6*t**4 + 0*t - 2 + 1/6*t**3 + 1/120*t**5 - 3/2*t**2. Let w(a) be the second derivative of g(a). Factor w(i).
(i - 2)*(i - 1)/2
Let 8*p**3 - 23*p**2 - 3*p**3 + 8*p**2 = 0. What is p?
0, 3
Let d = 31 + -28. Find c, given that 5*c**5 - 109*c + 18*c**4 + 12*c**4 + 124*c + 50*c**2 + 60*c**d = 0.
-3, -1, 0
Let f = 15/92 - 11/1196. Factor 2/13*s + f*s**3 - 4/13*s**2 + 0.
2*s*(s - 1)**2/13
Factor 10 + 8*x - 1 - 2*x - 3*x**2.
-3*(x - 3)*(x + 1)
Factor -81 + 5*p**3 - p**4 + 0*p**3 + 82 - 3*p**3 - 2*p.
-(p - 1)**3*(p + 1)
Let m(u) be the third derivative of u**6/1260 - 2*u**5/315 - 11*u**4/252 - 2*u**3/21 + 2*u**2 + 44. Determine h, given that m(h) = 0.
-1, 6
Let i(m) be the third derivative of -m**5/12 + 10*m**4 - 480*m**3 + 95*m**2 - 3*m. Find u, given that i(u) = 0.
24
Let m(p) = -8*p**2 + 134*p - 141. Let i(y) = -39*y**2 + 669*y - 702. Let n(u) = 5*i(u) - 24*m(u). Find f such that n(f) = 0.
1, 42
Let u(d) = d**2 + 3*d - 1. Let l be u(-4). Factor -4*y**2 - y**2 - 16*y - 4*y**l - 12*y**2 + y**2.
-4*y*(y + 2)**2
Let d(m) be the first derivative of -m**6/10 - m**5/25 + 3*m**4/20 + m**3/15 - 44. Let d(n) = 0. What is n?
-1, -1/3, 0, 1
Let y(i) = 3*i**2 - 30*i - 33. Let v(m) = -2*m**2 + m + 3. Let c(r) = -3*v(r) - y(r). Factor c(x).
3*(x + 1)*(x + 8)
Let c(o) = -o - 1. Let a(j) be the first derivative of -j**3 + 6*j**2 + 3*j + 26. Let v(t) = a(t) + 6*c(t). Suppose v(p) = 0. Calculate p.
1
Find g such that 18/5*g**2 - 2/5*g**3 - 48/5*g + 32/5 = 0.
1, 4
Let z(d) be the second derivative of -d**5/10 + 11*d**4/6 + 394*d. Factor z(k).
-2*k**2*(k - 11)
Let k(x) = 0*x + 2 + x - 1 + 0. Let p(n) = 2*n**3 + 2*n**2 - 5*n - 5. Let b(i) = -3*k(i) - p(i). Solve b(u) = 0.
-1, 1
Let n be 12/(-60) + (-456)/(-5). Let m = n + -89. Factor -m*l**3 - 1/2*l**5 + 5/2*l + 2*l**4 - l**2 - 1.
-(l - 2)*(l - 1)**3*(l + 1)/2
Let s = -35 - -39. What is h in 6*h**3 + 67*h**2 - 3*h**3 - 2*h**s - 63*h**2 - h**3 = 0?
-1, 0, 2
Suppose 7 = 8*n - 25. Suppose -7*a + 22 = n*a. Factor -2/7*m - 2/7*m**a + 2/7*m**3 + 2/7.
2*(m - 1)**2*(m + 1)/7
Let t be (-2)/(-1) - (-4 - -2). Suppose -3*k - t = 4*g - 2, 3*k + 2*g = 2. Factor n**2 + 24*n - 2*n**k + n**2 + 36 + 4*n**2.
4*(n + 3)**2
Let j(k) be the second derivative of 7*k**5/20 - 55*k**4/12 + 52*k**3/3 + 8*k**2 - 34*k. Factor j(y).
(y - 4)**2*(7*y + 1)
Let i(a) be the third derivative of -a**7/840 + a**6/240 + 7*a**5/240 + a**4/24 + 9*a**2 - 26*a. Factor i(c).
-c*(c - 4)*(c + 1)**2/4
Let c(h) be the second derivative of -2/7*h**3 - 5*h + 0 - 1/21*h**4 + 0*h**2. Factor c(f).
-4*f*(f + 3)/7
Let w(x) be the second derivative of -x**6/75 + 3*x**5/50 - x**4/10 + x**3/15 + 4*x - 14. Find v such that w(v) = 0.
0, 1
Let o(r) be the third derivative of r**8/432 - 2*r**7/945 - 385*r**2. Factor o(f).
f**4*(7*f - 4)/9
Let k(o) be the third derivative of o**8/448 + 9*o**7/560 + 3*o**6/80 + o**5/40 + 34*o**2. Factor k(f).
3*f**2*(f + 2)**2*(2*f + 1)/8
Let y(i) be the third derivative of -i**6/60 - i**5/210 + 53*i**2 - 1. Factor y(x).
-2*x**2*(7*x + 1)/7
Let z(y) be the first derivative of -1/18*y**6 + 0*y - 14 - 1/15*y**5 - 1/3*y**2 + 1/9*y**3 + 1/4*y**4. Suppose z(j) = 0. Calculate j.
-2, -1, 0, 1
Let q = -86278/7 + 12360. Determine u, given that -2/7*u**2 - q + 44/7*u = 0.
11
Let z(r) be the third derivative of 0*r**4 - 3*r**2 + 0*r**3 + 1/10*r**5 + 0*r - 3/70*r**7 + 0 + 1/40*r**6. Find t, given that z(t) = 0.
-2/3, 0, 1
Let s be -4 + (-15)/(-105)*31. Solve 15/7*k - 6/7 - 12/7*k**2 + s*k**3 = 0 for k.
1, 2
Let q(s) be the first derivative of -s**3/24 + 63*s**2/16 + 65*s/4 + 630. Find x such that q(x) = 0.
-2, 65
Factor -2/7*r**2 - 12/7*r - 16/7.
-2*(r + 2)*(r + 4)/7
Let a(c) be the third derivative of 3*c**5/50 + c**4/6 + c**3/15 + 52*c**2 + 2. Factor a(b).
2*(b + 1)*(9*b + 1)/5
Let s = 7052 + -49346/7. Factor s*m**2 + 3/7*m**4 + 12/7*m + 3/7 + 12/7*m**3.
3*(m + 1)**4/7
Let n(m) be the first derivative of m**3 - 57*m**2/2 + 54*m - 126. Solve n(q) = 0.
1, 18
Let x be (11 - 6) + -7 + 2 + 36/24. Find s such that -9/2*s**4 - 9/2*s**3 + 0 - x*s**2 - 1/6*s = 0.
-1/3, 0
Factor 32/7*o - 4/7*o**2 + 80/7.
-4*(o - 10)*(o + 2)/7
Let a(x) be the first derivative of 121/12*x**4 + 46/3*x**2 - 8/3*x - 25 - 286/9*x**3. Factor a(u).
(u - 2)*(11*u - 2)**2/3
Let p be 5/(1/(-24)*-20). Let n(s) be the first derivative of 1/9*s**6 - 1/3*s**2 - 1/2*s**4 - 1/15*s**5 + 0*s - p + 7/9*s**3. Determine r so that n(r) = 0.
-2, 0, 1/2, 1
Let g(a) be the second derivative of -1/2*a**2 + 0 - 1/96*a**4 + 0*a**3 - 1/60*a**5 - 8*a. Let d(t) be the first derivative of g(t). Solve d(h) = 0.
-1/4, 0
Factor 41*c + c**2 + 0*c - 13*c + c**2.
2*c*(c + 14)
Let y(w) be the first derivative of -w**4/12 - w**3/6 + w**2 - 15*w - 3. Let i(q) be the first derivative of y(q). Let i(s) = 0. Calculate s.
-2, 1
Suppose 2*t - 3*l - 12 - 3 = 0, 0 = -4*t + 2*l + 26. Suppose -2*q**3 + 2*q + t - 6 + 6*q**2 - 2 - 4*q**4 = 0. What is q?
-1, 1/2, 1
Let 2/7*u**2 + 356/7*u + 15842/7 = 0. What is u?
-89
Suppose 13*z - 18 = -135. Let n be 1 - (3/z + 1). What is c in 2/3*c**4 + n*c + 0*c**3 + 0 - 2/3*c**2 - 1/3*c**5 = 0?
-1, 0, 1
Factor -15/2*c - 9/4*c**2 - 3/4*c**4 + 0 + 9/2*c**3.
-3*c*(c - 5)*(c - 2)*(c + 1)/4
Let -45 + 57/4*g - 3/4*g**2 = 0. What is g?
4, 15
Let g(u) be the first derivative of u**6/39 + 2*u**5/13 - u**4/13 - 56*u**3/39 - 8*u**2/13 + 64*u/13 - 815. Determine z, given that g(z) = 0.
-4, -2, 1, 2
Let g(b) = -116*b**2 + 100*b - 20. Suppose -x + 36 = 3. Let w(f) = -23*f**2 + 20*f - 4. Let s(d) = x*w(d) - 6*g(d). Factor s(o).
-3*(3*o - 2)*(7*o - 2)
Let c(x) = x - 2. Let z(l) = -8*l**2 - 114*l + 80. Let v(b) = -8*c(b) + z(b). Factor v(r).
-2*(r + 16)*(4*r - 3)
Let -33/5*k**3 + 9/5*k**4 - 18/5 + 9/5*k**2 + 33/5*k = 0. What is k?
-1, 2/3, 1, 3
Suppose -7*r + 9*r - 6 = 0. Suppose -4*f - 17 = -5*k, r*k - 19 = -2*f - 0*f. Factor 3/2*z**f + 0 + 0*z.
3*z**2/2
Let y(g) = g**3 + 4*g**2 + 4*g + 3. Let t be y(-2). Suppose -t*w + 15 = 5*b, -5*b - w + 15 = 4*w. Factor -i**b + 2*i + 0*i**2 + 2*i**2 - 11 - i + 9.
-(i - 2)*(i - 1)*(i + 1)
Suppose -34 = 3*k + 5*x, 2*x = 5*k + 21 - 47. Factor 1/2*j**3 - 1/2*j + 1/2 - 1/2*j**k.
(j - 1)**2*(j + 1)/2
Let c = 67457/2745 - -14/549. Let g = -102/5 + c. Factor -6/5 + 21/5*m**3 + 6/5*m**2 - g*m.
3*(m - 1)*(m + 1)*(7*m + 2)/5
Factor 0 + 6*i + 2/3*i**2.
2*i*(i + 9)/3
Let c = 3 - -7. Suppose 4*n - 2*n**4 + 2*n**2 - c*n**5 + 8*n**5 + 10*n**3 + 8*n**2 - 4*n**3 = 0. What is n?
-1, 0, 2
Suppose 17*t = f + 22*t - 7, -4*f + t + 7 = 0. What is w in 200/3 + 2/3*w**f - 40/3*w = 0?
10
Suppose -2050*p**3 + 1890*p**2 - 9558 + 9053 - 4940*p**2 - 525*p**4 - 5*p**5 - 2025*p = 0. What is p?
-101, -1
Let -2427*d**3 - 4 - 26*d + 0 + 2409*d**3 - 40*d**2 = 0. Calculate d.
-1, -2/9
Let z(y) be the second derivative of -y**5/135 - 5*y**4/54 - 8*y**3/27 - y**2 + 31*y. Let g(b) be the first derivative of z(b). Factor g(d).
-4*(d + 1)*(d + 4)/9
Let -6/19*u**4 - 12/19*u - 16/19 + 14/19*u**3 + 22/19*u**2 - 2/19*u**5 = 0. What is u?
-4, -1, 1, 2
Let u be 3*((-14)/(-3))/7. Solve 15*d**3 - 2*d**4 + 1 + 12*d + 18*d**u + 5*d**4 - 3*d**3 + 2 = 0.
-1
Let p(l) be the second derivative of l**6/720 + l**5/240 + 5*l**3/6 - 6*l. Let n(k) be the second derivative of p(k). Solve n(u) = 0.
-1, 0
Solve -2/3*r**2 + 10/3*r + 16 = 0 for r.
-3, 8
Let c be 2 + -3 + 6/2. Suppose -4 - 2*p**c - 7*p**2 - p**3 + p**2 - p**3 - 10*p = 0. What is p?
-2, -1
Let k(x) be the first derivative of -x**5/30 + x**4/9 + 3*x**2 + x - 10. Let p(w) be the second derivative of k(w). Solve p(s) = 0.
0, 4/3
Let q(a) be the first derivative of a**6/2 - 27*a**5/5 + 45*a**4/2 - 44*a**3 + 36*a**2 + 28. Determine b so that q(b) = 0.
0, 2, 3
Let w(r) be the second derivative of r**10/7560 - r**9/945 + r**8/420 + r**4/6 + 9*r. Let b(j) be the third derivative of w(j). Factor b(t).
4*t**3*(t - 2)**2
Let v(n) be the third derivative of n**8/1680 + n**7/210 - n**6/300 - n**5/30 + n**4/120 + n**3/6 - 399*n**2. What is b in v(b) = 0?
-5, -1, 1
Let p be ((-3)/(-6))/(2/2). Suppose -4*g + 4*a + 2 = -6, -16 = -4*g - 4*a. Suppose -p*o**5 + 1 + 7/2*o - o**4 + o**g + 4*o**2 = 0. Calculate o.
-1, 2
Factor 681065*d + 16*d**2 - 681093*d + 6*d**3 - 40 - 2*d**3.
4*(d - 2)*(d + 1)*(d + 5)
Let t be (-166)/(-913)*(-22)/(-30). What is y in t*y**2 + 0 - 2/15*y**3 + 0*y = 0?
0, 1
Suppose 