*3 + 0. Let l(i) = 0. What is i?
1, 2
What is b in -1/5*b**3 + 0 + 14/5*b**2 + 3*b = 0?
-1, 0, 15
Let j(x) = 6*x**2 - 1281*x + 1347. Let c(i) = -i**2 + 322*i - 337. Let l(r) = 9*c(r) + 2*j(r). Factor l(t).
3*(t - 1)*(t + 113)
What is h in 0 + 6/7*h - 1/7*h**2 = 0?
0, 6
Suppose 2*u**4 + 17*u + 20*u - 49*u + 14*u**3 - 16*u**2 + 12*u = 0. What is u?
-8, 0, 1
Let m(s) = -2*s**4 - 11*s**3 + 36*s**2 + 112*s + 64. Let b(h) = 3*h**4 + 10*h**3 - 37*h**2 - 112*h - 64. Let q(g) = 3*b(g) + 4*m(g). Factor q(z).
(z - 8)**2*(z + 1)**2
Let w(u) be the second derivative of u**4/102 + 380*u**3/51 + 36100*u**2/17 + 327*u. Factor w(y).
2*(y + 190)**2/17
Let x = 82944/5 + -16587. Find k such that 0*k - 3/5*k**5 + 3/5*k**4 + x*k**2 + 3*k**3 + 0 = 0.
-1, 0, 3
Suppose 5*i - 8*v + 5*v - 96 = 0, v + 102 = 5*i. Let a be (-7)/196 + 6/i. Factor 1/4 - 1/2*j + a*j**2.
(j - 1)**2/4
Let t = 433 - 430. Find b, given that 7/3*b - 7/3*b**3 - 11/3*b**2 + t*b**4 + 2/3 = 0.
-1, -2/9, 1
Let s = 11/152 - -5091/1064. Factor -8/7*z**3 + 8/7 + s*z**2 - 40/7*z.
-2*(z - 2)**2*(4*z - 1)/7
Suppose -5*s**3 - 95*s**2 + 25 - 51 + 26 = 0. Calculate s.
-19, 0
Solve -3 - 11/4*m + 1/4*m**2 = 0.
-1, 12
Let w(j) be the second derivative of j**7/42 + j**6/50 - 17*j**5/100 - 19*j**4/60 + 2*j**2/5 - 27*j. Factor w(x).
(x - 2)*(x + 1)**3*(5*x - 2)/5
Let j = -360 - -364. Let z(s) be the first derivative of -3 - 4/3*s + 4/9*s**3 + 1/6*s**j - 1/3*s**2. Factor z(h).
2*(h - 1)*(h + 1)*(h + 2)/3
Let d(q) = -3 + 4*q - 1 + 4*q**3 - 12*q**3 + 8*q**2. Let r(h) = -7*h**3 + 8*h**2 + 4*h - 5. Let y(u) = 3*d(u) - 4*r(u). Solve y(f) = 0.
-1, 1, 2
Let o(t) be the first derivative of -1/7*t**2 + 0*t + 8 + 1/21*t**3 + 1/28*t**4. Determine r, given that o(r) = 0.
-2, 0, 1
Let s(a) = a + 2. Let n be s(-14). Let z be (n/(-2))/((-48)/(-6)). Factor 0 + 3*c**5 + 0*c + 0*c**4 + z*c**2 - 9/4*c**3.
3*c**2*(c + 1)*(2*c - 1)**2/4
Let q = -1149 - -1149. Let r(s) be the third derivative of 1/105*s**7 + 10*s**2 + 1/24*s**4 + 0 + 1/80*s**6 - 3/40*s**5 + 0*s**3 + q*s. Factor r(p).
p*(p - 1)*(p + 2)*(4*p - 1)/2
Suppose 3*p - 26 = -4*u, -13 = -2*u - p - 1. Factor -146 - 43*z - 47*z + 551 + u*z**2.
5*(z - 9)**2
Let t(v) be the second derivative of -44*v + 0 + 121/4*v**2 + 1/24*v**4 + 11/6*v**3. Determine n, given that t(n) = 0.
-11
Let j(z) be the first derivative of -22 + 16*z - 44/3*z**3 + 40*z**2. Suppose j(k) = 0. What is k?
-2/11, 2
Let j(h) be the third derivative of -h**5/80 - 9*h**4/16 + 309*h**2. Factor j(q).
-3*q*(q + 18)/4
Factor -13 - 2 + 3*o**2 + 4 - 3*o + 5.
3*(o - 2)*(o + 1)
Suppose 0 = -0*h - 2*h - 2. Let k be h - (-3 + (-1 - -1)). Find s such that 2*s**2 + s - 2*s + s - k*s = 0.
0, 1
Let c(s) = -s**2 - 10*s + 10. Let d(f) = -f**2 - f - 1. Let w(o) = -c(o) + 2*d(o). Factor w(j).
-(j - 6)*(j - 2)
Let x(u) be the first derivative of -9*u**6/8 - 33*u**5/20 - 3*u**4/8 - 50. Determine r so that x(r) = 0.
-1, -2/9, 0
Let p(f) be the second derivative of f**5/100 + 3*f**4/20 + f**3/5 - 8*f**2/5 - 2*f - 449. Solve p(a) = 0 for a.
-8, -2, 1
Suppose 22/5*z**3 - 54/5*z**2 - 2/5*z**4 + 56/5 - 22/5*z = 0. What is z?
-1, 1, 4, 7
Let l(h) = -h**3 - 9*h**2 + 3*h + 6. Let c be l(-9). Let q be 192/210 - 6/c. Let 4/5 + q*v + 2/5*v**2 = 0. What is v?
-2, -1
Let r(t) be the first derivative of t**7/2240 - t**6/320 - 17*t**3/3 - 2*t + 3. Let q(m) be the third derivative of r(m). Suppose q(u) = 0. Calculate u.
0, 3
Let d be (-4)/10*(-110)/528*18. Factor 0*s + 0 - 3/2*s**3 - d*s**2.
-3*s**2*(s + 1)/2
Let s be -35*36/(-150) - (-8)/(-1). Suppose s*u**2 - 1/5*u**3 + 3/5*u + 0 = 0. Calculate u.
-1, 0, 3
Find b such that 3*b**5 + 496*b**3 + 789*b**2 - 67*b**3 - 1296*b**2 + 75*b**4 = 0.
-13, 0, 1
Let m(l) = -5*l**3 + 12*l**2 - 12. Let k(i) = 4*i**3 - 10*i**2 - i + 13. Let u(x) = 4*k(x) + 3*m(x). Suppose u(g) = 0. What is g?
-2, 2, 4
Let b(x) be the third derivative of -x**6/300 - x**5/25 - 11*x**4/60 - 2*x**3/5 + 2*x**2 + 275. Determine l, given that b(l) = 0.
-3, -2, -1
Let b(s) = -5*s**3 - 24*s**2 - 69*s - 42. Let i(z) = -z**3 + 3*z**2. Let y(t) = -b(t) + 2*i(t). Suppose y(v) = 0. What is v?
-7, -2, -1
Suppose -3*b - 5*b = -1080. Find l such that -24*l**4 + 87*l - 177*l**2 + 6*l**3 - 42 + 27 - 12*l**5 + b*l**3 = 0.
-5, 1/2, 1
Let a(g) be the third derivative of g**8/672 - g**6/120 + g**4/48 + 34*g**2. Factor a(l).
l*(l - 1)**2*(l + 1)**2/2
Let x = 562/2849 + 36/407. Factor 104/7*b + 36/7*b**2 - 2/7*b**3 - x*b**4 + 80/7.
-2*(b - 5)*(b + 2)**3/7
Suppose -5*w - 3*t = -10 - 25, 0 = -2*w + 4*t + 40. Suppose 4*s + s - w = 0. Factor 0 + 2/9*x**s - 4/9*x.
2*x*(x - 2)/9
Suppose -64 = -i - 4*p, 4*p - p = 5*i - 251. Let 8*s**2 + 28*s - 20*s**4 - i*s**3 - 3*s**5 - s**5 + 12 + 28*s**3 = 0. Calculate s.
-3, -1, 1
Determine o so that -28/3*o - 78*o**2 - 42*o**4 + 0 - 358/3*o**3 + 26/3*o**5 = 0.
-1, -2/13, 0, 7
Factor 31*q**3 + 24*q - 26*q - 29*q**3.
2*q*(q - 1)*(q + 1)
Let v(f) be the second derivative of f**8/6720 - f**7/840 + f**6/360 - 5*f**4/6 - 4*f. Let u(r) be the third derivative of v(r). Factor u(x).
x*(x - 2)*(x - 1)
Let x(j) = -j**2. Let p(a) be the second derivative of -4*a**3 + 31*a + 2. Let u(o) = p(o) + 4*x(o). Suppose u(w) = 0. What is w?
-6, 0
Suppose 0 = -x - 2*t + 10, -4*x + 47*t - 51*t = -24. Factor -4/5 - 32/5*d**3 + 24/5*d**x + 0*d + 12/5*d**4.
4*(d - 1)**3*(3*d + 1)/5
Suppose 3*p = 5*c + 9, -p + 154 - 151 = 5*c. Factor 6*n**2 + 3/2*n**4 + 0 + 6*n**3 + c*n.
3*n**2*(n + 2)**2/2
Suppose 4*y = -4*m + 28, y - m - 15 = -4*m. Let r be (42/(-20))/7 - (-28)/35. Factor 0 + 0*k - 3/4*k**y + r*k**2 + 1/4*k**4.
k**2*(k - 2)*(k - 1)/4
Let y = 58 + -55. Determine f, given that 3*f**2 - 11*f**4 - 15*f**2 + 14*f**4 + 0*f**3 + 9*f**y = 0.
-4, 0, 1
Let b(h) be the third derivative of 25*h**8/112 + 239*h**7/14 + 15319*h**6/40 + 24913*h**5/20 + 1610*h**4 + 1058*h**3 + 219*h**2. Determine w so that b(w) = 0.
-23, -1, -2/5
Let z(s) be the second derivative of -s**8/2240 + s**7/560 - s**6/480 + 5*s**3/2 + 13*s. Let r(f) be the second derivative of z(f). Factor r(p).
-3*p**2*(p - 1)**2/4
Let a(i) be the first derivative of 4/21*i**3 - 1/14*i**4 + 0*i - 1/7*i**2 + 8. Determine r so that a(r) = 0.
0, 1
Factor 4/3 - 2/9*r**3 - 4/3*r**2 + 2/9*r.
-2*(r - 1)*(r + 1)*(r + 6)/9
Factor -36992/9 + 544/9*i - 2/9*i**2.
-2*(i - 136)**2/9
What is n in 0 + 2*n**3 - 10/23*n**4 - 20/23*n**2 - 16/23*n = 0?
-2/5, 0, 1, 4
Determine p so that 2/13*p**2 + 20/13 + 14/13*p = 0.
-5, -2
Let q be -3*(30/(-72) - 2/8). Determine y, given that -14*y**2 - 5*y**2 + y**4 - 9*y**3 + 18 - 39*y + 48*y**q = 0.
1, 2, 3
Suppose -103 = -30*r + 126 - 49. Factor 15/2 + 57/2*k - r*k**2.
-3*(k - 5)*(4*k + 1)/2
Suppose -126 = -14*g + 16*g. Let v be (-170)/(-36) + -1 + (-49)/g. Determine h, given that -3/2*h**2 - 3 + v*h = 0.
1, 2
Let f(o) be the second derivative of o**7/3780 + o**6/216 + o**5/45 - 5*o**4/6 - 6*o. Let i(l) be the third derivative of f(l). Factor i(q).
2*(q + 1)*(q + 4)/3
Let d(l) = 6*l**3 + 169*l**2 + 716*l + 320. Let h(s) = -7*s**3 - 168*s**2 - 717*s - 320. Let f(y) = -3*d(y) - 4*h(y). Factor f(u).
5*(u + 8)**2*(2*u + 1)
Let t(f) be the second derivative of -1/12*f**3 + 0*f**2 - 2*f + 5/48*f**4 - 6 - 3/80*f**5. Let t(m) = 0. What is m?
0, 2/3, 1
Let z(h) = 14*h**3 + h**2 + 2*h - 2. Let x be z(1). Let w = x + -43/3. Factor -1/3*d - w*d**2 + 7/3*d**3 - 4/3*d**4 + 0.
-d*(d - 1)**2*(4*d + 1)/3
What is b in -7*b - 4 + 10*b**2 - 11/4*b**3 = 0?
-4/11, 2
Let c be (-6)/8 - (-488)/(-32). Let n be ((-2)/c)/((-2)/(-4)). Factor 0*z - 1/4*z**2 + n.
-(z - 1)*(z + 1)/4
Let r(l) be the first derivative of 4 - l**4 - 8/3*l**3 - 2*l**2 + 0*l. Factor r(u).
-4*u*(u + 1)**2
Suppose -5*b + 10 = 4*c - 4*b, -8 = -2*c - 2*b. Factor 6/5*q - 3*q**c - 3/5*q**4 + 0 + 12/5*q**3.
-3*q*(q - 2)*(q - 1)**2/5
Let b = -33822 - -33826. Suppose 98/23*s**b + 252/23*s**3 + 72/23*s + 218/23*s**2 + 8/23 = 0. What is s?
-1, -2/7
Let i(c) = c**3 - 4*c**2 - 15*c + 20. Let x(f) = -15*f**3 + 63*f**2 + 240*f - 321. Let y(t) = -33*i(t) - 2*x(t). Solve y(q) = 0.
-2, 1, 3
Factor -27/7 + 55/7*l + 1/7*l**3 - 29/7*l**2.
(l - 27)*(l - 1)**2/7
Let q(f) = f**4 - f**3. Let y(n) = 7*n**4 - 10*n**3 - 45*n**2 - 12*n + 60. Let i(o) = 4*q(o) - y(o). Factor i(w).
-3*(w - 5)*(w - 1)*(w + 2)**2
Factor 30*z**3 + 10*z**4 - 48*z**2 + 66*z**2 + 0*z**3 + 4*z**4