**3. Let r(y) = 0. What is y?
0
Let t(l) be the third derivative of 1/16*l**6 - 5/48*l**4 + 0 - 1/12*l**5 + 0*l**3 - 6*l**2 + 0*l. Factor t(r).
5*r*(r - 1)*(3*r + 1)/2
Let d be (-33)/(-15) + (-2)/10. Suppose 2*f - 8 = -4*s + 2*s, 3*s - 2 = d*f. What is y in y + s*y - 5*y**2 + 0*y**2 + 2*y**2 = 0?
0, 1
Let b(p) = p**3 - 5*p**2 - 3*p - 13. Let x be b(6). Determine n, given that 2*n**2 - 10 + 11*n**2 + 5*n - x*n**3 - 3*n**2 = 0.
-1, 1, 2
Let i = 3496/9 + -388. Factor i*v**2 + 0 + 0*v**4 + 2/3*v**3 + 0*v - 2/9*v**5.
-2*v**2*(v - 2)*(v + 1)**2/9
Let z(f) = 8*f**4 - 50*f**3 + 11*f**2 + 69*f. Let v(q) = -44*q**4 + 276*q**3 - 60*q**2 - 380*q. Let l(m) = 5*v(m) + 28*z(m). Factor l(y).
4*y*(y - 4)*(y - 2)*(y + 1)
Find s, given that -20/3 - 8*s - 4/3*s**2 = 0.
-5, -1
Factor -2/5*d**2 + 21/5*d - 18/5 - 1/5*d**3.
-(d - 3)*(d - 1)*(d + 6)/5
Let x(n) be the second derivative of 7*n + 1/160*n**5 + 0 + 0*n**2 - 1/48*n**3 - 1/48*n**4 + 1/120*n**6. What is l in x(l) = 0?
-1, -1/2, 0, 1
Let o(m) be the second derivative of -m**4/36 - 7*m**3/18 - 5*m**2/3 - 26*m. Factor o(c).
-(c + 2)*(c + 5)/3
Let s = 21510 - 86037/4. Factor 1/2 - 5/4*p - 1/4*p**4 + 1/4*p**3 + s*p**2.
-(p - 1)**3*(p + 2)/4
Let k(o) be the second derivative of -o**7/63 + o**6/15 - 2*o**4/9 + 6*o + 11. Factor k(v).
-2*v**2*(v - 2)**2*(v + 1)/3
Let c(k) be the third derivative of -k**8/6720 + k**7/3780 + 5*k**4/6 + 25*k**2. Let r(t) be the second derivative of c(t). Factor r(g).
-g**2*(3*g - 2)/3
Determine g, given that 2 + 1/2*g**2 - 2*g = 0.
2
Let y = -29945 - -118497/4. Let c = 321 + y. What is l in -l + c*l**2 + 1 = 0?
2
Let n(a) be the second derivative of a**7/840 - 2*a**2 - 3*a. Let q(f) be the first derivative of n(f). Solve q(t) = 0.
0
Let x(c) = -2 + 25*c**2 + 11*c**2 - 4*c**5 + 13 - 12*c**3 - 9*c**4. Let f(a) = a**5 + 2*a**4 + 3*a**3 - 9*a**2 - 3. Let u(w) = -22*f(w) - 6*x(w). Factor u(g).
2*g**2*(g - 1)*(g + 3)**2
Let u(v) = v**3 - 22*v**2 - 4*v - 17. Let s(d) = -5*d**2 - 1. Let w(h) = -5*s(h) + u(h). Factor w(z).
(z - 2)*(z + 2)*(z + 3)
Let i = -17 + 45. Let a = i + -11. Let -3*w - 33 - a - 17*w - 2*w**2 = 0. What is w?
-5
Let h(o) be the first derivative of -1/13*o**2 - 2/39*o**3 + 4/13*o + 7. Suppose h(g) = 0. Calculate g.
-2, 1
Let d(a) be the second derivative of a**4/54 + 11*a**3/27 + 2*a**2 - 118*a. Factor d(k).
2*(k + 2)*(k + 9)/9
Let v = -181 + 181. What is g in 3/8*g**4 + 0*g + v + 3/4*g**3 + 0*g**2 = 0?
-2, 0
Let j(g) = -7*g**2 - 86*g + 12. Let i(a) = 12*a**2 + 172*a - 21. Let z(w) = 4*i(w) + 7*j(w). Solve z(d) = 0.
0, 86
Suppose -3*m - d = -10, 0 = -m - 2*m + 2*d + 25. Suppose -4*n**2 - m - 11 + 16*n**2 - 4*n**3 = 0. What is n?
-1, 2
Let j be 816/72 - (-6)/(-45). Let 2*y**5 + 0 + j*y**3 + 0*y + 16/5*y**2 + 44/5*y**4 = 0. What is y?
-2, -2/5, 0
Suppose 7*v + 221 = 270. Let f(i) be the first derivative of v + 2/33*i**3 + 4/11*i + 3/11*i**2. Factor f(j).
2*(j + 1)*(j + 2)/11
Let c(v) be the first derivative of 7*v**6/33 + 102*v**5/55 + 63*v**4/22 - 182*v**3/33 - 30*v**2/11 + 177. Determine s so that c(s) = 0.
-5, -3, -2/7, 0, 1
Let y be (6/56)/((-3)/(-59)). Let d = y + -13/7. Factor -d*r**3 - 1/2*r - 3/4*r**2 + 0.
-r*(r + 1)*(r + 2)/4
Let q = 43 + -39. Find l, given that q*l**2 + 3*l + 2*l + 3*l = 0.
-2, 0
Let f = 127 + -14. Find q, given that -10*q**2 - 2*q - 133*q**3 + 0 + 17*q + 5*q**5 + f*q**3 + 10 = 0.
-1, 1, 2
Let g be ((-30)/9 + 4)/(9 + -8). Factor 8/3*w**3 + g*w**4 + 6 - 8*w - 4/3*w**2.
2*(w - 1)**2*(w + 3)**2/3
Let y(c) be the third derivative of -c**8/30240 + c**6/1080 + c**5/3 + 9*c**2. Let l(j) be the third derivative of y(j). Suppose l(k) = 0. What is k?
-1, 1
Let x(i) = -15*i - 11. Let l be x(-1). Let u(c) be the second derivative of c**3 - l*c + 2*c**2 + 7/10*c**5 - 2*c**4 + 0. Factor u(w).
2*(w - 1)**2*(7*w + 2)
Suppose 3*l = 5*v - 41, -l - 15 - 12 = -3*v. Factor v*i - 2 + 3 - 5*i**4 + 4 + 0*i - 10*i**3.
-5*(i - 1)*(i + 1)**3
Let 19*q**2 - 47*q**2 + 10*q**2 + 13*q**2 - 5*q + 5*q**3 + 5*q**4 = 0. Calculate q.
-1, 0, 1
Let k be (-4)/(-8 + 4) - -6. Let b(u) = -13*u**2 - u + 7. Let t(c) = -4*c**2 + 2. Let f(y) = k*t(y) - 2*b(y). Determine q so that f(q) = 0.
0, 1
Let p be ((74/(-12))/37)/((-2)/4). Let x = -7 - -9. Factor p*f + 2/3 - 1/3*f**x.
-(f - 2)*(f + 1)/3
Let q(x) be the second derivative of 0*x**3 - 2/21*x**7 + 0 + 0*x**2 - 12/5*x**5 - x**6 - 19*x + 8/3*x**4. Let q(m) = 0. What is m?
-4, 0, 1/2
Let f(j) be the second derivative of j**5/140 - j**4/21 - 2*j**3/3 - 16*j**2/7 - 4*j - 45. Factor f(t).
(t - 8)*(t + 2)**2/7
Suppose 0 = -8*c - 11 + 27. Factor 20*v**4 + 3*v**2 + 7*v**2 - 95*v**c - 24 - 23*v**2 + 12*v**3 + 100*v.
4*(v - 1)**2*(v + 3)*(5*v - 2)
Let a(m) be the second derivative of -m**8/13440 - m**7/1680 + m**5/60 + 2*m**4/3 + 3*m. Let j(d) be the third derivative of a(d). Factor j(i).
-(i - 1)*(i + 2)**2/2
Let d be 5/10*20/50. Let 1/5 + 1/5*s**3 - d*s - 1/5*s**2 = 0. What is s?
-1, 1
Let x(r) be the third derivative of 1/15*r**5 + 0 + 0*r**3 - 4*r**2 + 1/6*r**4 + 0*r. Let x(m) = 0. Calculate m.
-1, 0
Suppose 4*w - 3 = 3*w. Let a = 1 + w. Solve 4*y**3 - a*y**5 + 0*y**5 + 0*y**3 + 14*y**5 - 14*y**4 = 0.
0, 2/5, 1
Suppose 5*p - 17 = 13. Factor -5*a + p*a + 4*a + 5*a**2 - 30.
5*(a - 2)*(a + 3)
Suppose 228 = -44*p + 48*p. Let o = -169/3 + p. Solve -6*k**2 - 4*k - o - 8/3*k**3 = 0 for k.
-1, -1/4
Let h(o) = 41*o - 7. Let z be h(-2). Let n = -89 - z. Determine k, given that 0*k**2 - 1/5*k**4 - 2/5*k**3 + 1/5*k**5 + n*k + 0 = 0.
-1, 0, 2
Let q(p) = -1. Let r(y) = 324*y**2 + 156*y + 31. Let g(h) = -3*q(h) - r(h). Let m = -1139 - -1138. Let b(l) = l + 1. Let t(j) = m*g(j) - 12*b(j). Factor t(n).
4*(9*n + 2)**2
Let u(o) be the third derivative of o**7/210 - o**6/10 - o**5/60 + o**4/2 - 274*o**2. Factor u(c).
c*(c - 12)*(c - 1)*(c + 1)
Let l(y) = -2*y**3 - 85*y**2 + 280*y - 267. Let m(v) = -3*v**3 - 85*v**2 + 280*v - 268. Let u(q) = 8*l(q) - 7*m(q). Solve u(d) = 0 for d.
2, 13
Let s be ((-10)/15)/((-15)/36). Let z be (120/(-25) - -5)*-2 - -2. Suppose 0 - z*g - s*g**2 - 2/5*g**3 = 0. Calculate g.
-2, 0
Suppose 7*i + 9 - 44 = 0. Let 117*x + i*x**3 - 50*x**2 + 43*x - 428 + 268 = 0. What is x?
2, 4
Let l(y) be the third derivative of -3*y**6/8 - 2*y**5 - 10*y**4/3 - 106*y**2. Let l(b) = 0. What is b?
-4/3, 0
Suppose 8*p - 9*p = -65. Solve -j - 21*j**5 + 27*j**3 + 80*j**4 - 15*j**2 - p*j**4 - 5*j = 0 for j.
-1, -2/7, 0, 1
Let r(y) be the second derivative of -y**7/560 + 13*y**6/720 - y**5/15 + y**4/12 - 4*y**3/3 - 5*y. Let g(w) be the second derivative of r(w). Factor g(h).
-(h - 2)**2*(3*h - 1)/2
Suppose 144/5 + 54/5*y + 2/5*y**2 = 0. What is y?
-24, -3
Let i be (-35)/(-63) + (-4)/9. Let z(m) be the second derivative of i*m**7 + 0*m**2 + 0*m**4 + 0*m**3 + 6*m + 2/45*m**6 + 0*m**5 + 0. Factor z(d).
2*d**4*(7*d + 2)/3
Let j be 0/(3 + -6) - (-28)/42. Let o(t) = -t + 7. Let d be o(7). Let -1/3*z**4 + 2/3*z + 1/3*z**2 + d - j*z**3 = 0. Calculate z.
-2, -1, 0, 1
Let l = 3244 - 32329/10. Let w = -18/5 + l. Let -8*a**2 - 2*a**4 + 3/2*a + w*a**3 + 1 = 0. Calculate a.
-1/4, 1, 2
Let t(n) be the third derivative of -n**6/240 + 7*n**5/120 + 5*n**4/8 + 115*n**2 - n. Find z, given that t(z) = 0.
-3, 0, 10
Let h(x) be the first derivative of -2*x**6 - 36*x**5/5 + 105*x**4/4 - 24*x**3 + 15*x**2/2 + 104. Let h(g) = 0. What is g?
-5, 0, 1/2, 1
Let a be 32/14 + (-223 - -221). Factor -2/7 + 2/7*l**3 - 2/7*l + a*l**2.
2*(l - 1)*(l + 1)**2/7
Let q(x) be the third derivative of 13*x**2 + 1/8*x**4 - 1/40*x**6 - x**3 + 0*x + 0 + 3/20*x**5 - 1/70*x**7. Suppose q(c) = 0. Calculate c.
-2, -1, 1
What is q in -60*q - 29*q**2 - 15*q**2 + 11072 - 4*q**3 - 11136 - 44*q = 0?
-8, -2, -1
Let f(t) be the third derivative of -t**7/56 - 7*t**6/96 - t**5/16 + 5*t**4/32 + 5*t**3/12 - 2*t**2 + 14*t. Factor f(z).
-5*(z + 1)**3*(3*z - 2)/4
Let k = -14251 + 28503/2. Factor z + k*z**5 + 7/2*z**2 + 0 + 9/2*z**3 + 5/2*z**4.
z*(z + 1)**3*(z + 2)/2
Let m(c) = -2*c**4 + 4*c**3 + 6*c**2 + 8*c - 8. Let v(q) = -q**3 - q**2 - q + 1. Let k(i) = m(i) + 8*v(i). What is l in k(l) = 0?
-1, 0
Let x(q) = 7*q**4 + 39*q**3 + 121*q**2 - 162*q - 10. Let h(d) = 8*d**4 + 40*d**3 + 120*d**2 - 162*d - 12. Let z(l) = -5*h(l) + 6*x(l). What is f in z(f) = 0?
-9, 0, 1
Factor 86/5*o**2 - 12/5*o**3 - 14/5*o + 0.
-2*o*(o - 7)*(6*o - 1)/5
