Let g(b) be the first derivative of b**3 - 6*b**2 + 12*b - 6. Solve g(l) = 0.
2
Suppose 2*i - i = 3*f, -3*i = -4*f. Let -1/5*t + f + 1/5*t**2 = 0. Calculate t.
0, 1
Let s = 497 - 497. Factor -n**2 + s + 4/5*n**3 + 1/5*n.
n*(n - 1)*(4*n - 1)/5
Let u(v) be the third derivative of 0*v + 3*v**2 + 0 - 3/160*v**5 - 1/480*v**6 + 1/6*v**3 - 1/16*v**4. Let d(o) be the first derivative of u(o). Factor d(p).
-3*(p + 1)*(p + 2)/4
Suppose -6*u + 4*u + 14 = 3*q, -q = -u + 2. Suppose 4/5*b + q*b**2 + 8/5*b**3 + 2/5*b**4 + 0 = 0. Calculate b.
-2, -1, 0
Let -2*i + 0*i**4 - 3*i**4 + 3*i**2 + 2*i**4 = 0. What is i?
-2, 0, 1
Let m(x) = -x**2 + 5*x + 5. Let f be m(5). Let v = f - 2. Solve 2/3*b + 2/3*b**v + 0 - 4/3*b**2 = 0.
0, 1
Let m(d) be the first derivative of 15*d**2 + 3 - 56/3*d**3 - 4*d. Factor m(p).
-2*(4*p - 1)*(7*p - 2)
Let a(j) be the third derivative of -j**7/420 - j**6/72 - j**5/30 - j**4/24 + j**3/3 - j**2. Let q(k) be the first derivative of a(k). What is i in q(i) = 0?
-1, -1/2
Let m(g) = g**2 - 3*g. Let j(d) = 6*d**2 - 16*d. Suppose -4 - 4 = -2*o. Suppose -o = -i - i. Let v(x) = i*j(x) - 11*m(x). Let v(f) = 0. Calculate f.
-1, 0
Let s(q) = q - 4. Let y be s(4). Suppose y = -4*a + 4 + 20. Solve 2 - 3*r - r + a*r**2 - 2*r**3 - 2*r = 0 for r.
1
Let w = 108 + -320/3. Let j = -9 + 13. Solve 0 + 2/3*f + 0*f**3 - 2/3*f**5 - 4/3*f**2 + w*f**j = 0.
-1, 0, 1
Let y(x) be the first derivative of 1/8*x**4 - 5 - 1/12*x**2 + 1/9*x**3 + 0*x. Determine p so that y(p) = 0.
-1, 0, 1/3
Let y(o) be the second derivative of -5*o**7/63 + o**6/6 - 5*o**4/36 - o. Find p, given that y(p) = 0.
-1/2, 0, 1
Let 27*j**4 + 44*j**3 + 4*j - 47*j**4 - 28*j**2 + 0*j**4 = 0. What is j?
0, 1/5, 1
Find n, given that 5*n**2 + 5/3*n - 10/3 = 0.
-1, 2/3
Suppose 4*g + 7 = 7. Let y(t) be the first derivative of 0*t + 3/4*t**4 - 2*t**3 + g*t**2 - 1. Determine s so that y(s) = 0.
0, 2
Let z(j) be the third derivative of 0*j + 0 + 0*j**3 - 1/16*j**4 - 3/40*j**5 - j**2 - 1/140*j**7 - 3/80*j**6. Let z(f) = 0. What is f?
-1, 0
Let m be (-4)/(-14)*70/110. Factor 0*q**2 + 0 + 0*q + 2/11*q**3 + m*q**4.
2*q**3*(q + 1)/11
Factor 4/3*r**3 - 2*r**2 + 0 + 0*r - 2/9*r**4.
-2*r**2*(r - 3)**2/9
Let l(u) be the third derivative of u**2 + 7/60*u**5 - 1/12*u**4 + 0*u + 0*u**3 + 0. Solve l(r) = 0 for r.
0, 2/7
Let q be ((-12)/(-54))/((-8)/6)*-2. Factor -1/3*y**5 + 0 + 1/3*y**3 + 1/3*y**2 + 0*y - q*y**4.
-y**2*(y - 1)*(y + 1)**2/3
Let f(q) be the second derivative of -q**7/14 - q**6/5 + q**4/2 + q**3/2 + q. Factor f(u).
-3*u*(u - 1)*(u + 1)**3
Let q(y) be the first derivative of 1/7*y**3 + 0*y**2 + 1 + 0*y. Factor q(i).
3*i**2/7
Let u(o) be the third derivative of o**8/168 + o**7/15 + 19*o**6/60 + 5*o**5/6 + 4*o**4/3 + 4*o**3/3 + 2*o**2. Find f, given that u(f) = 0.
-2, -1
Let h be 4/20 + (-44)/(-80). Determine i, given that 0*i - 1/4*i**3 - h*i**2 + 1 = 0.
-2, 1
Suppose 3/4*c**2 + 1/4*c**4 - 3/4*c**3 + 0 - 1/4*c = 0. Calculate c.
0, 1
Let j(i) be the third derivative of i**8/84 - 2*i**7/105 - i**6/30 + i**5/15 - 12*i**2. Find s such that j(s) = 0.
-1, 0, 1
Let m(j) be the second derivative of 1/20*j**6 - 1/4*j**5 - 4*j + 7/24*j**4 - j**2 + 0 + 1/3*j**3. What is l in m(l) = 0?
-2/3, 1, 2
Factor 0 - 4/5*z**2 - 2/5*z**3 + 0*z.
-2*z**2*(z + 2)/5
Let m(b) be the third derivative of -b**8/84 - 16*b**7/21 - 64*b**6/3 - 1024*b**5/3 - 10240*b**4/3 - 65536*b**3/3 + 15*b**2. Suppose m(t) = 0. Calculate t.
-8
Let n(w) be the third derivative of 0 + 0*w**3 + 0*w**6 + 0*w - 3*w**2 - 1/525*w**7 + 0*w**4 + 1/150*w**5. Solve n(v) = 0 for v.
-1, 0, 1
Let b = -327/14 + 47/2. Let h(w) be the first derivative of 1/21*w**6 + 0*w + 1 + 0*w**4 - b*w**2 + 4/35*w**5 - 4/21*w**3. Factor h(d).
2*d*(d - 1)*(d + 1)**3/7
Let w be 203/(-42) + 5 + (-1)/(-2). Factor w*f - 2/3*f**3 - 2/3*f**2 + 2/3.
-2*(f - 1)*(f + 1)**2/3
Factor 0 + 8*h - 3/2*h**3 + 1/4*h**4 + 0*h**2.
h*(h - 4)**2*(h + 2)/4
Let n(a) be the first derivative of -a**4/4 + a**3/3 + a - 1. Let b(k) = 4*k**3 - 6*k**2 - 2*k + 2. Let p(q) = b(q) + 2*n(q). Let p(d) = 0. What is d?
-1, 1, 2
Suppose -5*h - 11 = -4*b + 12, -3 = 3*b + 3*h. Suppose -b*p = -3*l + 6, -5*p = -2*p - 3*l + 3. Factor 6*u**p - u - 6*u**2 - 2*u**4 + 4*u - u.
-2*u*(u - 1)**3
Let l(r) = r**3 + 5*r**2 + 3*r + 4. Let t be l(-4). Find m, given that -2*m - t*m - 3*m**2 + 3*m - 2*m = 0.
-3, 0
Let l = 181/640 - -15/128. Determine v, given that 3/5*v**2 + 1/5*v**3 + l*v + 0 = 0.
-2, -1, 0
Factor 3 - p**2 - 2 + 8*p**2 - 5 - 12*p.
(p - 2)*(7*p + 2)
Let i = -2 - -4. Let s be (-6 + 8)*(-2)/(-12). Factor s*v + 0 - 1/3*v**i.
-v*(v - 1)/3
What is v in -1/2*v**4 - 1/3*v**2 + 4/3*v - 13/6*v**3 + 0 = 0?
-4, -1, 0, 2/3
Let x(d) be the third derivative of -d**7/315 + d**5/30 - d**4/18 + 10*d**2. Let x(y) = 0. Calculate y.
-2, 0, 1
Suppose 4*t + 8*u - 3*u = 32, u - 19 = -5*t. Let d(a) be the first derivative of -t - 1/2*a**2 + 1/4*a**4 + 0*a - 1/10*a**5 + 1/6*a**3. Factor d(x).
-x*(x - 2)*(x - 1)*(x + 1)/2
Let q(t) = 4*t + 4. Let s be q(-1). Let 2/3*l**3 - 2*l**2 + s*l + 0 = 0. What is l?
0, 3
Let u(p) = 3*p**2 - 4*p + 8. Let g(o) = -2*o**2 + 2*o - 4. Let i(n) = 7*g(n) + 4*u(n). Factor i(d).
-2*(d - 1)*(d + 2)
Let w be (-4 + 8 + -4)/(-2 - -4). Let d(a) be the first derivative of 1/3*a**6 + a**2 + w*a**5 - 1 + 0*a**3 - a**4 + 0*a. Factor d(o).
2*o*(o - 1)**2*(o + 1)**2
Let s(y) = -7*y**2 - 3*y + 1. Let t(p) = -6*p**2 - 2*p + 2. Let u(c) = -2*s(c) + 3*t(c). Factor u(m).
-4*(m - 1)*(m + 1)
Let l = 1 + 2. Let 2*v**5 + 0*v**5 + 2*v**l - v**5 - 3*v**3 = 0. Calculate v.
-1, 0, 1
Let p = -1469/5 - -295. What is l in 0*l**2 - 2/5 - 8/5*l**3 + p*l = 0?
-1, 1/2
Let a(i) be the second derivative of -i**7/21 - i**6/15 + i**5/10 + i**4/6 + 6*i. Factor a(m).
-2*m**2*(m - 1)*(m + 1)**2
Suppose 0 = 3*y + 4*o + 29, -y + 4 = -2*o - 3. Let d = y + 7/2. Determine p so that -1/2 + d*p**2 - 3/4*p = 0.
-1/2, 2
Suppose 13 = 2*b - i, -4 = 3*b - i - 21. Let x(v) = -v**2 + 6*v - 6. Let d be x(b). Solve -d*l**5 + 0*l + 0 + 1/2*l**3 - 3/2*l**4 + 0*l**2 = 0.
-1, 0, 1/4
Factor 0*b + 1/3*b**3 - 1/3*b**2 + 0.
b**2*(b - 1)/3
Let h(n) be the third derivative of -1/20*n**5 + 0 + 6*n**2 - n**3 + 0*n - 3/8*n**4. Factor h(i).
-3*(i + 1)*(i + 2)
Let a(p) be the second derivative of p**4/12 + 11*p**3/6 + 13*p**2/2 - 3*p. Let m be a(-10). Factor -7*k**4 + 3*k**4 + 2*k - 4*k**m - 2*k**3.
-2*k*(k + 1)**2*(2*k - 1)
Let g(w) = w**3 + 2*w**2 + w + 2. Let q = 8 + -10. Let h be g(q). Determine i so that -4/3*i**4 + 0 + 2/3*i**5 + 2/3*i**3 + h*i**2 + 0*i = 0.
0, 1
Let k be (-5*(12/(-15) - 0))/2. What is h in -18/13*h + 12/13*h**k - 2/13*h**3 + 0 = 0?
0, 3
Let i(u) = -10*u**4 - 14*u**3 - 4*u**2 - 14*u + 14. Let t(v) = -2*v**4 - 3*v**3 - v**2 - 3*v + 3. Let l(f) = -3*i(f) + 14*t(f). Factor l(h).
2*h**2*(h - 1)*(h + 1)
Let z(t) = t + 2 + 2 - 2. Let q be z(0). Let 4*i**3 - 2*i**3 + 0*i**2 - q*i**2 = 0. What is i?
0, 1
Let y(f) = f**3 + 3*f**2 - f - 1. Let t be y(-3). Suppose 10 = 2*i + t. Solve -2*z**i + z**2 + z**4 + 2*z**4 - 3*z**3 + 5*z**3 = 0 for z.
-1, 0
Let b(n) be the third derivative of -n**5/15 + n**4/3 - 10*n**2. Factor b(r).
-4*r*(r - 2)
Let g(c) be the third derivative of 1/48*c**8 + 0*c + 3/20*c**5 + 0*c**3 - 1/12*c**4 - 3/70*c**7 - 1/24*c**6 + 0 + 3*c**2. Factor g(n).
n*(n - 1)**2*(n + 1)*(7*n - 2)
Let k be (5 + 1)/(8 - 10). Let q be (k - -2 - -4) + -3. Factor q + 2/3*o**4 - 2/3*o**3 + 0*o**2 + 0*o.
2*o**3*(o - 1)/3
Let s(r) be the third derivative of 1/60*r**5 + 0 - 1/6*r**4 + 2*r**2 + 2/3*r**3 + 0*r. Determine f so that s(f) = 0.
2
Let c(f) be the second derivative of 5*f**4/12 - 5*f**3/2 - 45*f**2 - 40*f. Factor c(m).
5*(m - 6)*(m + 3)
Let b be 43/6 - (-5)/(-10) - 5. Factor -4/3 - 4*v - b*v**2.
-(v + 2)*(5*v + 2)/3
Suppose 0 = 5*t - 11 + 1. Factor r**5 + 0*r + r - t*r**3 + 0*r**5.
r*(r - 1)**2*(r + 1)**2
Let s(j) be the third derivative of -j**5/15 + 8*j**3/3 + 9*j**2. Factor s(c).
-4*(c - 2)*(c + 2)
Let t(i) = -i**3 - 4*i**2 - 7*i - 2. Let a(s) = s. Let w(p) = -4*a(p) - 2*t(p). Factor w(c).
2*(c + 1)**2*(c + 2)
Let k(h) be the second derivative of 0*h**2 + 1/6*h**4 + 2*h + 0 - 1/3*h**3. Factor k(x).
2*x*(x - 1)
Let g be 2/(-14)*-1 -