 Let v(k) = 16*k**5 + 116*k**4 + 12*k**3 - 12*k**2 - 12. Let a(t) = 12*j(t) + v(t). Factor a(z).
4*z**3*(z + 3)*(7*z + 2)
Find y, given that -24*y**2 + y**2 + 5*y**2 + 2*y**5 + 22*y**2 - 2*y**4 + 2*y - 4*y**3 - 2 = 0.
-1, 1
Let f = 17 - 15. Suppose 8 = 4*a - 2*i - f*i, 18 = a + 3*i. Determine w, given that -1 + w**2 + a*w**2 - 4*w**2 - 2 = 0.
-1, 1
Suppose -10*j + 40 - 10 = 0. Factor -2 + j*w**2 - 19*w - 2*w**2 + 18*w.
(w - 2)*(w + 1)
Let c(d) be the third derivative of d**7/945 + d**6/54 - d**5/90 - 35*d**4/27 + 196*d**3/27 - 2*d**2 + 158. Suppose c(n) = 0. Calculate n.
-7, 2
Let d be (-680)/(-1224)*(-4)/(-10). Let 0 + 2*y + d*y**3 - 4/3*y**2 = 0. What is y?
0, 3
Let x be (-4)/((-1)/1) + 2. Suppose 19 - 124 = -15*t. Factor 1 - 3 + 0 - m**2 - t - x*m.
-(m + 3)**2
Let v(p) be the first derivative of -8*p**3/27 - 11*p**2/9 + 2*p/3 + 269. Solve v(a) = 0 for a.
-3, 1/4
Let d(g) be the third derivative of g**7/525 + 13*g**6/300 + 19*g**5/50 + 33*g**4/20 + 18*g**3/5 + 712*g**2. Factor d(p).
2*(p + 1)*(p + 3)**2*(p + 6)/5
Suppose -c = -5*f + 2, 4*f - 40 - 24 = -7*c. Factor 1/7*v**f + 0 - 8/7*v.
v*(v - 8)/7
Let t = 2298 - 6892/3. Suppose 5/9*g - 1/9*g**2 - t = 0. Calculate g.
2, 3
Let j be 1 + -3 + (-170)/(-65). Determine d, given that 8/13 - j*d + 2/13*d**2 = 0.
2
Suppose 0 = -5*p - 2*j + 120, 4*p + 2*j - 86 - 10 = 0. Suppose 0*u + p = 6*u. Factor 12/5*w**3 + 0 + 2/5*w - 8/5*w**2 - 8/5*w**u + 2/5*w**5.
2*w*(w - 1)**4/5
Let t = -88/7 - -1510/119. Determine q so that 6/17 - t*q**2 - 4/17*q = 0.
-3, 1
Suppose 0 = t - 3*i - 8, -5*t - 3*i + 8 = -2*i. Suppose -t*p = 3*p. Let -2*k + p*k - 2*k**5 + 8*k**4 + 0*k**5 - 12*k**3 + 0*k + 8*k**2 = 0. Calculate k.
0, 1
Let z(x) = 6*x**3 + 8*x**2 + 20*x + 20. Let u(v) = v**3 - v**2 - v + 1. Let t(j) = j + 4. Let n be t(-8). Let p(y) = n*u(y) + z(y). Factor p(s).
2*(s + 2)**3
Suppose -22*y + 4*r = -23*y + 20, 5*y + 3*r - 15 = 0. Let 0*g - 10/3*g**5 - 6*g**3 + y - 8*g**4 - 4/3*g**2 = 0. What is g?
-1, -2/5, 0
Factor -1/4*q**3 + 0 - 13/2*q**2 - 12*q.
-q*(q + 2)*(q + 24)/4
Let r(k) be the second derivative of -9*k - 1/240*k**6 - 1/80*k**5 + 0*k**3 + 1/336*k**7 + 0*k**4 + 0*k**2 + 0. Suppose r(s) = 0. What is s?
-1, 0, 2
Suppose -5*u + 5 = -5. Let c = -7 + 7. Find y such that -y**3 - y**4 + 0 - 42*y**u + y + c + 43*y**2 = 0.
-1, 0, 1
Let d(z) be the first derivative of -3*z**4/8 + 7*z**3/2 - 9*z**2 - 18. Factor d(j).
-3*j*(j - 4)*(j - 3)/2
Let f(z) be the second derivative of -z**7/63 - 4*z**6/45 + 7*z**4/9 + 17*z**3/9 + 2*z**2 - 55*z - 3. Solve f(u) = 0 for u.
-3, -1, 2
Let r(j) be the third derivative of j**5/210 - j**4/28 - 3*j**2. Let r(t) = 0. Calculate t.
0, 3
Let c(k) be the first derivative of -k**3 - 3*k**2 + 189*k + 684. Factor c(d).
-3*(d - 7)*(d + 9)
Suppose 1 - 76 = -25*s. Let t(r) be the third derivative of -1/12*r**s - 1/30*r**5 + 5/48*r**4 + 0*r + 0 - 6*r**2. Solve t(u) = 0 for u.
1/4, 1
Determine d, given that -36 - 41 + 152*d**3 - 124*d + 84*d**2 - 28*d + 2891*d**4 - 2911*d**4 + 13 = 0.
-1, -2/5, 1, 8
Suppose 0 = f + 2*f - 5*c - 110, 0 = -3*f - 4*c + 128. Factor 8*u**3 + 14*u**2 + 24 + 5*u**3 - 2*u**4 - f*u - 9*u**3.
-2*(u - 2)**2*(u - 1)*(u + 3)
Suppose 2*j = 4*a, -10*j + a - 10 = -12*j. Let d(q) be the second derivative of -3/10*q**5 + q + q**3 + 5/4*q**j + 0*q**2 - 1/2*q**6 + 0. Factor d(u).
-3*u*(u - 1)*(u + 1)*(5*u + 2)
Suppose 7*u = 5*u + 2. Let k be u/(10/(-45) + 34/72). Suppose 1/4*f**k - 1/4*f**3 + 0 - 1/4*f**2 + 1/4*f = 0. Calculate f.
-1, 0, 1
Let y(o) = -2*o - 5. Suppose -19*i = -18*i + 4. Let s be y(i). Factor s*m**2 + 9 - 4*m + 7*m + 9*m.
3*(m + 1)*(m + 3)
Let i be ((-2)/10)/((-9)/72). Let w = i + -14/15. Find o, given that 0 - w*o + 1/3*o**2 = 0.
0, 2
Let a(z) be the second derivative of z**7/21 + z**6/15 - z**5/5 + 120*z. Factor a(i).
2*i**3*(i - 1)*(i + 2)
Let x = 6043/69 + -596/23. Let o = -61 + x. Find r such that 0*r + o*r**2 - 2/3 = 0.
-1, 1
Find i, given that 48*i + 50*i**3 + 36 - 108*i**3 + 59*i**3 - 2*i**2 + 15*i**2 + 0*i**2 = 0.
-6, -1
Determine i so that 10/3*i - 3 - 1/3*i**2 = 0.
1, 9
Let d(t) be the first derivative of 0*t**3 - 3/2*t**2 + 3/4*t**4 - 17 + 0*t. Solve d(f) = 0 for f.
-1, 0, 1
Let q be (-63)/6*6/(-9). Let -9*x**2 - q*x**2 + 22*x - 4 - 2*x = 0. Calculate x.
1/4, 1
Let h(i) be the third derivative of i**5/150 - 3*i**4 + 540*i**3 - 294*i**2 - 2. Factor h(s).
2*(s - 90)**2/5
Suppose 20/3*b**2 + 2/3*b**3 + 34/3*b + 16/3 = 0. Calculate b.
-8, -1
Factor -336/5*b + 3016/5*b**2 + 0 - 6732/5*b**3 - 162/5*b**4.
-2*b*(b + 42)*(9*b - 2)**2/5
Let i(d) = d**2 - 1. Let q(b) = -10*b**2 + 18*b + 12. Let n(h) = -12*i(h) - q(h). Let n(t) = 0. What is t?
-9, 0
Let b(w) be the first derivative of 4*w**4 - 460*w**3/3 + 166*w**2 + 112*w - 352. Solve b(j) = 0 for j.
-1/4, 1, 28
Suppose 68/5*g**4 + 0*g - 578/5*g**3 + 0 + 0*g**2 - 2/5*g**5 = 0. What is g?
0, 17
Suppose 0 = 4*j + 4*f, 0 = -j + 5*f - 7 + 31. Solve -12*r**2 - r**3 + r**j - 21*r - 8 + 5*r**3 + r + 3*r**4 = 0 for r.
-1, 2
Let z(o) be the first derivative of -o**6/12 + o**5/2 + o**4/4 - 5*o**3/3 - o**2/4 + 5*o/2 + 260. What is m in z(m) = 0?
-1, 1, 5
Let 2/7*y**2 + 52/7*y - 240/7 = 0. Calculate y.
-30, 4
Find b such that -2*b**4 + 0 + 4/7*b**5 - 10/7*b**2 + 2/7*b + 18/7*b**3 = 0.
0, 1/2, 1
Determine f, given that -15/4*f - 1/4*f**2 - 7/2 = 0.
-14, -1
Let q = 50 + -38. Suppose 6*l - 10*l + q = 0. Suppose 3/4*s**2 + 0 + 1/2*s + 1/4*s**l = 0. What is s?
-2, -1, 0
Let o be ((-24)/(-180)*(-15)/3)/(3 - 5). Let -3*j - o*j**2 + 10/3 = 0. What is j?
-10, 1
Let s = 328 + -326. Find c such that 9/4*c**3 + 0*c + 0 - 3/4*c**s = 0.
0, 1/3
Let t(y) be the second derivative of 0 + 2/39*y**3 - 3*y - 1/78*y**4 + 0*y**2. Factor t(u).
-2*u*(u - 2)/13
Suppose 0 = -2*l - l. Suppose -b - 1 + 5 = l. Factor -s**3 - 3 - 2*s**2 + 0*s**2 + s + b + 1.
-(s - 1)*(s + 1)*(s + 2)
Let d = -31330 - -31333. Suppose 72/11*l**2 - 2/11*l**d - 864/11*l + 3456/11 = 0. What is l?
12
Let z(r) be the second derivative of 2*r**5/5 + 25*r**4/3 + 625*r**3/12 - 186*r. Factor z(t).
t*(4*t + 25)**2/2
Let y = 2167/274440 + 1/2287. Let v(m) be the third derivative of -y*m**6 - 1/3*m**3 + 0*m - 1/70*m**7 + 1/24*m**4 - 4*m**2 + 0 + 1/12*m**5. Factor v(j).
-(j - 1)*(j + 1)**2*(3*j - 2)
Factor 12*m**3 - 60*m + 76*m**2 - 27*m**2 - 4*m**4 + 3*m**2.
-4*m*(m - 5)*(m - 1)*(m + 3)
Let a(p) = -p**3 + 7*p**2 - 6*p - 7. Let q be a(6). Let s(y) = y**2 + 9*y + 15. Let w be s(q). Suppose -d + d**2 + d**3 + 5 - w - 5 = 0. Calculate d.
-1, 1
Let k(a) be the first derivative of -a**6/3 + 2*a**5/5 + 88. Let k(g) = 0. What is g?
0, 1
Let r(u) be the first derivative of 2*u**3/45 + 46*u**2/15 + 1058*u/15 - 189. Solve r(l) = 0 for l.
-23
Let g be (-2)/4*(-56)/(-12)*-6. Suppose -f = -17 + g. Suppose 4*u**4 - 5/3*u**5 + 2/3*u**2 - 3*u**f + 0*u + 0 = 0. What is u?
0, 2/5, 1
Let k(u) be the third derivative of 1/30*u**4 - 1/75*u**7 + 7/150*u**5 + 0*u - 2 - 1/168*u**8 + 1/100*u**6 - 3*u**2 + 0*u**3. Determine f so that k(f) = 0.
-1, -2/5, 0, 1
Let t = -23 + 31. Suppose p = 5*l - t, -2*l = -p + 6*p - 14. Let 0*z**3 - 1/2*z**4 + 0*z - 1/2 + z**l = 0. What is z?
-1, 1
Let y(d) be the first derivative of 2*d**3 + d**2 - 10 + d**3 - 4*d**3 + 2*d**2. Factor y(n).
-3*n*(n - 2)
Let m = -21 - -10. Let j be (-482)/m + 2/11. Factor 2250*f**5 + 66*f**3 + 1650*f**4 - 596*f**3 - 7 - 1 - 258*f**2 - j*f + 140*f.
2*(3*f + 2)**2*(5*f - 1)**3
Factor 0*d + d**2 - 6*d - 13*d + d**3 - 45 - 2*d.
(d - 5)*(d + 3)**2
Suppose 31*w**3 - 3*w**2 - 75*w**3 - 5*w**2 - 50*w**4 + 14*w**4 = 0. What is w?
-1, -2/9, 0
Let n = -2558/21 - -862/7. Let k(u) be the third derivative of 1/10*u**5 + 1/15*u**6 + 3*u**2 + 0 - 1/3*u**4 + 1/105*u**7 + 0*u - n*u**3. Factor k(o).
2*(o - 1)*(o + 1)*(o + 2)**2
Let h(t) be the third derivative of t**6/60 - t**5/30 + 325*t**2. Factor h(z).
2*z**2*(z - 1)
Let o(d) be the third derivative of -d**5/140 - 47*d**4/56 + 24*d**3/7 + 2*d**2 - 35. Factor o(u).
-3*(u - 1)*(u + 48)/7
Suppose 5 - 32 = -3*q. Let f be (20/(-15))/((-6)/q). Suppose 70/3*k**4 + 0*k + 8/3*k**f + 0 - 16*k**3 = 0. Calculate k.
0, 2/7, 2/5
Let m(q) be the first derivative of q**5/55 - q**4/11 - 163. Factor m(c).
c**3*(c - 4)/11
Let z be ((-117)/(-975))/(6/20). Factor -z*s**2 + 12/5 + 2/5*s.
-2*(s - 3)*(s + 2)/5
Let n = 87 + -83. Suppose 3*z - n