-t + 3. Suppose -5*p - 4*d + 8 = 0, 18 = l*p - 3*d - 7. Factor 3*n**2 + 2*n**4 - 5 + 5 + 3*n**3 - 3*n - 5*n**p.
-3*n*(n - 1)**2*(n + 1)
Let g be (12/42)/(1/21). Suppose -11*i + 15 = -g*i. Determine y, given that y - 12*y**2 - y**i + y**2 + 3*y**4 + 8*y**2 = 0.
-1, 0, 1/3, 1
Let p(h) = -9*h**2 + 25*h + 17. Let j(o) = -4*o**2 + 12*o + 9. Let y(m) = 7*j(m) - 3*p(m). Let f be y(10). Factor 8*w**4 + w**3 + 5*w**5 - 2*w**2 - w**2 + w**f.
w**2*(w + 1)**2*(5*w - 2)
Let w = 17565/4 + -4391. Solve -1/4*i**3 + w*i + 1/2 - 1/2*i**2 = 0 for i.
-2, -1, 1
Let q(y) be the third derivative of y**7/210 + y**6/60 - y**5/60 - y**4/12 + 8*y**2 - 19. Solve q(c) = 0 for c.
-2, -1, 0, 1
Let g(w) = -12*w + 770. Let j be g(64). Find l, given that 20/3*l**3 - 20*l**4 + 0 + 0*l**j + 0*l + 25/3*l**5 = 0.
0, 2/5, 2
Determine f, given that 2*f**5 + 0*f**5 + 44*f**4 + 118*f**3 - 528*f**2 + 242*f - 92*f**4 + 214*f**3 = 0.
0, 1, 11
Factor 0 + 1/2*a**2 + 47/2*a.
a*(a + 47)/2
Suppose -5*c = 5*z - 0*c - 10, -3*z - 2*c = -5. Factor -16*i - 3*i**2 - z - i**2 - 11.
-4*(i + 1)*(i + 3)
Factor -5*v**3 + 26*v**2 + 12*v**2 + 21*v**2 - 44*v**2.
-5*v**2*(v - 3)
Factor 1251 - 10139 + 48092 + m**2 + 396*m.
(m + 198)**2
Suppose -2*i + 6 = -58. Suppose 2*k = -6*k + i. What is u in -1/2*u**k + 0*u + u**3 + 0 - 1/2*u**2 = 0?
0, 1
Let w = 208772/5 + -41890. Let l = w + 136. Factor -2/5*o**2 + 2/5*o**4 + 0 + 2/5*o - l*o**3.
2*o*(o - 1)**2*(o + 1)/5
Let y(t) be the first derivative of -4*t**3/15 - 58*t**2/5 + 24*t + 79. Determine x, given that y(x) = 0.
-30, 1
Let t(l) = -l**3 - 12*l**2 + 12*l - 6. Let b(o) = 3*o**3 + 36*o**2 - 34*o + 17. Let g(k) = -6*b(k) - 17*t(k). Factor g(h).
-h**2*(h + 12)
Suppose -p + 4 - 1 = 0. Let j(z) be the second derivative of 0*z**p - 5*z + 0*z**2 + 1/12*z**4 + 0. Determine c so that j(c) = 0.
0
Let a(z) = z**2 + 11*z + 4. Let j be a(-10). Let n be (-8)/12*9/j. Suppose -17*b**2 - 2*b + 1 + 16*b**2 - n = 0. Calculate b.
-2, 0
Let s(j) be the second derivative of -1/120*j**4 + 3*j**2 - 1/30*j**3 - 5*j + 0 + 1/150*j**5. Let p(k) be the first derivative of s(k). Factor p(i).
(i - 1)*(2*i + 1)/5
Let x be 5*((-55)/(-22))/((-10)/(-4)). Let f(p) be the third derivative of -2*p**2 + 0 - 1/8*p**3 + 1/240*p**x + 0*p - 1/48*p**4. Solve f(z) = 0.
-1, 3
Let a(f) be the first derivative of -f**5/4 - 5*f**4/2 + 55*f**3/12 + 45*f**2/4 - 54. Factor a(z).
-5*z*(z - 2)*(z + 1)*(z + 9)/4
Let u(q) be the first derivative of 2/9*q**3 + 2/5*q**5 - 1/18*q**6 - 11/12*q**4 + 2*q**2 + 10 - 8/3*q. Factor u(c).
-(c - 2)**3*(c - 1)*(c + 1)/3
Let o(x) = -x**4 + x**3 - 4*x**2 - x - 1. Let l(c) = -2*c**4 + 4*c**3 - 13*c**2 - 4*c - 3. Let y(k) = -l(k) + 3*o(k). Let y(h) = 0. Calculate h.
-1, 0, 1
Let k = -15 - -15. Let n = 0 - k. Factor 17*s + 3*s - 16*s**2 + 4*s**3 + 4 - 12 + n*s**3.
4*(s - 2)*(s - 1)**2
Determine a, given that 0*a**3 - 14*a**2 - 144 + 4*a**3 - 6*a**2 - 213*a + 226*a - 141*a = 0.
-2, 9
Let d(l) = l**3 + l**2 - 2*l + 2. Let u(c) = -226*c**3 - 451*c**2 - 225*c + 4. Let a(s) = d(s) - u(s). Find y, given that a(y) = 0.
-1, 2/227
Factor 22/7*w**3 - 62/7*w**2 + 0 - 2/7*w**4 + 6*w.
-2*w*(w - 7)*(w - 3)*(w - 1)/7
Suppose 0 = -2*i + 5*y + 15, 4*i - 4*y + 15 = 27. Let w(j) be the first derivative of i*j**3 + 0*j**2 - 3 - 1/45*j**6 - 2/75*j**5 + 0*j + 0*j**4. Factor w(a).
-2*a**4*(a + 1)/15
Factor 79/4*t + 5*t**2 + 15 + 1/4*t**3.
(t + 1)*(t + 4)*(t + 15)/4
Suppose -4*l = 5 - 41. Let q = 13 - l. Factor -2*f**5 + 0*f**3 - 4*f**q + 4*f**5 - 3*f**3 + 5*f**3.
2*f**3*(f - 1)**2
Let t = -3212/39 + 1296/13. Solve -t*p + 16/3 - 14/3*p**2 = 0 for p.
-4, 2/7
Let g = -3159/35 - -452/5. Let s(r) be the third derivative of g*r**3 - 1/21*r**4 - 11*r**2 + 0 + 0*r + 1/210*r**5. Factor s(q).
2*(q - 3)*(q - 1)/7
Let j(g) be the first derivative of g**4/5 + 16*g**3/5 - 24*g**2 + 256*g/5 - 557. Find x such that j(x) = 0.
-16, 2
What is b in 84/5*b**4 + 6/5*b**2 + 99/5*b**3 + 3*b**5 + 0 - 24/5*b = 0?
-4, -1, 0, 2/5
Let s = 70 - 68. Solve 26 - 11 - 16*p - 29 - 2*p**s = 0 for p.
-7, -1
Let t(q) be the third derivative of q**7/70 + 11*q**6/20 + 121*q**5/20 - 2*q**2 + 2. Factor t(h).
3*h**2*(h + 11)**2
Let z(h) be the third derivative of 1/112*h**8 + 0 - 8*h**2 + 0*h**5 - 1/40*h**6 + 0*h + 0*h**4 + 0*h**7 + 0*h**3. Factor z(m).
3*m**3*(m - 1)*(m + 1)
Let x(a) = 6*a - 35. Let g be x(-7). Let v be 10/(-15) + (4 - g/(-24)). Find j such that 0 - 1/8*j**2 - v*j = 0.
-1, 0
Let y = 923/310 + -135/62. Let 6/5 - y*s - 2/5*s**2 = 0. What is s?
-3, 1
Let q(d) be the first derivative of -4*d**5/5 + 8*d**4 - 8*d**3 - 16*d**2 + 28*d - 745. What is u in q(u) = 0?
-1, 1, 7
Let 116/7*l**4 + 4/7*l**5 + 2344/7*l**2 + 2132/7*l + 1000/7*l**3 + 676/7 = 0. Calculate l.
-13, -1
Let f(h) = 4*h**2 - 212*h - 62. Let w(r) = 15*r**2 - 847*r - 248. Let k(j) = 26*f(j) - 6*w(j). Solve k(s) = 0.
-2/7, 31
Let s(g) = -2*g**2 - 4*g - 8. Let d(j) be the second derivative of -j**4/6 - j**3/2 - 4*j**2 + 12*j. Let y(z) = -4*d(z) + 5*s(z). Suppose y(h) = 0. What is h?
-2
Let i(w) = w**3 - 3*w**2 + 2*w + 6. Let u(m) = 2*m**3 - 5*m**2 + 4*m + 11. Let y(d) = 11*i(d) - 6*u(d). What is r in y(r) = 0?
-2, -1, 0
Let q(z) = 8*z**2 - 36*z + 170. Let j(f) = f**2 - 4*f + 19. Suppose 57 + 3 = 10*v. Let a(t) = v*q(t) - 52*j(t). Solve a(p) = 0.
-4, 2
Let x be (-1 - -11)/((-4)/(-2)). Let a be (x - -2) + 0 - 3. Determine f, given that -3*f**2 + 0*f**2 + f**3 - a*f**3 = 0.
-1, 0
Let u(m) = -19*m**3 + 47*m**2 - 52*m + 8. Let q(w) = 64*w**2 - 39*w**3 + 49*w**2 - 105*w - 20*w**2 + 15. Let c(z) = 4*q(z) - 9*u(z). Factor c(v).
3*(v - 2)*(v - 1)*(5*v - 2)
Factor -20*x**2 - 1523*x + 5*x**3 + 1523*x.
5*x**2*(x - 4)
Let i(q) be the second derivative of 0 - 1/15*q**3 + 6*q + 1/30*q**4 - 2/5*q**2. Factor i(o).
2*(o - 2)*(o + 1)/5
Let a(w) be the first derivative of -1/12*w**6 + 0*w**2 + 2/5*w**5 + 0*w + 11/8*w**4 - 51 + w**3. Let a(s) = 0. What is s?
-1, 0, 6
Factor 332/7*m**3 + 0*m**2 + 2/7*m**4 + 0*m + 0.
2*m**3*(m + 166)/7
Let i(n) be the second derivative of n**9/15120 - n**7/2520 + 11*n**4/12 + 20*n. Let z(u) be the third derivative of i(u). Solve z(w) = 0.
-1, 0, 1
Factor 361/8*j**3 - 17*j**4 - 225/8*j**2 - 27/8 - 189/8*j + 2*j**5.
(j - 3)**3*(4*j + 1)**2/8
Factor 104/7 + 8/7*a**2 + 212/7*a.
4*(a + 26)*(2*a + 1)/7
Let 18 - 5*d**3 + 3*d - 19*d**2 + 2*d**3 + 3*d**4 - 25*d**2 + 23*d**2 = 0. Calculate d.
-2, -1, 1, 3
Let p(q) = -q**2 - 12*q + 19. Let r(m) = -12*m + 21. Let k(b) = -3*p(b) + 2*r(b). Factor k(l).
3*(l - 1)*(l + 5)
Let b(u) be the third derivative of u**5/12 + 5*u**4/12 - 5*u**3/2 - 332*u**2. Factor b(q).
5*(q - 1)*(q + 3)
Let j(l) be the third derivative of l**9/15120 - l**8/6720 - l**7/2520 + l**6/720 + 5*l**4/8 - 8*l**2. Let i(f) be the second derivative of j(f). Factor i(n).
n*(n - 1)**2*(n + 1)
Let q be (2 + 1 - 3) + -1. Let y be 0*(q - (2 + -2)). Factor -7*g + 3*g**2 + y*g**3 - g**3 + 4*g**3 + g.
3*g*(g - 1)*(g + 2)
Let t(w) = w**3 + 2*w**2 - 7*w + 6. Let u be t(-4). Factor -5*k**u + 3*k**2 + 31*k + 14 - 19*k.
-2*(k - 7)*(k + 1)
Factor -30*y**2 + 312*y - 4056/5.
-6*(5*y - 26)**2/5
Let m be ((-16)/(-5))/(18/135). Factor m*g**3 + 2763*g**2 - 2779*g**2 - 16*g**4 + 3*g**5 + 4*g + g**5.
4*g*(g - 1)**4
Let v = -4779 - -4781. Factor 27/5*l**v + 0 - 6/5*l.
3*l*(9*l - 2)/5
Find r such that 11*r**3 + 25*r + 24*r**2 + 14*r - 3*r - 3*r**4 - 14*r**3 = 0.
-2, 0, 3
Let m be 10*(12 - 230/20). Factor -3/7*t**3 - 1/7*t**2 - 1/7*t**m - 3/7*t**4 + 0*t + 0.
-t**2*(t + 1)**3/7
Let i = 20493 + -20491. Suppose 4/11 - 14/11*n + 2/11*n**4 + 18/11*n**i - 10/11*n**3 = 0. What is n?
1, 2
Factor -2*u + 5*u**2 + 80 + 9*u - 64*u - 28*u.
5*(u - 16)*(u - 1)
Let w be 5/((-800)/632) - -4. Let y(t) be the third derivative of -1/30*t**5 + 0*t + 5/36*t**4 + 0 - w*t**6 - 1/9*t**3 + 4*t**2. Find l such that y(l) = 0.
-1, 1/3
Let y(j) = 3*j**4 - 5*j**3 - 4*j**2 + j - 5. Let z(v) = 3*v**4 - 6*v**3 - 3*v**2 - 6. Let h(t) = 6*y(t) - 5*z(t). Determine c, given that h(c) = 0.
-2, 0, 1
Let h(s) be the third derivative of -s**6/60 + s**5/6 - s**4/2 + 107*s**2 + s. Find w such that h(w) = 0.
0, 2, 3
Let i(w) = -w**2 + 13. Let f be i(0). Determine t so that 6 - 1 + f*t**2 + 2*t**2 - 8*t - 12*t = 0.
1/3, 1
Let r be (-1)/(4/(-24)) - 0. What is s in -r*s**3 - 9*s**2 + 7*s**2 + s**3 = 0?
-2/5, 0
Let u(i) be the second