x**3 + x**2 - 1. Let l(s) = -12*s**4 + 12*s**3 - 16*s**2 + 16. Let w(h) = l(h) + 16*r(h). Find o, given that w(o) = 0.
0, 1
Let p = 103 - 100. Determine o so that 21/4*o**2 + 3/2*o**p - 9*o**4 - 3/4 - 6*o**5 + 0*o = 0.
-1, -1/2, 1/2
Suppose t + 0*t + 2 = 0. Let l(o) = -o**4 + 8*o**3 + 15*o**2 + 8*o + 2. Let n(b) = -b**4 + b**2. Let a(i) = t*l(i) + 6*n(i). Factor a(v).
-4*(v + 1)**4
Let b(q) be the second derivative of q**5/16 - q**4/16 - q**3/12 - q. Determine m so that b(m) = 0.
-2/5, 0, 1
Let r(t) = 1 + 2*t + 3*t - 3*t - 3*t. Let s be r(-2). Factor 0 - d**2 + d**4 - 1/2*d + 1/2*d**5 + 0*d**s.
d*(d - 1)*(d + 1)**3/2
Let a(q) = 3*q**3 - 2*q**2 + 1. Let y be a(1). Let u(j) be the first derivative of 1/3*j**3 - 2*j - 1/2*j**y - 2. Factor u(h).
(h - 2)*(h + 1)
Solve 0 - 3*q**2 + 9/2*q + 1/2*q**3 = 0 for q.
0, 3
Let j = 18 + -18. Let d(i) be the second derivative of 0 + 0*i**2 + j*i**4 + 1/70*i**5 + 0*i**3 - 1/35*i**6 + 2/147*i**7 + i. Factor d(v).
2*v**3*(v - 1)*(2*v - 1)/7
Let m(r) be the second derivative of r**7/70 + 2*r**6/25 + 9*r**5/50 + r**4/5 + r**3/10 + 7*r. Find n such that m(n) = 0.
-1, 0
Let o(t) be the second derivative of -2/15*t**3 + 1/25*t**5 + 1/5*t**2 + 0 + 5*t - 1/75*t**6 + 0*t**4. Suppose o(p) = 0. What is p?
-1, 1
Let t(k) = -6*k**3 - 24*k**2 - 4*k - 2. Let s(z) = -5*z**3 - 23*z**2 - 3*z - 3. Let h(a) = 4*s(a) - 6*t(a). Determine m, given that h(m) = 0.
-3, -1/4, 0
Let z = -7 + 9. Factor 3*t + 3*t**2 - 10*t**3 + 3*t**2 + 0*t**z + t.
-2*t*(t - 1)*(5*t + 2)
Let a(r) be the third derivative of r**7/160 + r**6/240 - 7*r**5/160 - r**4/16 + r**3/2 - 7*r**2. Let n(g) be the first derivative of a(g). Factor n(b).
3*(b - 1)*(b + 1)*(7*b + 2)/4
Suppose 5*p + 2*g + 0*g - 36 = 0, g - 30 = -4*p. Let a = 8 - p. Find o such that a*o + 0 - 1/3*o**3 - 1/3*o**2 = 0.
-1, 0
Suppose 5*d + 6 = 21. Suppose -2*q = -5*p + 2 - 18, 3*q + 3*p = d. Factor -8/9*f**2 - 10/9*f - 2/9*f**q - 4/9.
-2*(f + 1)**2*(f + 2)/9
Let f(c) be the second derivative of -c**7/840 + c**6/240 + c**5/20 + c**4/4 - 3*c. Let x(g) be the third derivative of f(g). What is t in x(t) = 0?
-1, 2
Let d(i) be the second derivative of -i**6/120 + i**5/20 + i**4/24 - i**3/2 - 9*i**2/8 + 7*i. Factor d(u).
-(u - 3)**2*(u + 1)**2/4
Let v(x) be the third derivative of -x**6/360 - x**5/180 + 11*x**2. Let v(j) = 0. Calculate j.
-1, 0
Determine n so that 5*n**3 + 5*n**2 + 2*n**4 + 4032*n - 7*n**4 - 4037*n = 0.
-1, 0, 1
Suppose 3*o + 3*v - 15 = 0, 3*o + 12*v - 13*v + 5 = 0. Determine z so that 3/4*z**5 + 0*z**2 + 0*z + 1/2*z**3 - 5/4*z**4 + o = 0.
0, 2/3, 1
Let f(l) be the second derivative of l**6/50 + 24*l**5/25 + 96*l**4/5 + 1024*l**3/5 + 6144*l**2/5 - 16*l. Factor f(i).
3*(i + 8)**4/5
Let v(g) be the first derivative of -g**7/140 - g**6/120 - 4*g**3/3 + 3. Let x(d) be the third derivative of v(d). Factor x(c).
-3*c**2*(2*c + 1)
Let a(w) be the third derivative of 5*w**8/336 + w**7/14 + w**6/8 + w**5/12 - 18*w**2. Factor a(k).
5*k**2*(k + 1)**3
Let l(d) = 9*d**3 - 63*d**2 + 120*d - 51. Let v(m) = -9*m**3 + 62*m**2 - 119*m + 52. Let a(i) = 2*l(i) + 3*v(i). Factor a(u).
-3*(u - 3)**2*(3*u - 2)
Factor -j**5 + j**4 - 45*j**2 + 2*j**5 - 4*j**3 + 41*j**2.
j**2*(j - 2)*(j + 1)*(j + 2)
Let r(d) be the second derivative of -2*d**7/21 + 3*d**5/5 + 2*d**4/3 - 4*d - 1. Let r(h) = 0. Calculate h.
-1, 0, 2
Let n(c) be the first derivative of -2 - 1/60*c**5 + 3*c + 0*c**4 + 0*c**3 + 0*c**2. Let z(g) be the first derivative of n(g). What is h in z(h) = 0?
0
Let i(v) be the first derivative of 0*v + v**3 + 9/2*v**2 + 8. What is w in i(w) = 0?
-3, 0
Let b(o) be the first derivative of o**7/105 + o**6/60 - o**5/15 + o**2 + 4. Let v(i) be the second derivative of b(i). Factor v(j).
2*j**2*(j - 1)*(j + 2)
Suppose 0 = -4*w + 2*b + 20, 3*w - 20 = -w + 3*b. Suppose 3*n + 11 = 4*k, -k = -4*n + 2 - 8. Factor -2*y**3 - y**2 + y**2 - k*y**w + 2*y**2 + 4*y**5 - 2*y**4.
2*y**2*(y - 1)**2*(y + 1)
Let -51*n + 19 + 42*n**2 + 11*n + 4*n**3 - 14*n**4 - 11 = 0. What is n?
-2, 2/7, 1
Let r = -587 + 15851/27. Let v(a) be the first derivative of 2/9*a**2 + r*a**3 - 1 + 2/9*a. Factor v(m).
2*(m + 1)**2/9
Let h be (-20 + 20)*4/(-16). Factor 1/4*n**3 - 3/4*n**2 + h*n + 0.
n**2*(n - 3)/4
Let y be 6/(-14)*1248/(-117). Factor -16/7*q - 2/7*q**2 - y.
-2*(q + 4)**2/7
Suppose 2*o + 9 + 7 = -4*u, 15 = 5*o - u. Suppose -3 - 3 = -o*i. Solve -d**4 + 0*d + 2*d**i + 2*d**2 - d**2 - 4*d + 2*d = 0 for d.
-1, 0, 1, 2
Find f such that 3/2*f**3 - 1/2 - 3/2*f - 1/2*f**2 + f**4 = 0.
-1, -1/2, 1
Let y(i) be the second derivative of -3*i**7/14 - 3*i**6/20 + 3*i**5/40 + 7*i**4/72 + i**3/36 + 8*i. Suppose y(j) = 0. What is j?
-1/3, 0, 1/2
Suppose a + 2 = -5*h - 3*a, -4*a = -4*h + 20. Factor 0*m - m + 6 - 9*m**h + 3*m**4 + 4*m - 3*m**3.
3*(m - 2)*(m - 1)*(m + 1)**2
Find d, given that 0*d + 1/4*d**2 + 0 = 0.
0
Let l(g) be the second derivative of -1/48*g**4 + 4*g + 1/24*g**3 + 0 + 0*g**2. Factor l(j).
-j*(j - 1)/4
Let y(b) = -4*b**4 - b**2 - 3*b + 2. Let c(s) = 9*s**4 + 3*s**2 + 7*s - 5. Let h(z) = 3*c(z) + 7*y(z). Factor h(x).
-(x - 1)**2*(x + 1)**2
Let m(g) be the first derivative of -3/2*g**2 + 1 + 23/4*g**4 + 12/5*g**5 + 3*g**3 - g. What is q in m(q) = 0?
-1, -1/4, 1/3
Let t(i) be the third derivative of 1/945*i**7 - 1/108*i**4 - i**2 + 0 + 0*i**3 - 1/270*i**5 + 1/540*i**6 + 0*i. What is c in t(c) = 0?
-1, 0, 1
Let d(k) be the second derivative of k**6/5 + 9*k**5/20 - 3*k**4/4 - k**3 + 17*k. Factor d(v).
3*v*(v - 1)*(v + 2)*(2*v + 1)
Factor 0*q**2 + 0 + 0*q + 3/7*q**3 - 3/7*q**4.
-3*q**3*(q - 1)/7
Let c = 288 + -288. Factor 3/4*p**4 + c - 3/4*p**2 + 3/4*p - 3/4*p**3.
3*p*(p - 1)**2*(p + 1)/4
Let w(j) be the third derivative of -j**7/84 + 7*j**6/240 + j**5/40 - 7*j**4/48 + j**3/6 + 7*j**2. Suppose w(f) = 0. What is f?
-1, 2/5, 1
Let r(z) = z**2. Let k be r(2). Let s(f) be the first derivative of 1/2*f + 1/2*f**2 - 1/4*f**k - 1/10*f**5 + 2 + 0*f**3. Factor s(g).
-(g - 1)*(g + 1)**3/2
Let v(r) be the third derivative of 0 - 1/60*r**5 + 0*r**3 + 1/24*r**4 - 3*r**2 + 0*r. Suppose v(m) = 0. What is m?
0, 1
Factor 2/3*k - 1/3*k**2 - 1/3.
-(k - 1)**2/3
Let r(t) be the second derivative of -243*t**6/10 + 243*t**5/5 + 72*t**4 + 104*t**3/3 + 8*t**2 + 6*t. Let r(b) = 0. Calculate b.
-2/9, 2
Let p(z) be the first derivative of z**5 + 20*z**4 + 160*z**3 + 640*z**2 + 1280*z + 3. Solve p(x) = 0 for x.
-4
Let w = -440 - -443. Factor 1/5*y**w - 3/5*y + 2/5 + 0*y**2.
(y - 1)**2*(y + 2)/5
Let n(r) be the second derivative of -r**5/30 + r**4/9 - r**3/9 - 15*r. Factor n(w).
-2*w*(w - 1)**2/3
Let d(m) be the first derivative of -m**6/15 + 8*m**5/25 - m**4/2 + 4*m**3/15 - 9. Solve d(j) = 0.
0, 1, 2
Let c(j) = j - 1. Let l be c(1). Determine m so that l*m**3 + m**3 - 2*m**3 + 2*m**3 = 0.
0
Let n be ((-32)/28)/(-4)*14. Let p be 36/10 + 4/10. Factor -2*h**3 + 3*h**p + h**5 + h**5 - n*h**2 + 0 + 1.
(h - 1)*(h + 1)**3*(2*h - 1)
Factor 0 - 16/5*g**3 + 16/5*g**2 + 4/5*g**4 + 0*g.
4*g**2*(g - 2)**2/5
Factor -6*b**3 + 3*b**3 - b**2 + 2*b**4 + b**4 - 6*b + b**5 - 10*b**2.
b*(b - 2)*(b + 1)**2*(b + 3)
Let b(u) = -u**3 + 8*u**2 + 8*u + 11. Let v be b(9). Find o, given that -2*o + o**2 + 2*o**2 + 0*o**v + o**3 - 4*o**2 = 0.
-1, 0, 2
Let y(h) be the second derivative of h**9/12096 - h**7/1680 + h**5/480 - h**3/3 + 3*h. Let i(m) be the second derivative of y(m). Factor i(w).
w*(w - 1)**2*(w + 1)**2/4
Suppose 0 = -0*d - 5*d + 70. Solve 0*o + 24*o**2 - d*o**3 + 4*o + 4*o = 0.
-2/7, 0, 2
Let y(u) = -2*u - 19. Let g be y(5). Let i = g + 117/4. Determine j, given that -1/2 - i*j**2 + 3/4*j = 0.
1, 2
Let v(j) be the third derivative of -j**7/1680 - j**6/720 + j**5/120 + 5*j**3/6 - 5*j**2. Let l(u) be the first derivative of v(u). Solve l(d) = 0 for d.
-2, 0, 1
Let p be 24/105*1/4*14. Find l, given that 4/5*l**5 + 0 - p*l**3 + 0*l + 0*l**2 + 0*l**4 = 0.
-1, 0, 1
What is y in y + 1/4*y**2 - 1/4*y**3 - 1 = 0?
-2, 1, 2
Let d(h) = 3*h**5 + h**4 + h**2 + h + 1. Let v(q) = -q**5 + q**4 - q**2 - q - 1. Let y(j) = d(j) + v(j). Factor y(x).
2*x**4*(x + 1)
Suppose -3*q - 2*q = 0. Suppose 3*w + q*w = 0. Factor 2/7*k**3 + 0*k**2 + w + 0*k.
2*k**3/7
Let p(s) = 3*s + 1. Let w be p(1). Let n be (w/(-30))/((-12)/15). Solve 1/6*u**2 + n*u**3 - 1/6 - 1/6*u = 0.
-1, 1
Let n = 9/5 - -4/5. Suppose 2/5 + 3/5*t**4 -