k**3.
3*(k - 1)*(k + 1)*(k + 2)**2/4
Let n(k) be the second derivative of -k**4/18 - 2*k**3/3 - 3*k**2 + 4*k. Factor n(z).
-2*(z + 3)**2/3
Let n = -22 - -22. Suppose 0 = -3*a + 15, 3*o - 3*a + 0 + 9 = n. Find f, given that 2/3*f + 1/3 + 1/3*f**o = 0.
-1
What is x in -1/2*x**4 + 1/6*x**3 + 10/3*x**2 + 0 + 2*x = 0?
-2, -2/3, 0, 3
Let a(r) = -r**2 - 6*r - 1. Let c be a(-3). Let g be (5/(-4))/((-2)/c). What is j in -2/5*j + 8/5*j**3 + 8/5*j**4 + 4/5 - 6/5*j**g - 12/5*j**2 = 0?
-1, -2/3, 1
Let t(p) = -p**3 + 12*p**2 + 15*p - 10. Let u be t(13). Let m = 16 - u. Factor 0*w**2 + m + 2/7*w**3 - 2/7*w.
2*w*(w - 1)*(w + 1)/7
Let p(y) be the second derivative of -y**4/60 + y**3/15 - y**2/10 - 8*y. Factor p(g).
-(g - 1)**2/5
Suppose 0*y - 4 = -4*z - y, 0 = 5*z + 2*y - 8. Factor 2/9*d**5 - 2/9*d**3 + z*d - 2/9*d**2 + 2/9*d**4 + 0.
2*d**2*(d - 1)*(d + 1)**2/9
Let a(p) = p. Let o be a(2). Suppose 3*z - 16 = 4*n, 4 = 4*z + 4*n - 8. Factor 1 - 5*r**2 - o*r**3 + 4*r**z + 5*r**3 - 4*r + r.
(r - 1)*(r + 1)**2*(4*r - 1)
Let k be 0 - ((-12)/5 - (-18)/45). Solve -4/15 + 2/5*i - 2/15*i**k = 0 for i.
1, 2
Suppose 1 = -2*t + 1. Factor t - 10*n**4 - 48/5*n**2 + 8/5*n + 18*n**3.
-2*n*(n - 1)*(5*n - 2)**2/5
Let f(k) be the first derivative of -k**4/4 - 2*k**3/3 + 8. Factor f(m).
-m**2*(m + 2)
Let i(t) be the first derivative of -2*t**6 - 51*t**5/5 + 17*t**3 + 6*t**2 - 12. Find h, given that i(h) = 0.
-4, -1, -1/4, 0, 1
Let h(i) be the second derivative of -i**8/13440 - i**7/5040 + i**4/4 + 3*i. Let g(q) be the third derivative of h(q). Factor g(f).
-f**2*(f + 1)/2
Let o(p) be the second derivative of -25*p**6/9 - 55*p**5/6 - 35*p**4/3 - 68*p**3/9 - 8*p**2/3 + 35*p. Factor o(r).
-2*(r + 1)*(5*r + 2)**3/3
Let p(b) be the first derivative of -3*b - 1/4*b**2 + 1/8*b**3 - 3/80*b**5 - 2 + 1/24*b**4. Let k(s) be the first derivative of p(s). Let k(v) = 0. Calculate v.
-1, 2/3, 1
Suppose 2*b - 6 = 4. Suppose -4*f + b*r = 2, 4*r = f + 10 - 4. Let 1 + 19/2*v + 57*v**3 + 34*v**f + 45*v**4 + 27/2*v**5 = 0. Calculate v.
-1, -2/3, -1/3
Let c(z) be the second derivative of z**7/7 - 2*z**6/3 + z**5 - 5*z**3/3 + 2*z**2 + 3*z. Factor c(i).
2*(i - 1)**4*(3*i + 2)
Let i(c) = -c**3 + c**2 - 3*c - 3. Let y(g) be the first derivative of -g**4/2 + g**3/3 - 2*g**2 - 4*g + 3. Let r(w) = 3*i(w) - 2*y(w). Factor r(d).
(d - 1)*(d + 1)**2
Let f(j) be the second derivative of -2*j - 1/2*j**2 - 1/150*j**5 - 1/15*j**3 + 1/30*j**4 + 0. Let g(p) be the first derivative of f(p). Factor g(c).
-2*(c - 1)**2/5
Let c = -1441/5 + 6679/20. Let m = 46 - c. Determine q so that -1/4 - m*q**2 - 1/2*q = 0.
-1
Determine f so that 0*f + 3/5*f**5 - 1/5*f**2 + 0 - 3/5*f**3 + 1/5*f**4 = 0.
-1, -1/3, 0, 1
Let m = 8 - 4. Suppose m*g - 10 = -2. Let 0*i - 1/4*i**g + 0 = 0. What is i?
0
Let g = 84 - 81. Let o(m) be the third derivative of 1/100*m**6 - 3/40*m**4 + 3/350*m**7 + 0*m - g*m**2 - 1/50*m**5 - 1/10*m**3 + 1/560*m**8 + 0. Factor o(l).
3*(l - 1)*(l + 1)**4/5
Let j(n) be the third derivative of n**5/30 + n**4/3 + 4*n**3/3 - 34*n**2. Factor j(m).
2*(m + 2)**2
Let o(w) = -w**2 + 5*w - 6. Let p be o(2). Factor -4/9*f**3 + p - 2/9*f**4 - 2/9*f**2 + 0*f.
-2*f**2*(f + 1)**2/9
Let k(j) be the second derivative of j**4/4 + j**3 + 3*j**2/2 + 26*j. Factor k(t).
3*(t + 1)**2
Solve 5 - 16*v + 10*v - 3*v**2 - 5 - 3 = 0 for v.
-1
Let r(y) be the third derivative of -y**6/30 - y**5/15 + 2*y**4/3 + 8*y**3/3 + 12*y**2. Solve r(j) = 0.
-2, -1, 2
Suppose -2*r - 2*i - 12 = -0*i, -r + 4*i + 19 = 0. Let k be 39/27 - 3/r. Factor 2*t**5 + 8/9*t - k*t**2 - 20/3*t**4 + 74/9*t**3 + 0.
2*t*(t - 1)**2*(3*t - 2)**2/9
Let i(d) be the third derivative of -d**8/672 - d**7/140 - d**6/80 - d**5/120 - 5*d**2. Find l, given that i(l) = 0.
-1, 0
Let j(q) = -q**2 - 5*q - 1. Let n be j(-2). Suppose 15 = -0*r + n*r. Factor t + r - 2 - t**2 - t**3 + 0*t**2.
-(t - 1)*(t + 1)**2
Let v(l) be the second derivative of 2/5*l**5 - 2*l + 0 + 4/3*l**3 + 1/15*l**6 + l**2 + l**4. Factor v(r).
2*(r + 1)**4
Solve -4/5 - 2/5*b**4 + 2/5*b**3 - 2/5*b + 6/5*b**2 = 0.
-1, 1, 2
Let c be 0/((16/(-4))/(-1)). Let w(f) be the second derivative of 1/30*f**5 + 1/9*f**3 + 0*f**2 - 1/9*f**4 - f + c. Factor w(y).
2*y*(y - 1)**2/3
Let a(t) = -t - 1. Let d be a(-4). Suppose -5*o = -d*o - 4. Factor r**3 + o*r**3 - 2*r**4 - r**3.
-2*r**3*(r - 1)
Let x = 7 - 1. Suppose x = o - 0*o. Factor 2 - o*d**3 - 4*d**2 + 18*d**2 - 9*d - d.
-2*(d - 1)**2*(3*d - 1)
Suppose 2*f + 15 = u, 5*f = 3*f - 5*u - 45. Let a be (-2)/(-3)*(-45)/f. Factor 56/9*j + 100/9*j**a + 8/9 + 130/9*j**2.
2*(2*j + 1)*(5*j + 2)**2/9
Factor -3/2*w + 1/2 + 3/2*w**2 - 1/2*w**3.
-(w - 1)**3/2
Suppose -21*n + 6 = -18*n. Find j, given that 4/3*j - 2 - 2/9*j**n = 0.
3
Let r = -543/5 + 109. Solve r*y - 2/5*y**2 + 0 = 0.
0, 1
Let c(j) be the first derivative of -j + 4 + 4*j**2 + 1/6*j**4 + 4/3*j**3. Let u(f) be the first derivative of c(f). Find n such that u(n) = 0.
-2
Let z(u) be the second derivative of u**5/60 - u**4/12 + u**3/6 - u**2/2 - 3*u. Let n(m) be the first derivative of z(m). Find s such that n(s) = 0.
1
Suppose 15*g + 26*g**2 - 22*g**3 + 2*g**4 + 8 + 34*g**3 + 9*g = 0. Calculate g.
-2, -1
Let a(d) be the first derivative of 3*d**6/20 - 3*d**5/10 + d**4/8 + 2*d - 6. Let r(l) be the first derivative of a(l). Suppose r(z) = 0. Calculate z.
0, 1/3, 1
Suppose k - 1 = 6. Let z = k - 4. Determine x, given that 0 + 0*x + 2/5*x**z + 2/5*x**2 = 0.
-1, 0
Let k be 3 + -10 - (-1 + 1). Let q(s) = -s + 5. Let b be q(k). Factor b - 12 - 2*d**2 + 2*d.
-2*d*(d - 1)
Factor 0*i - 1/9*i**3 + 2/3*i**2 + 0.
-i**2*(i - 6)/9
Let y = 77 - 74. Factor 0 - 1/2*j**2 + 0*j + 1/2*j**y.
j**2*(j - 1)/2
Let n = 214 - 214. Let 0*b + n - 2/5*b**2 = 0. Calculate b.
0
Let r(t) = t - 4. Let u be r(8). Suppose -b - u*b + 3 = 4*a, -5*b + 4*a = -27. Suppose -7 - b + f**2 + 5 - f + 3 = 0. What is f?
-1, 2
Let k = 30 + -61/2. Let t = 1/10 - k. Suppose -3/5*y**3 + 0 - 1/5*y - 1/5*y**4 - t*y**2 = 0. Calculate y.
-1, 0
Factor 2/5*n**3 + 1/5*n**4 - 1/5*n**5 + 0*n**2 + 0 + 0*n.
-n**3*(n - 2)*(n + 1)/5
Let v be 8/(-14) - -3*19/63. Factor -v*c**5 - 5/3*c**4 - 10/3*c**2 - 5/3*c - 1/3 - 10/3*c**3.
-(c + 1)**5/3
Find r, given that 2165*r**2 + 1 - 1 - 6*r - 2168*r**2 = 0.
-2, 0
Let q(i) = -12*i**2. Let o(c) = 13*c**2 - c. Let t(s) = -4*o(s) - 5*q(s). Determine f, given that t(f) = 0.
-1/2, 0
Find c, given that c + 8*c**3 - 4*c**2 + 4 + 6*c - 15*c = 0.
-1, 1/2, 1
Let b be (32/(-20))/(2/(-10)). Suppose 2*g - b = 4. Solve 3 - 4*c + 0*c + g*c**2 - 5 = 0.
-1/3, 1
Let b(c) = -c**3 - 3*c**2 + 2*c - 4. Let w be b(-4). Let z = w + -2. Factor z*d**3 + 2*d**4 - 2*d**5 + 2*d**5 - 2*d**5 - 2*d**2.
-2*d**2*(d - 1)**2*(d + 1)
Let z be ((-36)/(-81))/((-1)/(-1)). Suppose 2/9*n + z - 2/3*n**2 = 0. What is n?
-2/3, 1
Let t be (115/(-3))/((-16)/12). Let c = 29 - t. Factor 1/4*f**3 - c*f**2 + 0 + 1/4*f**4 - 1/4*f.
f*(f - 1)*(f + 1)**2/4
Let i(c) be the first derivative of 7/900*c**6 + 0*c**2 + 1 + 0*c + 3/100*c**5 + 1/30*c**4 - 1/3*c**3. Let y(u) be the third derivative of i(u). Factor y(w).
2*(w + 1)*(7*w + 2)/5
Let q be (4/(-5))/(5/(-25)). Factor -9*y**2 - q*y - 3 + 16*y + 3*y - 27*y**3.
-3*(y + 1)*(3*y - 1)**2
Let j(i) = -i**2 - 5*i**3 - 9*i**3 - 10*i**2 + 20*i + 6. Let c(d) = -5*d**3 - 4*d**2 + 7*d + 2. Let h(u) = -11*c(u) + 4*j(u). What is a in h(a) = 0?
-1, 2
Determine t, given that 3/2*t**2 + t + 0 - 7/8*t**5 + 33/8*t**4 - 23/4*t**3 = 0.
-2/7, 0, 1, 2
Let a(d) be the second derivative of -3/2*d**2 + 1/3*d**3 + 0 - 1/36*d**4 - 2*d. Determine y so that a(y) = 0.
3
Let u(o) be the second derivative of -o**6/20 + 3*o**5/40 + o**4/8 - o**3/4 - 5*o. Factor u(p).
-3*p*(p - 1)**2*(p + 1)/2
Factor 2/5*u**2 - 8/5*u + 8/5.
2*(u - 2)**2/5
Let v(x) = -6*x**3 + 2*x**2 + 5. Let n(f) = 7*f**3 - 2*f**2 - 6. Suppose 4*s - s = -18. Let r(o) = s*v(o) - 5*n(o). Find a, given that r(a) = 0.
0, 2
Let a(x) = x**2 - 8*x + 1. Let b be a(8). Suppose b = r - 2. Solve 3 + h + r - 2 - 2 - h**2 = 0.
-1, 2
Let b(y) = -48*y**3 + 55*y**2 + 77*y - 23. Let a(t) = -95*t**3 + 110*t**2 + 155*t - 45. Let g(k) = -3*a(k) + 5*b(k). Factor g(r).
5*(r - 2)*(r + 1)*(9*r - 2)
Let k(h) = -h**2 - 6*h - 3. Let p be k(-2). Factor p - 3 + 4*f**2 + 0*f**2 - f**2 + 5*f.
(f + 1)*(3*f + 2)
Let q = 15 - 9. Let g(f) be the third derivative of 0*f**