*3
Let t(n) be the first derivative of 3*n**5/5 + 27*n**4/10 + 24*n**3/5 + 21*n**2/5 + 9*n/5 + 4. Let t(z) = 0. What is z?
-1, -3/5
Let o(r) be the second derivative of 49*r**6/240 - 21*r**5/20 + 13*r**4/32 + 17*r**3/12 + 3*r**2/4 + 6*r. What is c in o(c) = 0?
-2/7, 1, 3
Let c(y) be the third derivative of 0*y**3 - 1/24*y**4 + y**2 + 1/120*y**6 + 0*y - 1/60*y**5 + 1/210*y**7 + 0. Factor c(k).
k*(k - 1)*(k + 1)**2
Let k = -2/431 + -1706/3879. Let o = -1/9 - k. Determine n so that o*n**2 + 0 + 1/3*n = 0.
-1, 0
Let g(t) be the first derivative of -t**6 - 2*t**5 + 25*t**4/2 - 10*t**3 - 10*t**2 + 16*t + 15. Let g(l) = 0. Calculate l.
-4, -2/3, 1
Factor 53 - f - 53 + 3*f - f**2.
-f*(f - 2)
Suppose 9 = -3*j + 6*j. Factor 2*r**2 + 4*r + 5*r**3 - 4*r**3 - 3*r**j.
-2*r*(r - 2)*(r + 1)
Let c be -4 + 561/9 + -1. Let p = 58 - c. Solve -4/3 - 2*s - p*s**2 = 0.
-2, -1
Let x(c) = 3*c**4 + c**2 - 2. Let f(h) be the second derivative of 7*h**6/30 + h**4/4 - 5*h**2/2 + h. Let a(q) = -4*f(q) + 10*x(q). Find d, given that a(d) = 0.
-1, 0, 1
Suppose 0 = 2*f - 7*f + 15. Find w, given that -3*w**5 - w**4 + 3*w**5 - 2*w**5 + f*w**5 = 0.
0, 1
Let k(b) be the second derivative of b**7/21 + b**6/5 - 2*b**4/3 + 7*b. Factor k(p).
2*p**2*(p - 1)*(p + 2)**2
Let y = -6 + 8. Let f(p) be the second derivative of 0*p**y + 2*p - 1/54*p**4 + 1/27*p**3 + 0. Factor f(x).
-2*x*(x - 1)/9
Suppose -s + 0 + 3 = 0. Suppose -22 = -4*b - 5*r + 3*r, -3*r = -4*b - s. Let -g**4 + g**2 - g**3 - g**5 + 2*g**b + 0*g**2 = 0. What is g?
-1, 0, 1
Let b(p) be the second derivative of -p - 1/120*p**6 + 1/48*p**4 + 1/168*p**7 - 1/80*p**5 + 0 + 0*p**3 + 0*p**2. Factor b(t).
t**2*(t - 1)**2*(t + 1)/4
Suppose -4*l - 3*u = -l + 12, -12 = -3*l + 3*u. Factor l + 1/4*q**5 + 1/4*q**3 + 0*q + 1/2*q**4 + 0*q**2.
q**3*(q + 1)**2/4
Let f(x) = 4*x**3 + 34*x**2 + 4*x. Let w(z) = z**3 + 7*z**2 + z. Let j(t) = -3*f(t) + 14*w(t). Suppose j(v) = 0. What is v?
0, 1
Let c = -3 - 0. Let v = c - -5. What is r in -2/3 - 1/3*r + 1/3*r**v = 0?
-1, 2
Let 42/23*r - 6/23*r**4 + 196/23 - 318/23*r**2 + 86/23*r**3 = 0. Calculate r.
-2/3, 1, 7
Let h be 9/11 - 2/(-11). Suppose -z + h + 3 = 0. Suppose z*k**4 + 0*k**2 - 2*k**5 + 2*k**3 + 4*k**5 + 0*k**2 = 0. What is k?
-1, 0
Suppose -1 = -3*k + 11. Factor 4*y**4 + 6*y - k*y**3 - 3 + 0 - y**4 - 2*y**3.
3*(y - 1)**3*(y + 1)
Factor -k**2 + 124 - 120 - 7*k + 2*k**2 + 3*k.
(k - 2)**2
Let m(b) be the first derivative of 2/9*b + 2 - 2/9*b**2 + 2/27*b**3. Suppose m(y) = 0. Calculate y.
1
Factor b**2 + 3*b - 2 + 3 + 1 - 6*b.
(b - 2)*(b - 1)
Let o be (-2)/(-7) - (-24)/14. Let -3*b**o - 2*b**2 + 6*b**2 + b = 0. What is b?
-1, 0
Suppose 4*p + h - 24 = 3*h, -4*h = 16. Factor 12*x + 9*x**4 - 2*x**2 + 0 - p*x**2 - 12*x**3 + 0*x**2 - 3.
3*(x - 1)**2*(x + 1)*(3*x - 1)
Let m be (-20)/(-11) + (-6)/(-33). Factor -20 + 4*f**2 - 19*f**2 + 51*f + m.
-3*(f - 3)*(5*f - 2)
Suppose z = 4*j - 15, 2*z + 0*j + 2 = j. Let p be (z - 1) + (4 - 2). Determine a so that -5*a**p + a**2 - a**3 + 3*a**3 + 0*a**2 + 2*a = 0.
0, 1
Let t(w) = w**2 - 4*w - 3. Let f be t(5). Let b(c) be the first derivative of f - 3/8*c**2 + 1/2*c + 1/12*c**3. Find h, given that b(h) = 0.
1, 2
Let v(j) be the second derivative of -1/21*j**3 + 0 + 1/70*j**5 + 1/7*j**2 - 2*j - 1/42*j**4. Factor v(k).
2*(k - 1)**2*(k + 1)/7
Let k = -3 - -5. Let o = k + 0. Solve -3*a + 0*a + a**o + a**3 - 1 + 2*a = 0 for a.
-1, 1
Let w be (4 - (-52)/(-10))*-1. Solve -2/5*u**2 + 0*u + 6/5*u**3 - w*u**4 + 2/5*u**5 + 0 = 0.
0, 1
Let x(g) be the first derivative of g**4/24 - g**3/12 - g + 1. Let f(t) be the first derivative of x(t). Find i, given that f(i) = 0.
0, 1
Let m(x) = -23*x**2 + 34*x - 12. Let b(p) = -2*p - 6. Let q be b(-6). Let o(h) = 11*h**2 - 17*h + 6. Let l(k) = q*m(k) + 13*o(k). What is f in l(f) = 0?
2/5, 3
Let q be (-100)/15*(-3)/4. Let a(t) be the second derivative of 1/24*t**4 + 0*t**2 - 1/40*t**q + 1/12*t**3 + 0 + t - 1/60*t**6. Solve a(l) = 0.
-1, 0, 1
Let h = 22 - 6. Suppose -18*l**2 + 3 + h*l**2 - 3 - 4*l = 0. What is l?
-2, 0
Find k such that -9/8*k**3 - 6 + 69/8*k**2 - 15*k = 0.
-1/3, 4
Let n(x) be the third derivative of -x**6/480 - x**5/120 - x**4/96 + x**2. Factor n(t).
-t*(t + 1)**2/4
Suppose 3 = -r - 9. Let u be r/30 - 48/(-70). Factor -u*j + 0 + 2/7*j**2.
2*j*(j - 1)/7
Find b, given that -1/3*b**3 + 1/3*b - 1/6*b**4 + 0 + 1/6*b**2 = 0.
-2, -1, 0, 1
Suppose 130*v - 126*v - 8 = 0. Let 0 + g + 1/2*g**v = 0. Calculate g.
-2, 0
Let f be 6*4/(-16)*-2. Solve l**2 - 3*l + 0 + 1 + 2*l + f*l = 0.
-1
Let t(r) = -9*r**3 - 9*r**2 + 26*r + 26. Let f(m) = -3*m**3 - 3*m**2 + 9*m + 9. Let q(i) = 17*f(i) - 6*t(i). Factor q(h).
3*(h - 1)*(h + 1)**2
Let o(i) = -84*i**2 - 90*i - 20. Let z(u) be the first derivative of -17*u**3/3 - 9*u**2 - 4*u - 1. Let y(f) = -3*o(f) + 14*z(f). Factor y(j).
2*(j + 1)*(7*j + 2)
Let l(d) be the third derivative of 1/168*d**6 + 1/56*d**4 - 3/140*d**5 + 1/42*d**3 + 0 + 0*d - 3*d**2. What is u in l(u) = 0?
-1/5, 1
Solve 2/9*w**2 + 0*w - 2/9*w**3 + 0 = 0.
0, 1
Let w(q) be the second derivative of -q**3 - 1/4*q**4 - 4*q + 0 - 2*q**2 - 1/40*q**5. Factor w(x).
-(x + 2)**3/2
Let q(a) = -a**2 + 4*a + 3. Suppose 0 = -2*k - 3*k + 20. Let g be q(k). Suppose -3/5*h**2 - 1/5*h**g - 1/5 - 3/5*h = 0. What is h?
-1
Let q = -161 + 161. Let l(p) be the third derivative of 1/12*p**4 + 0*p**3 - 3*p**2 + 1/60*p**5 + q*p - 1/120*p**6 + 0. Factor l(a).
-a*(a - 2)*(a + 1)
Let a = -25 + 79/3. Factor 4/3*t**3 + 0*t**2 - a*t - 2/3 + 2/3*t**4.
2*(t - 1)*(t + 1)**3/3
Let x(g) = -17*g**3 - 42*g**2 - 77*g - 30. Let f(q) = 6*q**3 + 14*q**2 + 26*q + 10. Let l(s) = -11*f(s) - 4*x(s). Suppose l(n) = 0. Calculate n.
-5, -1
Let l(f) = -2*f - 6. Let k(q) = -q**2 - 5*q - 4. Let j be k(-5). Let z be l(j). Factor -2 + u - 2*u**2 + 3*u**z + 0*u**2.
(u - 1)*(u + 2)
Factor 4/7*d + 2/7*d**2 + 0.
2*d*(d + 2)/7
Let d(r) be the second derivative of -r**7/3780 + r**6/540 - r**5/180 - r**4/12 - 3*r. Let t(i) be the third derivative of d(i). Factor t(k).
-2*(k - 1)**2/3
Let o(p) be the third derivative of p**5/330 - p**3/33 + 19*p**2. Factor o(f).
2*(f - 1)*(f + 1)/11
Let x = 5/6 - 1/2. Factor -1/3 - x*d**2 + 2/3*d.
-(d - 1)**2/3
Let i(v) be the second derivative of 4*v + 0*v**2 + 0 - 1/6*v**3 - 5/24*v**4. Find c, given that i(c) = 0.
-2/5, 0
Let b(n) be the third derivative of n**7/245 - n**6/420 - n**5/105 + 3*n**2. Let b(s) = 0. Calculate s.
-2/3, 0, 1
Let v(m) = -4*m**5 + 3*m**4 + 3*m**2 - 3*m - 3. Let n(q) = q**5 - q**4 - q**2 + q + 1. Let z(y) = -6*n(y) - 2*v(y). Suppose z(x) = 0. What is x?
0
Let s(m) = -m**5 + m**4 + 11*m**2 - 11*m - 11. Let x(g) = -2*g**2 + 2*g + 2. Let t(j) = 2*s(j) + 11*x(j). Suppose t(v) = 0. Calculate v.
0, 1
Let v(p) be the second derivative of 1/4*p**4 + 0 + 3*p**2 + 3/2*p**3 + 10*p. Find r, given that v(r) = 0.
-2, -1
Factor -2/5*q**5 + 2/5*q**3 + 0 + 0*q + 0*q**2 + 0*q**4.
-2*q**3*(q - 1)*(q + 1)/5
Factor -1/3*c**4 + 1/6*c + 1/3*c**2 - 1/6*c**3 + 0.
-c*(c - 1)*(c + 1)*(2*c + 1)/6
Let i(g) = -4*g - 1. Let r(p) = -p. Let t(z) = 2*i(z) - 7*r(z). Let k be t(-4). Factor -4 + 3 + 0 + 5*o**k + 4*o.
(o + 1)*(5*o - 1)
Let -27*r**5 - 8*r + 4 + 99*r**4 + 90*r**2 + 6 - 7 - 19*r - 138*r**3 = 0. Calculate r.
1/3, 1
Let y = -24 - -25. Let n = y + -1. Let -1/6*j**3 + 0*j - 1/6*j**2 + n + 1/6*j**5 + 1/6*j**4 = 0. Calculate j.
-1, 0, 1
Let w(u) be the first derivative of 0*u - 4*u**3 + 6*u**2 + 1 - 15/4*u**4 + 9/5*u**5. Factor w(m).
3*m*(m - 2)*(m + 1)*(3*m - 2)
Let i be 12/81*9/6. Suppose -2/9*n**4 + 2/9*n**3 + 0 - 2/9*n + i*n**2 = 0. What is n?
-1, 0, 1
Let k be 5/((-10)/(-4)) - 44. Let u be k/(-9) - 16/4. What is m in 2/3*m**2 - u*m + 0 = 0?
0, 1
Let q(v) = v**2 - 2*v. Let n be q(4). Suppose 2*d - 5*z - 6 = -2*z, -3*d - 4*z = n. Find o, given that 2/5*o**3 + 2/5*o**2 + d + 0*o = 0.
-1, 0
Let x(f) be the third derivative of -f**9/68040 + f**8/30240 - f**4/8 - 4*f**2. Let s(q) be the second derivative of x(q). Factor s(r).
-2*r**3*(r - 1)/9
Suppose -1 = -8*i + 7*i. Let d be ((-68)/52 + i)/(-2). Find u, given that d*u**2 + 0 - 2/13*u**3 + 0*u = 0.
0, 1
Let t(s) be the second derivative of s**7/231 - s**5/55 + s**3/33 + 3*s. What is l in t(l) = 0?
-1, 0, 1
Let l(c) = -2*c. Let a(v) = -v**4 + v**2 + v. Let m = 21 - 13. Let b(q) = -q + 10. Let s be b(m). Let n(g) 