(s) = d(s) - 30*o(s). Let j(u) = 0. What is u?
-8, 1
Solve 2/3*h + 0 + 2/9*h**3 + 8/9*h**2 = 0.
-3, -1, 0
Let k = -8 - -8. Let n(x) be the first derivative of 1 + 6*x**2 - 3 - 3*x - 3*x**2 - x**3 + k*x**3. Suppose n(p) = 0. What is p?
1
Let s(f) = 74*f**3 - 11468*f**2 + 5725*f - 697. Let x(p) = -445*p**3 + 68810*p**2 - 34350*p + 4185. Let k(b) = 35*s(b) + 6*x(b). Factor k(j).
-5*(j - 143)*(4*j - 1)**2
Let s(a) be the second derivative of 2/75*a**5 - 1/450*a**6 - 1/10*a**4 + 0*a**2 - 5*a + 0 - 2/3*a**3. Let h(d) be the second derivative of s(d). Factor h(q).
-4*(q - 3)*(q - 1)/5
Let a = 75 - 147/2. Let f = 135/2 - 267/4. Suppose f*n**2 + 3/4 + a*n = 0. Calculate n.
-1
Factor -289*j**2 + 32*j + 4*j + 165*j**2 + 126*j**2.
2*j*(j + 18)
Let j(n) be the first derivative of -n**6/15 + 42*n**5/25 - 27*n**4/2 + 478*n**3/15 + 72*n**2/5 - 648*n/5 + 96. Suppose j(z) = 0. What is z?
-1, 2, 9
Let j be 478/(-160) + 1 + 2. Let o(y) be the second derivative of -7*y - 1/48*y**4 + 1/24*y**3 - j*y**5 + 1/120*y**6 + 0 + 0*y**2. Factor o(x).
x*(x - 1)**2*(x + 1)/4
Let a(m) = m**2 + 5*m + 6. Let f be a(-4). Find l, given that l**5 - 19*l**f + 19*l**2 + 4*l**3 - 6*l**4 + l**5 = 0.
0, 1, 2
Suppose -3*m - 2 = -4*m. Let g(b) = -b. Let r(k) = 2*k**3 + 6*k**2 + 20*k - 6. Let l(j) = m*r(j) + 44*g(j). Factor l(v).
4*(v - 1)*(v + 1)*(v + 3)
Let d(r) be the third derivative of r**8/168 - 2*r**7/35 + 3*r**6/20 + 2*r**5/15 - r**4 + r**2 - 139. What is o in d(o) = 0?
-1, 0, 2, 3
Let f(a) be the first derivative of -3*a**5/10 + 111*a**4/4 - 1213*a**3/2 - 4329*a**2 - 9126*a + 423. Factor f(u).
-3*(u - 39)**2*(u + 2)**2/2
Let o(f) be the second derivative of f**8/1120 - f**7/224 + f**6/120 - f**5/160 + 13*f**3/2 + 21*f. Let w(p) be the second derivative of o(p). Factor w(i).
3*i*(i - 1)**2*(2*i - 1)/4
Let p(t) = 6*t**2 + 139*t - 4384. Let c(q) = -5*q**2 - 138*q + 4380. Let s(k) = -7*c(k) - 6*p(k). Factor s(b).
-(b - 66)**2
Let c(m) be the third derivative of m**5/120 - m**4/8 + 3*m**3/4 + 56*m**2 - 2. Factor c(h).
(h - 3)**2/2
Let p(w) be the second derivative of -w**4/18 + 16*w**3/9 - 5*w**2 - 100*w. Factor p(q).
-2*(q - 15)*(q - 1)/3
Factor -17787/4*b - 231/4*b**2 - 456533/4 - 1/4*b**3.
-(b + 77)**3/4
Let x(t) = 5*t**3 - 87*t**2 + 148*t + 4. Let d(l) = 85*l**3 - 1480*l**2 + 2515*l + 70. Let a(y) = -2*d(y) + 35*x(y). Suppose a(s) = 0. Calculate s.
0, 2, 15
Factor 10/3 + 17/3*q + q**2 - 1/3*q**4 - 5/3*q**3.
-(q - 2)*(q + 1)**2*(q + 5)/3
Determine r, given that 3*r**3 - 75/4*r**2 + 39/2*r - 15/4 = 0.
1/4, 1, 5
Let g = 800 - 793. Let i(h) be the second derivative of -2*h + 1/6*h**4 - 1/42*h**g + h**2 - 2/15*h**6 - 1/5*h**5 + 0 + 5/6*h**3. Suppose i(w) = 0. Calculate w.
-2, -1, 1
Let l(f) be the first derivative of -f**5/100 + f**4/10 - 2*f**3/5 - 11*f**2/2 - 12. Let b(s) be the second derivative of l(s). Factor b(a).
-3*(a - 2)**2/5
Let t(q) be the second derivative of -3*q**5/20 - 127*q**4/12 - 80*q**3/3 + 82*q**2 + 3*q - 20. What is p in t(p) = 0?
-41, -2, 2/3
Let f be ((-3)/(-21)*12)/(4/(-308)*-33). Suppose -6/13*u**2 + 2/13*u**f - 8/13 - 4/13*u**3 + 16/13*u = 0. Calculate u.
-2, 1, 2
Suppose 2*x = -x + 15. Let b(o) = -2*o**2 + 15*o - 45. Let l(m) = 2*m**2 - 16*m + 46. Let q(g) = x*l(g) + 4*b(g). What is u in q(u) = 0?
5
Let a(p) = -p - 4. Let m be a(-6). Factor 4*f + 3 - f**2 + 3*f**m - 2*f**2 + f**2.
(f + 1)*(f + 3)
Factor 44/9*z**2 + 4 - 4/9*z**3 - 76/9*z.
-4*(z - 9)*(z - 1)**2/9
Let 3/2*c**4 - 51/2*c - 15 + 15/2*c**3 - 9/2*c**2 = 0. What is c?
-5, -1, 2
Find m such that 10/11*m + 128/11*m**4 - 42/11*m**5 - 4/11 + 36/11*m**2 - 128/11*m**3 = 0.
-2/7, 1/3, 1
Let f = -27 + 30. Factor -h**5 + 0*h - 18*h**f + 0*h + 19*h**3.
-h**3*(h - 1)*(h + 1)
Factor -280/9*r**4 + 0 - 16/9*r**5 - 44*r**3 - 32/9*r - 194/9*r**2.
-2*r*(r + 16)*(2*r + 1)**3/9
Factor 34*c**3 + 5 + 56*c**3 - 5 - 190*c + 106*c**2 - c**2 - 5*c**4.
-5*c*(c - 19)*(c - 1)*(c + 2)
Let b(i) be the third derivative of i**6/30 + i**5/5 + i**4/3 - 8*i**2 + 2*i. Factor b(j).
4*j*(j + 1)*(j + 2)
Let k(v) be the first derivative of 6*v**5/25 + 3*v**4/10 - 18*v**3/5 + 33*v**2/5 - 24*v/5 + 202. Factor k(d).
6*(d - 1)**3*(d + 4)/5
Let s(c) = 28*c**3 + 16*c**2 - 12. Let d(f) = 78*f**3 + 49*f**2 - f - 38. Let q(z) = 4*d(z) - 11*s(z). Factor q(w).
4*(w - 1)*(w + 1)*(w + 5)
Let n be 10/(-30)*(-8 + (-924)/(-120)). Solve n*b**2 - 3/5 + 1/10*b = 0 for b.
-3, 2
Let l be 2/4 + (-9)/(-6). Find r such that 307 - 309 + 3*r**2 - 2*r + 2*r**3 - r**l = 0.
-1, 1
Let z(c) be the third derivative of -1/30*c**6 + 0*c**5 + 1/6*c**4 - 4*c**2 + 0 + 0*c + 0*c**3. Factor z(q).
-4*q*(q - 1)*(q + 1)
Suppose -h = 4*m - 12 - 15, 5*m = 15. Let y = h + -12. Factor -2 - 7*d**2 + 2*d - 2*d**3 - 8*d + 0*d**y + d**2.
-2*(d + 1)**3
Let z be (36/42)/((-4)/(-14)). Find v, given that 7 + 2*v**4 + v**5 - 2 - 5 - z*v**3 = 0.
-3, 0, 1
Let l(h) = -h**3 + 2*h**2 + 5*h - 5. Let d be l(2). Let a be (-1)/5*(d - (-260)/(-16)). Solve 3/4 + a*r + 9/4*r**2 + 3/4*r**3 = 0 for r.
-1
Let x(q) be the first derivative of -q**4/12 - 5*q**3/9 + q**2/6 + 5*q/3 + 574. Factor x(t).
-(t - 1)*(t + 1)*(t + 5)/3
Let p(j) be the second derivative of -j**7/21 - j**6/15 + 9*j**5/10 - 11*j**4/6 + 4*j**3/3 + 252*j. Let p(l) = 0. What is l?
-4, 0, 1
Factor 2/13*p**3 - 392/13 + 448/13*p - 58/13*p**2.
2*(p - 14)**2*(p - 1)/13
Let r be (166 - 167)/(20/(-8)). Factor 0 - 2/5*v**4 + 2/5*v**2 + r*v - 2/5*v**3.
-2*v*(v - 1)*(v + 1)**2/5
Let i(t) = 13*t**2 + 16*t - 5. Let d(c) = 32*c**2 + 40*c - 12. Let n(b) = -5*d(b) + 12*i(b). Factor n(z).
-4*z*(z + 2)
Let 4/7*v**4 + 64/7 + 40/7*v**3 + 132/7*v**2 + 160/7*v = 0. What is v?
-4, -1
Factor 54/7*q**3 + 2/7*q**4 + 146/7*q + 150/7*q**2 + 48/7.
2*(q + 1)**3*(q + 24)/7
Factor -1/2*i**3 - 88 - 52*i - 19/2*i**2.
-(i + 4)**2*(i + 11)/2
Determine c, given that -16/11*c + 2/11*c**2 + 0 = 0.
0, 8
Suppose -4*h - 2*q = q - 21, 3*h - 5*q = -6. What is d in 5*d**2 + 2*d + 240*d**4 - 4*d + 11*d**h - 236*d**4 = 0?
-2, -1, 0, 1/4
Let i(p) be the first derivative of -5*p**3 - 24*p**2 - 192*p/5 + 43. Find z, given that i(z) = 0.
-8/5
Let h(o) be the first derivative of 2*o**3/21 - 6*o**2/7 - 2*o + 248. Factor h(c).
2*(c - 7)*(c + 1)/7
Find r, given that 0*r**2 + 0*r + 0 + 2/9*r**4 + 2/9*r**5 - 4/9*r**3 = 0.
-2, 0, 1
Let o(i) be the third derivative of 1/4*i**5 + 0 + 0*i**3 - 1/6*i**4 + 0*i + 30*i**2 - 7/240*i**6. Factor o(w).
-w*(w - 4)*(7*w - 2)/2
Let t(m) = m**3 - 128*m**2 - 131*m + 283. Let k be t(129). Let 5/2 - 55/2*h**4 + 75/4*h**5 + 75/4*h - 75/2*h**3 + k*h**2 = 0. Calculate h.
-1, -1/3, -1/5, 1, 2
Let g(v) be the second derivative of v**5/70 + 17*v**4/21 + 289*v**3/21 - 13*v - 2. Factor g(m).
2*m*(m + 17)**2/7
Suppose c + 3 = 5*h - h, 3*c - 15 = 0. Suppose -2*m = -3*m + h. Factor -4*o**3 + o**2 - o**3 + 5*o**3 + o**4 - m*o**3.
o**2*(o - 1)**2
Let j(w) be the third derivative of -7*w**5/60 - 11*w**4/24 - 5*w**3/6 + 15*w**2. Let t(x) = 3*x**2 + 6*x + 3. Let n(r) = 3*j(r) + 5*t(r). Factor n(f).
-3*f*(2*f + 1)
Factor 0*k**2 + 0*k + 0 - 3/2*k**4 + 0*k**3 + 1/4*k**5.
k**4*(k - 6)/4
Find r such that -97 - 46*r + r**3 + 262 + 5*r**2 - 125 = 0.
-10, 1, 4
Let t = 18893/4 + -4723. Solve -t*p + 1/4*p**4 - 3/4*p**3 + 0 + 3/4*p**2 = 0.
0, 1
Let y = 4345 + -4339. Determine g, given that -45/2*g**3 - 24*g**2 - 9/2*g - y*g**4 + 3 = 0.
-2, -1, 1/4
Determine d so that 0 - 27/2*d**3 - 24*d - 36*d**2 - 3/2*d**4 = 0.
-4, -1, 0
Factor -1/3*u**2 - 4/3*u + 1/3*u**3 + 4/3.
(u - 2)*(u - 1)*(u + 2)/3
Let a(m) = 41*m - 94*m + 2*m**2 + 49*m + 3. Let x(o) = -8*o**2 + 17*o - 13. Let p(n) = -26*a(n) - 6*x(n). Let p(g) = 0. What is g?
0, 1/2
Let c be 0/2*27/(-540)*10. Find x such that -2/7*x**3 + 2/7*x**2 - 2/7*x**4 + 2/7*x + c = 0.
-1, 0, 1
Determine q, given that -69/2*q - 3/4*q**2 - 135/4 = 0.
-45, -1
Suppose -5*p - 11 = -2*b, 2*p - 3 = 3. Let f = 16 - b. Determine o, given that -5*o**f + 3*o**3 + 3 - 3 + 2*o = 0.
-1, 0, 1
Suppose 4*w - 15*i - 25 = -20*i, 3*i = 3*w + 15. Find g, given that w - 4/5*g**2 - 12/5*g = 0.
-3, 0
Factor 8/7 - 2/7*c**2 + 0*c.
-2*(c - 2)*(c + 2)/7
Suppose -2*p + 9 = -k, 0 = -5*p + 4*p - 2*k - 3. Suppose 3*z - 3*z**p + 4*z**2 + 0 - 3 - z**2 = 0. What is z?
-1, 1
Let j be 390/91 + ((-36)/(-21) - 2). Let w(k) be the first derivative of 4*k**2 + 5 - 3/2*k**j + 0*k**3 + 2/5*k**5 + 0*