t l be b(p). Suppose 22*r**3 - 5*r**2 + 24*r**4 - 53*r**5 + 13*r**l - 7*r**3 + 6*r**4 = 0. What is r?
-1/2, 0, 1/4, 1
Let o(x) be the first derivative of x**5/15 + x**4/12 - 5*x**3/9 + x**2/2 - 157. Factor o(d).
d*(d - 1)**2*(d + 3)/3
Let s(j) = -2*j**3 + 19*j**2 - 15. Let f be s(-11). Suppose 4*c**2 + f*c**5 + 4*c - 8 - c**3 - 4*c**4 - 4947*c**5 + 6*c**2 = 0. Calculate c.
-2, 1
Let v(f) = f**2 - f + 7. Let b(p) = 4*p**3 - 144*p**2 + 396*p - 284. Let m(w) = -b(w) - 4*v(w). Find z such that m(z) = 0.
1, 2, 32
What is o in -5*o**3 + 1675*o + 142 + 830*o**2 - 761 + 1605 - 146 = 0?
-1, 168
Factor 1300/3 + 2/3*o**3 - 470/3*o + 32/3*o**2.
2*(o - 5)**2*(o + 26)/3
Suppose r = -70*y + 68*y - 2, -3*r + 4 = -4*y. Let m(u) be the third derivative of u**2 + 0 + 0*u + r*u**5 - 4/21*u**3 - 1/210*u**6 + 1/14*u**4. Factor m(n).
-4*(n - 1)**2*(n + 2)/7
Let x(c) = -c**2 - 189*c + 1372. Let r be x(7). Let p(f) be the second derivative of -19*f + 2/3*f**2 + r + 0*f**3 - 1/36*f**4. Factor p(j).
-(j - 2)*(j + 2)/3
Let t be 194/388*(1 + -1)/(-2). Let l(m) be the second derivative of -28*m + 5/6*m**4 + 10*m**2 + t - 1/4*m**5 + 35/6*m**3. What is y in l(y) = 0?
-1, 4
Suppose 0*v + 5*v = g + 1, 0 = -3*v + 4*g + 4. Suppose 5*q + 4*b = 2*b + 6, 0 = 2*q + 2*b. Factor v + 0*s + 2/7*s**4 + 0*s**q + 4/7*s**3.
2*s**3*(s + 2)/7
Let h(o) be the first derivative of -o**6/27 - 62*o**5/45 - 40*o**4/3 - 5220. Factor h(c).
-2*c**3*(c + 15)*(c + 16)/9
Suppose 0 = 76*u - 7049 + 6669. Let i(g) be the first derivative of 0*g**4 + g**u + 0*g + 0*g**2 - 19 + 0*g**3 - 5/18*g**6. Determine j, given that i(j) = 0.
0, 3
Suppose 12*m - 27*m + 30 = 0. Factor 18 - a**m + 88*a - 212*a + 107*a.
-(a - 1)*(a + 18)
Let 49/5*j**3 + 1403/5*j - 2116/5 + 1/5*j**4 + 663/5*j**2 = 0. Calculate j.
-23, -4, 1
Factor -675*v**2 - 114776 + 114788 + 73*v**2 + 1802*v.
-2*(v - 3)*(301*v + 2)
Let c(q) be the second derivative of -q**6/21 + 9*q**5/35 + 34*q**4/21 + 8*q**3/7 - 5*q + 60. Let c(z) = 0. Calculate z.
-2, -2/5, 0, 6
Factor 2151*y - 95*y**2 - 445 + 2119*y + y**3 - 3731*y.
(y - 89)*(y - 5)*(y - 1)
Let j(a) be the first derivative of -a**5/240 + 7*a**4/48 - 13*a**3/24 - a**2 + 7*a + 36. Let f(s) be the second derivative of j(s). Factor f(h).
-(h - 13)*(h - 1)/4
Factor -65*i + 512 - 60*i - 515*i - 12*i**3 - 184*i**2.
-4*(i + 8)**2*(3*i - 2)
Let c(x) be the first derivative of x**5/60 + x**4/12 - 5*x**3/2 - 5*x**2 - 104. Let p(g) be the second derivative of c(g). What is d in p(d) = 0?
-5, 3
Let f(x) be the first derivative of -x**5/25 - x**4/10 + 19*x**3/5 - 27*x**2/5 - 984. Factor f(y).
-y*(y - 6)*(y - 1)*(y + 9)/5
Let u = -10717 - -10719. Find y, given that -2/9*y - 1/9*y**4 + 2/9*y**3 - 1/3 + 4/9*y**u = 0.
-1, 1, 3
Find p, given that -34650*p - 626/7*p**3 - 6/7*p**4 - 3090*p**2 + 24500 = 0.
-35, 2/3
Let p(s) be the first derivative of s**4/6 - 88*s**3/9 - 241*s**2/3 - 392*s/3 - 3667. Solve p(u) = 0.
-4, -1, 49
Suppose 10 = -y + 4*k, -4*y + 5*k = 2 - 6. Solve -132*m - y - 39 - 5*m**2 + 14*m**2 = 0 for m.
-1/3, 15
Let n = 406254 + -406252. What is k in 8/7*k + 3/7*k**n - 3/7*k**5 + 13/7*k**4 - 17/7*k**3 - 4/7 = 0?
-2/3, 1, 2
Let y(n) be the first derivative of -n**5/390 - 3*n**4/52 + 22*n**3/39 - 9*n**2/2 + 98. Let c(b) be the second derivative of y(b). Factor c(i).
-2*(i - 2)*(i + 11)/13
Suppose 29*k = 25*k + 64. Solve -k*u - 6*u**2 - 40 - u**2 + 9*u**2 = 0 for u.
-2, 10
Let h(u) be the second derivative of -5*u**4 - 1/5*u**5 - 107*u - 48*u**2 + 0 - 76/3*u**3. Factor h(w).
-4*(w + 1)*(w + 2)*(w + 12)
Let t(n) = -n + 3*n**2 + 9*n - 1 - n - 6*n. Let h(o) = -10*o**2 + 3. Let i(l) = 2*h(l) + 6*t(l). Factor i(w).
-2*w*(w - 3)
Suppose 0 = -s + 2*b + 17, s - 4*s - b = -44. Suppose -5*p - i = -s, 0*p = -2*p + i + 13. Let -6*x**2 + 2*x**p - 5*x**4 - 21*x**3 + 15*x**4 = 0. What is x?
-1/4, 0, 2
Find j such that -12*j**3 + 2/5*j**4 - 90 + 12*j + 448/5*j**2 = 0.
-1, 1, 15
Let t = -4953275/1234 + 4014. Let q = 3697/6170 + t. Let 0*p + 9/5*p**4 + 6/5*p**3 + 0*p**2 + q*p**5 + 0 = 0. Calculate p.
-2, -1, 0
Let r(d) be the second derivative of -11*d**8/3360 + d**7/84 + d**6/180 - 3*d**3 + 4*d - 2. Let y(c) be the second derivative of r(c). Factor y(x).
-x**2*(x - 2)*(11*x + 2)/2
Let s(o) be the first derivative of -4/3*o**3 - 1/15*o**5 - 1/2*o**4 - 4/3*o**2 - 17 + o. Let v(f) be the first derivative of s(f). Factor v(x).
-2*(x + 2)**2*(2*x + 1)/3
Let a be -1 - ((-45)/30 - 9/6). Let t = -10 + 19. Let -131 - t*m + 9*m**3 + 131 - 3*m**a + 3*m**4 = 0. What is m?
-3, -1, 0, 1
Let j = -1113 - -1293. Let i be (j/(-1200))/(1/(-16)). Solve -3/5*w**2 + 36/5 - i*w = 0.
-6, 2
Let s(v) be the third derivative of 2/285*v**6 - 185*v**2 - 7/57*v**3 + 1/95*v**5 - 2/57*v**4 + 0 + 0*v + 1/1995*v**7. Determine o so that s(o) = 0.
-7, -1, 1
Suppose 9967*g = 9576*g + 1173. Solve 2/5*p**4 - 8/5*p**g - 8/5 + 8/5*p + 6/5*p**2 = 0 for p.
-1, 1, 2
Let z(y) be the third derivative of -y**2 - 20*y + 1/36*y**5 + 0 + 0*y**3 - 10/9*y**4. Let z(p) = 0. Calculate p.
0, 16
Let q(s) be the first derivative of -s**8/8400 + s**7/1050 - s**6/360 + s**5/300 + 26*s**3 - 53. Let y(m) be the third derivative of q(m). Factor y(k).
-k*(k - 2)*(k - 1)**2/5
Let k = -3263 - -9808/3. Let s(t) be the first derivative of 13/4*t**4 + 11/2*t**2 + 2*t + k*t**3 + 3/5*t**5 + 9. Factor s(i).
(i + 1)**2*(i + 2)*(3*i + 1)
Suppose -40 = -12*c - 16. Suppose 48*n - 36 = 36*n. Suppose -2/3*j**4 + 0 + 0*j**c + 0*j - 2/3*j**n = 0. Calculate j.
-1, 0
Let v = 2446/7 + -37516/105. Let j = -1414/195 - v. Let 2/13*t**2 + 8/13 + j*t = 0. What is t?
-2
Find h such that 5*h**3 + 4*h**2 + 0*h - 1/2*h**5 + 1/2*h**4 + 0 = 0.
-2, -1, 0, 4
Let f(k) be the second derivative of k**6/120 - 19*k**5/20 + 37*k**4/8 - 29*k**3/3 + 14*k + 2. Let x(m) be the second derivative of f(m). Factor x(z).
3*(z - 37)*(z - 1)
Let r(z) be the first derivative of z**5/20 + 1111*z**4/16 + 68635*z**3/2 + 12765925*z**2/2 + 12663250*z - 5888. Determine s, given that r(s) = 0.
-370, -1
Let a(g) be the second derivative of -2*g**7/63 + 2*g**6/45 + 59*g**5/60 + 47*g**4/18 + 53*g**3/18 + 5*g**2/3 - 216*g - 2. Find l, given that a(l) = 0.
-2, -1, -1/2, 5
Let u be 756/16*11/(165/(-40)). Let z be 1 + (-2)/(-30) - (-84)/u. Factor 8/5*n + 2/5*n**4 + 0 - z*n**2 - 8/5*n**3.
2*n*(n - 4)*(n - 1)*(n + 1)/5
Let z(o) be the second derivative of o**8/2240 + o**7/120 + o**6/15 + 3*o**5/10 - 49*o**4/12 + o - 39. Let q(p) be the third derivative of z(p). Solve q(l) = 0.
-3, -2
Let k be 16/(-40)*15 - 214/(-6). Let j = k + -85/3. Factor 4/3*y**2 - 4/3*y + 4/3*y**3 - j.
4*(y - 1)*(y + 1)**2/3
Factor 762 - 70*d + 10*d - d**2 - 912 - 17*d + 0*d**2.
-(d + 2)*(d + 75)
Suppose -2*r = r - 9, 0 = -5*h - 3*r + 24. Suppose -5*g - t + 8 = 0, -50*t + 48*t = 4*g - 4. Factor -18/5*l + 3/5*l**3 + 0 + h*l**g.
3*l*(l - 1)*(l + 6)/5
Let 1641 - 3/4*i**3 + 1638*i + 1629/4*i**2 = 0. What is i?
-2, 547
Let r = -2606 - -2613. Let s = 2 - 0. Factor -26*g**2 + 10*g + 19*g**s + 10*g**2 + 1 + r.
(g + 2)*(3*g + 4)
Let b be -2*(-3)/(-2) + (3 - -9). Let r be (-2)/((-14)/(-35)) + b. Solve -2/5*k - 4/5*k**2 + 0*k**3 + 4/5*k**r + 2/5*k**5 + 0 = 0 for k.
-1, 0, 1
Let l(r) be the second derivative of r**6/90 + 59*r**5/60 - 247*r**4/36 + 313*r**3/18 - 21*r**2 + 254*r + 6. Factor l(a).
(a - 2)*(a - 1)**2*(a + 63)/3
Suppose -2*q = -0*q - 10. Let s(h) = -275*h + 3650. Let i(d) = d**2 - 274*d + 3649. Let b(y) = q*i(y) - 4*s(y). Factor b(w).
5*(w - 27)**2
Factor -215*l + 184899/4*l**2 + 215*l**3 - 46225 + 1/4*l**4.
(l - 1)*(l + 1)*(l + 430)**2/4
Let n = 830 - 831. Let v(f) = -2*f**3 - f. Let r(o) = 28*o**3 - 55*o**2 + 39*o. Let z(i) = n*r(i) - 4*v(i). Factor z(j).
-5*j*(j - 1)*(4*j - 7)
Let q(v) be the first derivative of -v**5/4 - 5*v**4/6 + 5*v**3/6 + 5*v**2 + 120*v - 249. Let j(y) be the first derivative of q(y). Solve j(n) = 0 for n.
-2, -1, 1
Suppose -448*h - 384 - 18*h**3 - 1/2*h**4 - 162*h**2 = 0. What is h?
-24, -8, -2
Let o = 4426 - 4423. Let n(v) be the second derivative of 0*v**2 + 0 - 1/24*v**o - 1/48*v**4 + 5*v. Factor n(b).
-b*(b + 1)/4
Let k be 1431/424 - (-1 - 33/(-24)). Suppose -m = -3*d + 7, 0*m - 9 = 3*m - 5*d. What is h in -m*h**3 - 150*h - h**3 - 250 + h**k + 6*h**2 - 36*h**2 = 0?
-5
Let g(t) = 45*t**4 - 13790*t**3 + 1039680*t**2 + 165*t + 110. Let f(p) = 5*p**4 -