
Let f(p) = -p**2 + 6*p + 12. Let j be f(6). Let c be (j/(-54))/2*-2. Factor -2/9*d - 4/9 + c*d**2.
2*(d - 2)*(d + 1)/9
Let v(y) be the third derivative of y**4/24 - 27*y**2. Let r(a) = -5*a**2 + 19*a. Let f(n) = r(n) + 6*v(n). What is i in f(i) = 0?
0, 5
Suppose -2*t = -4*t + 10. Suppose 2*g - 10 = -2*z, -3*z - 2*g = -10 - t. Find l such that -2*l - 7*l**3 + 23*l**2 - z*l**3 + 2 - 11*l = 0.
1/4, 2/3, 1
Suppose 13 = 9*g - 14. Factor -46*y**g - 24*y**4 - 48*y**2 - 4*y**5 - 56*y**3 - 16*y + 50*y**3.
-4*y*(y + 1)**2*(y + 2)**2
Let n(s) = 4*s**3 + 47*s**2 - 365*s + 319. Let i(j) = -5*j**3 - 49*j**2 + 366*j - 318. Let h(b) = -5*i(b) - 6*n(b). Solve h(y) = 0 for y.
1, 18
Let w(q) be the second derivative of -q**8/2240 - q**7/140 - 3*q**6/80 + 11*q**4/12 - q. Let y(d) be the third derivative of w(d). Determine l so that y(l) = 0.
-3, 0
Let i(m) = 15*m**4 - 11*m**3 - 38*m**2 + 17*m + 17. Let w(d) = 31*d**4 - 21*d**3 - 78*d**2 + 35*d + 33. Let t(k) = 7*i(k) - 3*w(k). Find a such that t(a) = 0.
-1, -5/6, 1, 2
Let c = 19192 + -19192. Factor c + 0*r - 4/7*r**2.
-4*r**2/7
Let l(m) = 52*m - 4. Let u be l(2). Determine k, given that 6*k**2 - 5*k**2 + 3*k**2 + 0*k**2 + 40*k + u = 0.
-5
Let p = -1/268 + 2417/1340. Let h = -78 - -396/5. Factor -6/5*w**2 - 3/5 + p*w**4 - 9/5*w + h*w**3 + 3/5*w**5.
3*(w - 1)*(w + 1)**4/5
Let m(q) = -q**5 + q**4 + q**3 - q**2. Let w(v) = 10*v**5 - 11*v**4 - 7*v**3 + 11*v**2. Let p(r) = -22*m(r) - 2*w(r). Factor p(t).
2*t**3*(t - 2)*(t + 2)
Suppose 19*j = 7*j. Let z(k) be the third derivative of -1/105*k**5 + 0*k + j*k**3 - 1/420*k**6 - 1/84*k**4 + 0 + 3*k**2. Factor z(s).
-2*s*(s + 1)**2/7
Suppose -16/5*b + 0*b**2 + 4/5*b**3 + 0 = 0. Calculate b.
-2, 0, 2
Suppose -98 - 453/2*k**2 - 9/2*k**3 - 296*k = 0. Calculate k.
-49, -2/3
Let j be 76/(-18) + (-6)/(-27). Let p be (j - -7)/(0 + 3). Factor p + 3 - 61*v**2 + 57*v**2.
-4*(v - 1)*(v + 1)
Let g(w) be the second derivative of w**4/78 + 34*w**3/39 + 289*w**2/13 - 12*w + 4. Find d, given that g(d) = 0.
-17
Suppose c + 2*z = -8, 0*c - z + 3 = 4*c. Factor 34*o**c + 10*o**3 - 61*o**2 + 5*o**4 + 32*o**2.
5*o**2*(o + 1)**2
Let y(x) be the second derivative of -1/39*x**4 + 0*x**2 + 48*x + 0 - 1/39*x**3 - 1/130*x**5. Factor y(b).
-2*b*(b + 1)**2/13
Let a(u) be the first derivative of 4/15*u**5 + 0*u**2 + 0*u + 0*u**3 - 2/9*u**6 - 45 + 0*u**4. Factor a(y).
-4*y**4*(y - 1)/3
Let s(d) be the first derivative of -d**6/1080 - d**5/36 - 25*d**4/72 - 3*d**3 + 13. Let r(w) be the third derivative of s(w). Find q such that r(q) = 0.
-5
Factor 81/7*l**3 + 0 + 0*l - 18/7*l**4 + 0*l**2 + 1/7*l**5.
l**3*(l - 9)**2/7
Let t(m) be the first derivative of 2*m**5/65 - 8*m**4/13 + 176*m**3/39 - 192*m**2/13 + 288*m/13 + 104. Factor t(s).
2*(s - 6)**2*(s - 2)**2/13
Suppose -6 + 5*b - 3*b**2 + 10*b**2 - 2*b + 3*b**2 - 7*b**2 = 0. Calculate b.
-2, 1
Let x(z) be the third derivative of -z**4/4 - 4*z**3/3 + 9*z**2. Let d(k) = k**2 - 11*k - 17. Let u(q) = 2*d(q) - 5*x(q). Factor u(a).
2*(a + 1)*(a + 3)
Let i be (-3)/(-10)*4520/(-45). Let o = 100/3 + i. Determine j so that o*j + 12/5 + 4/5*j**2 = 0.
-3, -1
Let u = -691/2 - -347. Let b(x) be the second derivative of 3/20*x**5 + 0 + x - 1/2*x**3 - u*x**2 + 1/4*x**4. Find n such that b(n) = 0.
-1, 1
Determine k, given that 10*k**4 - 16*k**4 - 10*k - 105*k**2 - 116*k**3 - 26*k - 20*k**4 - 10*k**4 - 4 = 0.
-2, -1/2, -2/9
Let t(b) be the first derivative of b**4/22 + 2*b**3/33 - 179. Find l, given that t(l) = 0.
-1, 0
Let n(f) = -f**2 - 6*f - 6. Let d be n(-4). Let -15*i**3 + 28*i**2 - 44*i**2 + d*i**4 - 3*i - 6*i**4 + 2 = 0. Calculate i.
-2, -1, 1/4
Let k(x) = x**2 - 2*x - 2. Let w be k(6). Let l be 1/(68/w + -3). What is g in -12*g**4 + 2*g + g**3 - 8*g + l*g**3 + 9*g**2 - 3 = 0?
-1/2, 1
Let z(w) be the first derivative of -w**3/3 - w**2/2 - w - 4. Let h(v) = -35*v**2 - 30*v - 25. Let d(r) = h(r) - 30*z(r). What is j in d(j) = 0?
-1, 1
Factor -110119 - 20*v - 15*v**2 + 5*v**3 + 110119.
5*v*(v - 4)*(v + 1)
Factor -448/3 - 150*b - 2/3*b**2.
-2*(b + 1)*(b + 224)/3
Let s(k) be the second derivative of 6*k + 0 - 1/8*k**5 + 1/72*k**6 + 0*k**2 + 13/6*k**3 + 0*k**4. Let u(t) be the second derivative of s(t). Factor u(g).
5*g*(g - 3)
Find s, given that 0*s**5 - 964*s**2 - 508*s**2 + 2835*s - 604*s**4 + 26*s**5 + 1712*s**3 + 192 + 34*s**5 - 2963*s = 0.
-1/3, 2/5, 2, 6
Let r(u) be the third derivative of -u**5/150 + 7*u**4/30 + 32*u**3/15 - 181*u**2. Factor r(m).
-2*(m - 16)*(m + 2)/5
Suppose -2*z + 6*z + 76 = 0. Let d = -7 - z. Determine b, given that 3 + 27*b**2 - 9*b**2 + 2 + 12*b + 3*b**4 - 2 + d*b**3 = 0.
-1
Determine b, given that 1/9*b**2 - 68/9 - 67/9*b = 0.
-1, 68
Let m(o) be the second derivative of -o**5/15 - o**4/6 - 3*o**2/2 - 15*o. Let z(c) be the first derivative of m(c). Factor z(q).
-4*q*(q + 1)
Let f(o) = -o**3 - 3*o**2 - 2*o - 2. Let q be f(-2). Let g be (-12)/21*(q + -5). What is b in 16 + 22*b**2 - 37*b + 53*b - 98*b**2 - 12*b**g + 56*b**3 = 0?
-1/3, 1, 2
Let t(p) be the second derivative of 2/35*p**5 - 3*p**2 + 1/84*p**6 - 6*p + 2/21*p**3 + 0 + 3/28*p**4. Let s(x) be the first derivative of t(x). Factor s(w).
2*(w + 1)**2*(5*w + 2)/7
Let f(n) be the third derivative of -n**8/84 - 4*n**7/105 + n**6/10 + 8*n**5/15 + 2*n**4/3 + 64*n**2. Let f(z) = 0. Calculate z.
-2, -1, 0, 2
Let m(j) = 3*j**4 + 85*j**3 + 153*j**2 - 115*j - 123. Let p(y) = y**4 - 3*y**3 - y**2 + y + 1. Let z(c) = -m(c) - 3*p(c). Let z(v) = 0. What is v?
-10, -3, -2/3, 1
Let q be ((26/380)/13)/(4/30). Let z = 35/76 + q. Factor -z*o - 3/4*o**4 + 1/4*o**5 + 0 + 1/4*o**3 + 3/4*o**2.
o*(o - 2)*(o - 1)**2*(o + 1)/4
Let o(c) be the third derivative of -c**9/12096 - c**8/2016 + c**7/336 + c**5/15 - 20*c**2. Let b(d) be the third derivative of o(d). Find u such that b(u) = 0.
-3, 0, 1
Let z(v) = -20*v**3 + 785*v**2 + 35*v - 770. Let m(t) = 3*t**3 - 112*t**2 - 5*t + 110. Let s(d) = -15*m(d) - 2*z(d). Factor s(p).
-5*(p - 22)*(p - 1)*(p + 1)
Let a be ((-2)/10)/(3/(-30)). What is d in d**2 + 10*d**5 - 4*d**5 + 10*d**4 - 15*d**4 - a*d**3 = 0?
-1/2, 0, 1/3, 1
Let p(l) be the first derivative of 4*l**3/3 + 16*l**2 + 60*l + 543. Factor p(g).
4*(g + 3)*(g + 5)
Let w(h) = -4*h**3 - 8*h**2 + 15*h + 2. Let k(p) = 2*p**3 + 3*p**2 - 8*p. Let j(m) = -7*k(m) - 3*w(m). Factor j(i).
-(i - 3)*(i + 2)*(2*i - 1)
Let a be 7 + -2 + (-24)/(-8). Let f(r) be the second derivative of a*r**2 - 11/3*r**4 - 16/3*r**3 - 3/5*r**5 + 0 + 5*r. Determine k so that f(k) = 0.
-2, 1/3
Let x(c) = c + c**2 - 3 + c**2 - 3*c**2 + 4. Let i(h) = 11*h**2 + 7*h + 3. Let n(l) = i(l) - 3*x(l). Factor n(s).
2*s*(7*s + 2)
Factor -12 + 10*q - 8/3*q**2 + 2/9*q**3.
2*(q - 6)*(q - 3)**2/9
Let p(f) be the first derivative of -f**5/15 - f**4/36 + 7*f**3/27 + f**2/18 - 4*f/9 + 29. Solve p(h) = 0 for h.
-4/3, -1, 1
Let c(s) be the first derivative of 0*s - 9*s**2 + s**3 - 33 + 3/4*s**4. Determine u, given that c(u) = 0.
-3, 0, 2
Suppose 9 + 7 = 4*r. Find a such that 108*a + 12*a**3 - 236*a + 112*a - r*a**4 = 0.
-1, 0, 2
Let u(g) be the second derivative of g**8/16800 - g**7/2100 + g**6/900 - 23*g**4/6 + 33*g. Let p(d) be the third derivative of u(d). Factor p(r).
2*r*(r - 2)*(r - 1)/5
Determine x, given that -4/11*x**3 + 20/11*x**4 + 2/11*x + 20/11 - 40/11*x**2 + 2/11*x**5 = 0.
-10, -1, 1
Let v = -11 + 7. Let g be (v/16)/(-2 - 9/(-12)). Determine p so that 0*p**4 + 0 + g*p**3 + 0*p - 1/5*p**5 + 0*p**2 = 0.
-1, 0, 1
Let v(g) be the first derivative of -g**5/230 + g**4/69 + g**3/69 - 2*g**2/23 - 26*g + 12. Let i(z) be the first derivative of v(z). Factor i(c).
-2*(c - 2)*(c - 1)*(c + 1)/23
Factor h**4 - 7 - 1 - 6*h + 6*h**3 + 10*h**2 - 3*h**4.
-2*(h - 4)*(h - 1)*(h + 1)**2
Let x(d) = -4*d. Let l be x(-1). Suppose -4*m + 6 = -2*m - 3*s, -15 = -5*m + 5*s. Determine g so that -9 - g**l + 21 - g**2 + m*g - 10 - 3*g**3 = 0.
-2, -1, 1
Let w(o) be the first derivative of -30*o - 35/2*o**2 - 25/4*o**4 - 20 + 30*o**3. Factor w(q).
-5*(q - 3)*(q - 1)*(5*q + 2)
Factor 430*b**3 - 33 - 155*b**2 + 1275*b - 1092 - 425*b**3.
5*(b - 15)**2*(b - 1)
Let y be 2/1 + (182/(-8))/13. Let c(r) be the second derivative of r - 6*r**2 - y*r**4 + 2*r**3 + 0. Solve c(b) = 0.
2
Factor 12*v + 3*v**3 - 103*v**2 + 33*v**2 + 55*v**2.
3*v*(v - 4)*(v - 1)
Let b(l) = -l**2 + 5*l + 4. Let f be b(5). 