et k be l(-5). Factor -4*h**4 + 5*h**k - h**2 + 0*h**2 + 4*h**3 - 4*h**5 + 0*h**2.
-4*h**2*(h - 1)*(h + 1)**2
Let j be -7 - (-12)/((-756)/(-455)). Suppose 0 - 2/9*h**2 + j*h = 0. What is h?
0, 1
Let m(o) = 50*o**2 - o + 1. Let t be m(1). Let z be 3 - (t/9 + (-6)/2). Factor 2/9*g - 2/9*g**5 - 4/9*g**2 + z*g**4 + 0*g**3 + 0.
-2*g*(g - 1)**3*(g + 1)/9
Suppose -k - 54 = -217. Suppose -k*a = -164*a + 2. Find b such that 11/2*b - 9/2*b**a - 1 = 0.
2/9, 1
Let t = -257/2 - -1667/6. Let u = -148 + t. Factor -j**4 + 0 - u*j + 11/3*j**3 - 8/3*j**2.
-j*(j - 2)**2*(3*j + 1)/3
Let z(t) be the third derivative of t**8/336 - t**7/210 - t**6/24 - t**5/20 - 3*t**2 + 32. Factor z(d).
d**2*(d - 3)*(d + 1)**2
Let h = -1273 - -1273. What is m in -2/11*m + h + 2/11*m**2 = 0?
0, 1
Suppose 4*q = 8, -3*y = y - q - 22. Let v(f) be the first derivative of -3/2*f**2 - 12/5*f**5 + 0*f - 1 - y*f**3 - 27/4*f**4. Factor v(r).
-3*r*(r + 1)**2*(4*r + 1)
Factor 2*t**4 - 2*t**3 - 7 + 2*t - 6*t**2 - 4 + 27 - 12.
2*(t - 2)*(t - 1)*(t + 1)**2
Let p(l) be the first derivative of l**3/15 + l**2 - 11*l/5 - 178. Factor p(b).
(b - 1)*(b + 11)/5
Let l(o) = 8*o**4 - 31*o**3 + 8*o**2 - 22*o. Let x(c) = -2*c**4 + 8*c**3 - 2*c**2 + 6*c. Let t(n) = 6*l(n) + 22*x(n). Let t(u) = 0. Calculate u.
0, 1/2, 2
Let w be ((-10)/(-8) - 1/4) + -9. Let o be 2/w - 22/(-24). Solve -2*y + 0 - o*y**2 = 0.
-3, 0
Let r(f) = 123*f + 3446. Let o be r(-28). Find n, given that -1/12 + 1/12*n**o + 0*n = 0.
-1, 1
Suppose 5 = -7*f + 8*f. What is r in 40*r**3 + 2 + 2*r**f + 2*r**5 - 6 - 40*r**2 + 20*r - 20*r**4 = 0?
1
Let w be (-27)/405*-105 + 0 + 26/(-4). Factor w*f**3 + f + 3/2*f**2 + 0.
f*(f + 1)*(f + 2)/2
Let p(m) = -9*m**2 - 6*m. Let x(f) = f**2 + 2*f - 2*f**2 - 3*f. Let c(l) = p(l) - 6*x(l). Factor c(i).
-3*i**2
Let h(s) = -28*s**3 + 1134*s**2 + 71442*s + 1500299. Let n(i) = -10*i**3 + 378*i**2 + 23814*i + 500100. Let k(u) = -6*h(u) + 17*n(u). Solve k(o) = 0.
-63
Let c be 1*(-7)/2*-2. Let b = 13 - c. Factor 4*q - 9*q**2 + b*q**3 - 3*q**3 + 2*q.
3*q*(q - 2)*(q - 1)
Suppose 3*r + 5*z - 21 = 0, -5*r - 15*z = -14*z - 13. Suppose 0 - 3/7*s**r + 6/7*s = 0. What is s?
0, 2
Let -8*r**2 + 4/3*r - 4/3*r**3 + 40 = 0. What is r?
-5, -3, 2
Suppose -4*s + 8*g - 4*g + 32 = 0, g = 5*s - 24. Factor 11*d**2 - s*d**2 - 8*d**2 - 1 - 2*d.
-(d + 1)**2
Suppose -4*o + y = 5*y - 64, 2*o = -5*y + 44. Find n, given that -o*n - 6*n**2 - 2*n**2 + 9*n**5 + 57*n**3 + 5*n**2 - 42*n**4 - 9*n**2 = 0.
-1/3, 0, 1, 2
Let o(k) be the first derivative of -k**5/5 + k**4/3 + 2*k**3/3 - 2*k**2 - 3*k - 4. Let d(j) be the first derivative of o(j). Find c, given that d(c) = 0.
-1, 1
Let x(b) be the second derivative of -b**5/20 - 5*b**4/12 - b**3/3 + 15*b**2/2 - 109*b. Let q be x(-3). Find p such that -2/15*p**q + 0*p**2 + 0 + 2/15*p = 0.
-1, 0, 1
Solve 5/2 + 2*s**2 + 17/4*s + 1/4*s**3 = 0.
-5, -2, -1
Let h(a) = -6*a + 4 + 18*a + a - 15. Let d be h(1). Factor 2/5*z**d + 0*z - 8/5.
2*(z - 2)*(z + 2)/5
Suppose -2*f = -10 - 8. Let h be (3/f)/((-1)/(-6)). Factor -14 + 6*u**2 + 14 + h*u**3 + 4*u.
2*u*(u + 1)*(u + 2)
Let b be (-2)/(-6)*0*14/(-70). Suppose -6*j + j + 4*u = -16, -j + u = -4. Factor -3/5*l**2 - 2/5*l + b*l**3 + 1/5*l**4 + j.
l*(l - 2)*(l + 1)**2/5
Let i be (340/(-187) + 2)/(20/55). Factor i*t**2 + 15*t + 225/2.
(t + 15)**2/2
Let s(i) be the second derivative of 34*i**6/15 + 19*i**5/5 - 32*i**4/3 - 8*i**3/3 + 804*i. Factor s(u).
4*u*(u - 1)*(u + 2)*(17*u + 2)
Let y(f) = 16*f - 4*f**4 + 21*f**3 - 4 - 1 - 15*f**2 - 13*f. Let u(s) = -3*s**4 + 21*s**3 - 15*s**2 + 3*s - 6. Let j(v) = 5*u(v) - 6*y(v). Factor j(d).
3*d*(d - 1)**2*(3*d - 1)
Let h = 63410/3 + -191722/9. Let p = h + 166. Solve -2/9*g**3 - 2/9*g**2 + 2/9*g**4 + 0 + p*g**5 + 0*g = 0.
-1, 0, 1
Let v(s) be the third derivative of -s**7/42 + s**6/12 + s**5/4 - 5*s**4/3 + 10*s**3/3 - 115*s**2. Suppose v(d) = 0. What is d?
-2, 1, 2
Let k = 1703/9 + -189. Factor -10/3*i + 14/9 - k*i**3 + 2*i**2.
-2*(i - 7)*(i - 1)**2/9
Let x(k) be the second derivative of -k**4/9 + 2*k**3/9 + 4*k**2/3 + 125*k. Factor x(t).
-4*(t - 2)*(t + 1)/3
Let q(k) be the second derivative of -3*k**5/100 + k**4/20 + k**3/10 - 3*k**2/10 + 78*k. Determine s so that q(s) = 0.
-1, 1
Let i(w) be the first derivative of -2*w**3/39 + 6*w**2/13 + 55. Suppose i(z) = 0. Calculate z.
0, 6
Let i(g) be the third derivative of g**8/336 + g**7/70 - g**6/120 - 11*g**5/60 - g**4/2 - 2*g**3/3 + 23*g**2. Factor i(n).
(n - 2)*(n + 1)**3*(n + 2)
Factor -3*u**3 - 2 + 1 + 12*u + 16 - 18*u**2 + 3*u**4 + 9.
3*(u - 2)**2*(u + 1)*(u + 2)
Let s(i) be the second derivative of i**6/432 + i**5/16 + 5*i**4/18 - 2*i**3/3 + i**2 - 46*i. Let l(c) be the second derivative of s(c). Factor l(t).
5*(t + 1)*(t + 8)/6
Let f(n) = 3*n**2 - 13*n - 5. Let q be f(5). Factor -q - 5/2*r**2 - 15/2*r.
-5*(r + 1)*(r + 2)/2
Suppose 5*m - 3*m = 0. Suppose -5*i - 3*f = -10, 60*f = -4*i + 56*f + 8. Factor 0 + m*b**i + 1/4*b**3 + 0*b.
b**3/4
Let n be ((-657)/2 + 0)*(-12)/(-21). Let o = n + 188. Suppose 2/7*y - 2/7*y**4 + o*y**2 + 0 - 2/7*y**3 = 0. What is y?
-1, 0, 1
Let r(w) = 21*w**4 - 19*w**3 - 2*w**2. Let u(p) = -10*p**4 + 9*p**3 + p**2. Let s = 10 + -4. Let j(t) = s*r(t) + 13*u(t). What is i in j(i) = 0?
-1/4, 0, 1
Let q be -4*(-890)/(-720) - -5. Let j(f) be the second derivative of 1/72*f**4 - 1/4*f**2 + 0 - q*f**3 + 8*f. Let j(y) = 0. Calculate y.
-1, 3
Let d(v) be the second derivative of v**7/6720 - v**6/960 - 3*v**5/320 - 13*v**4/6 + 9*v. Let s(g) be the third derivative of d(g). Factor s(k).
3*(k - 3)*(k + 1)/8
Let y(n) be the first derivative of -n**2 + 2*n - 4/3*n**3 + 2. Let w(t) = -7*t**2 - 3*t + 4. Let k(g) = -3*w(g) + 5*y(g). Find q such that k(q) = 0.
-1, 2
Suppose 2*l + 8 = 6*i - 4*i, 0 = i + 2*l + 2. Factor -2/5*r**i - 2/5*r**3 + 2/5 + 2/5*r.
-2*(r - 1)*(r + 1)**2/5
Let b(y) = -15*y + 5*y + 4*y + 0*y + y**2 - 4. Let l be b(7). Factor -1/2*i**4 - i**l + i + 0*i**2 + 1/2.
-(i - 1)*(i + 1)**3/2
Let -13*c**2 - 2*c + 8*c**3 - 1 - 7 + 5 + 7*c**4 + 3 = 0. What is c?
-2, -1/7, 0, 1
Let x be 2*1/13 - 3186/(-78). Factor -4*m**2 - 5 - 23 + x*m - 9*m.
-4*(m - 7)*(m - 1)
Let c(t) be the first derivative of t**4/12 - t**3/3 + t**2/3 + 4. Factor c(j).
j*(j - 2)*(j - 1)/3
Suppose 2*h + 4*q + 1 = 3*h, 5 = 5*q. Let z(d) be the second derivative of 0 - 1/10*d**h + 0*d**3 + 1/30*d**6 + 0*d**2 - d + 1/12*d**4. Factor z(b).
b**2*(b - 1)**2
Determine t, given that 13*t**2 - 12*t**2 + 4*t**4 - t**2 - 12*t**3 + 16*t = 0.
-1, 0, 2
Let i(u) be the second derivative of -5*u**4/24 - 10*u**3 - 115*u**2/4 + u + 70. Determine k so that i(k) = 0.
-23, -1
Let s = 15757 - 15755. Factor -29/2*k**3 - 53/2*k**s - 85/4*k - 1/4*k**5 - 25/4 - 13/4*k**4.
-(k + 1)**3*(k + 5)**2/4
Let m be (2/3)/(11/3). Let p be (-80)/(-128) - 44/(-32). Factor -4/11*b + 2/11 + m*b**p.
2*(b - 1)**2/11
Let w(i) = -3*i**3 - 9*i**2 - 18*i + 36. Let x(n) = -2*n**3 - 5*n**2 - 9*n + 18. Let g(k) = -6*w(k) + 10*x(k). Factor g(q).
-2*(q - 3)*(q - 2)*(q + 3)
Let p be (-1 - (-145)/125)/((-18)/(-15)). Determine j so that 4/15*j + 22/15*j**4 - 22/15*j**3 + p*j**2 - 2/5*j**5 + 0 = 0.
-1/3, 0, 1, 2
Let u(z) be the third derivative of -z**6/1320 + z**5/110 - z**4/22 + 4*z**3/33 - 30*z**2. Suppose u(l) = 0. What is l?
2
Suppose -2*s = 3*k - 13, -5*k + 18 = 3*s - 3. Suppose -4/7*t**4 + 2*t**k + 0 + 4/7*t**2 - 2*t**5 + 0*t = 0. Calculate t.
-1, -2/7, 0, 1
Let b = 20609 + -61699/3. Suppose -32*m + b - 2/3*m**3 - 10*m**2 = 0. Calculate m.
-8, 1
Let w be (-4 - (-172)/44)/((-95)/9120). Factor -w*o**3 + 0 + 0*o - 128/11*o**2 - 24/11*o**4 - 2/11*o**5.
-2*o**2*(o + 4)**3/11
Solve 69/4*r**2 + 0 + 9/2*r - 3*r**3 = 0.
-1/4, 0, 6
Let s(p) be the second derivative of -p**7/3360 - p**6/360 - p**5/120 - 3*p**3/2 + 19*p. Let r(k) be the second derivative of s(k). Factor r(y).
-y*(y + 2)**2/4
Let i(a) be the third derivative of -a**9/24192 + a**8/13440 + a**7/3360 - 8*a**3/3 + 3*a**2. Let v(r) be the first derivative of i(r). Let v(b) = 0. What is b?
-1, 0, 2
Suppose -1 = -7*l - 22. Let d be (2 + (-53)/21)*36/l. Factor -16/7*n - 2/7 - 8*n**3 - 8/7*n**5 - d*n**2 - 34/7*n**4.
-2*(n + 1)**4*(4*n + 1)/7
Let f be 249/99 - (-1)/((-11)/2). Let b = 8 + -20/3. Factor -1/3*a**5 - f*a**4 - 25/3*a**2 - b - 16/3*a - 19/3*a**3.
-(a + 1)**3*(a + 2)**2/3
Let c = 44 - 42. 