*c**3/9 + 457*c**2 + 984*c - 516. Factor q(f).
(f + 3)**2*(f + 4)*(f + 82)/3
Let r be (-53)/55 - (-31395)/23023. Factor 126/5 + 66/5*g - r*g**3 + 2/5*g**2.
-2*(g - 7)*(g + 3)**2/5
Let t(a) = -75*a - 372. Let n be t(-7). Let y be (-18)/n - 261/(-918). Factor y*i**5 + 5/2*i**4 + 20*i + 25/2*i**3 + 6 + 145/6*i**2.
(i + 1)**3*(i + 6)**2/6
Let o be (-34)/12 + 3 - 17/((-11220)/130). Let p(x) be the first derivative of -o*x - 14/33*x**3 + 15/11*x**2 - 17. Let p(h) = 0. What is h?
1/7, 2
Solve 184 - 1/3*o**3 - 410/3*o - 47*o**2 = 0.
-138, -4, 1
Let p(w) be the second derivative of w**7/168 - 23*w**6/120 + 41*w**5/40 - 59*w**4/24 + 77*w**3/24 - 19*w**2/8 - 613*w + 3. Factor p(t).
(t - 19)*(t - 1)**4/4
Let s be (224/(-170) - (-114)/969) + (-63)/(-15). Let 4/9*c + 1/9*c**s + 0 + 5/9*c**2 = 0. What is c?
-4, -1, 0
Suppose -35*g + 3 = -30*g + 2*v, -g = 96*v + 2007. Find d, given that -3/2*d**4 + 27/2 - 39*d + 36*d**2 - g*d**3 = 0.
-9, 1
Suppose r - 40 = -5*j, 2851*r - 5*j = 2850*r - 40. Suppose -1/7*w**5 - 8/7*w**3 + 0*w + 5/7*w**4 + r + 4/7*w**2 = 0. Calculate w.
0, 1, 2
Suppose -4*l - 9 = -7*l. Solve 15*s**3 + 3*s**2 + 5*s**3 - 11*s**l = 0 for s.
-1/3, 0
Let n(x) = x**3 + 28*x**2 - 18 + 22 - 34*x**2 + 9*x - 56. Let k be n(6). Factor -1/2*q + 0 + 1/4*q**k.
q*(q - 2)/4
Let j(q) be the third derivative of -5*q**2 + 1/140*q**5 + q + 0 + 1/8*q**4 - 9/7*q**3. Factor j(m).
3*(m - 2)*(m + 9)/7
Let c(b) = 3*b + 2. Let y be c(0). Let i = 2 + y. Factor -24*p - 3*p**2 - 3*p**3 + 15*p + 0*p**3 + 12*p + 3*p**i.
3*p*(p - 1)**2*(p + 1)
Let k(f) be the second derivative of 31 - 9*f**2 + f - 1/20*f**5 + 35/6*f**3 - 4/3*f**4. Factor k(d).
-(d - 1)**2*(d + 18)
Let m = -987 + 755/2. Let s = -5903/10 - m. Factor 144/5*i + 6/5*i**3 + s + 54/5*i**2.
6*(i + 1)*(i + 4)**2/5
Let f(c) be the first derivative of -5*c**4/4 - 125*c**3/3 + 5*c**2/2 + 125*c - 409. Determine l so that f(l) = 0.
-25, -1, 1
Suppose -8098347/4 + 4929/2*i - 3/4*i**2 = 0. Calculate i.
1643
Let d = 1/8323 - -24967/16646. Let x(h) be the first derivative of -9*h - 3*h**2 + 4*h**3 - 17 + d*h**4 - 3/5*h**5. Factor x(q).
-3*(q - 3)*(q - 1)*(q + 1)**2
Suppose -32*b = 32*b + 384. Let z be 2672/120 - (-4)/b. Factor 36*x**3 + 69/5*x**2 - z*x**4 + 6/5*x + 0.
-3*x*(x - 2)*(6*x + 1)**2/5
Let x = 4563/216085 - 7/1879. Let r(d) be the first derivative of -x*d**5 + 0*d**2 + 11 + 1/46*d**4 + 0*d + 2/69*d**3 - 1/69*d**6. Factor r(a).
-2*a**2*(a - 1)*(a + 1)**2/23
Find a such that 675 - 17*a - 685*a + 290 - 245*a - 5*a**2 - 13*a = 0.
-193, 1
Factor -16 + 1/3*g**2 + 47/3*g.
(g - 1)*(g + 48)/3
Factor -312/7*d**2 - 86/7*d**3 + 0*d + 0 - 2/7*d**4.
-2*d**2*(d + 4)*(d + 39)/7
Let v(g) be the third derivative of -2/105*g**7 + 1/12*g**4 + 0 + 0*g**3 - 1/60*g**6 + 0*g + 173*g**2 + 1/15*g**5. Factor v(j).
-2*j*(j - 1)*(j + 1)*(2*j + 1)
Let i(u) = -38*u**3 + 1696*u**2 - 44922*u. Let b(l) = 10*l**3 - 424*l**2 + 11230*l. Let o(j) = -11*b(j) - 3*i(j). Factor o(w).
4*w*(w - 53)**2
Let k(s) = -14*s - 54. Let z be k(-11). Suppose 6687*n + 32 + 131*n**4 + 836*n**3 - 6447*n + 664*n**2 + 349*n**4 + z*n**5 = 0. Calculate n.
-2, -1, -2/5
Let f = -4295/22 - -37447/110. Factor -231/5*r - 3/5*r**3 - 12*r**2 + f.
-3*(r - 2)*(r + 11)**2/5
Let x(i) be the third derivative of -i**5/15 - 91*i**4/6 - 356*i**3/3 + 695*i**2. Factor x(a).
-4*(a + 2)*(a + 89)
Let v be (10/12)/((3 - -1)/24). Factor 10*i**2 - 22 + 60*i + 162*i**3 + 30*i**4 - 217*i**3 - 18 - 5*i**v.
-5*(i - 2)**3*(i - 1)*(i + 1)
Let c(j) be the third derivative of -j**2 + 5/672*j**8 + 0*j**7 - 1/24*j**6 + 0*j**3 - 20 + 5/48*j**4 + 0*j**5 + 0*j. Solve c(z) = 0.
-1, 0, 1
Find a such that 28*a - 150 + 11988*a**3 - 5*a**4 + 187*a - 12063*a**3 + 15*a**2 = 0.
-15, -2, 1
Let m(n) be the first derivative of 7*n**3/15 - 11*n**2/2 + 42*n/5 + 1008. Factor m(z).
(z - 7)*(7*z - 6)/5
Let n be (0 + 1)/((-154)/(-56)). Let z be 4*(2 - 3)*38/(-418). Factor z - 2/11*m**3 + 2/11*m - n*m**2.
-2*(m - 1)*(m + 1)*(m + 2)/11
Factor 24*q**4 - 80*q**3 - 6*q**3 + 5*q - 86*q - 1144*q**5 + 1143*q**5 + 20 + 124*q**2.
-(q - 20)*(q - 1)**4
Let a(m) = m**2 + m. Let h(x) be the second derivative of -x**5/4 + 10*x**4/3 + 55*x**3/6 - 25*x**2 - 9*x. Let l(f) = 20*a(f) - h(f). Factor l(p).
5*(p - 5)*(p - 1)*(p + 2)
Let a be 33/(-132) + (1088/(-160))/((-8)/5). Factor 6/5*k**3 - 14/5*k + 2/5*k**a - 6/5*k**2 + 12/5.
2*(k - 1)**2*(k + 2)*(k + 3)/5
Suppose 1089*u + 33 = 1100*u. Let g(n) be the first derivative of -1/55*n**5 + 0*n**u + 0*n**2 - 1/44*n**4 + 0*n + 3. Suppose g(v) = 0. What is v?
-1, 0
Let t = 2202 + -13211/6. Let v(y) be the third derivative of 0*y - t*y**3 + 5*y**2 + 0 - 1/240*y**5 + 1/24*y**4. Factor v(q).
-(q - 2)**2/4
Let x(m) be the first derivative of -m**4/5 - 132*m**3 + 992*m**2/5 + 1859. Suppose x(g) = 0. What is g?
-496, 0, 1
Let v(r) be the second derivative of -r**5/70 - 15*r**4/14 - 27*r**3 - 2187*r**2/7 + 5871*r. Solve v(y) = 0.
-27, -9
Let d(z) be the second derivative of 2*z**3 - 9/20*z**5 + 0*z**2 - 1 + 0*z**4 + 7*z + 1/10*z**6. Factor d(m).
3*m*(m - 2)**2*(m + 1)
Factor 16*s + 127198 + 8*s - 127126 + 49*s - s**3.
-(s - 9)*(s + 1)*(s + 8)
Suppose -1087*o - 582*o + 17020 = 1988*o + 598*o. Find d, given that -704/23*d**2 - 2/23*d**o - 64/23*d**3 - 4608/23 - 3072/23*d = 0.
-12, -4
Let r(x) be the third derivative of 7*x - 2/39*x**4 - 1/1365*x**7 + 0 - 4*x**2 + 4/39*x**3 + 1/390*x**6 + 1/130*x**5. What is t in r(t) = 0?
-2, 1, 2
Let v(n) = -n**3 - n**2 + 27*n + 40. Let y be v(-5). Suppose 12*s + y*s - 51 = 0. Factor -1/5*u + 0 - 2/5*u**2 - 1/5*u**s.
-u*(u + 1)**2/5
Factor -85/2*d + 3/4*d**2 - 57/4.
(d - 57)*(3*d + 1)/4
Suppose -18*x + 147 - 147 = 0. Let k(z) be the third derivative of 0*z**3 + 1/210*z**5 + x - 1/84*z**4 + 0*z - 10*z**2. Suppose k(u) = 0. Calculate u.
0, 1
Let w = 3 - -1. Suppose -z - 14 = w*r - 1, z - 7 = r. Suppose 32*c + 16 - 6*c**5 - 20*c**4 - 28*c**z + 0*c**2 + 2*c**5 - 4*c**2 + 8*c**2 = 0. Calculate c.
-2, -1, 1
Let h = 163475 - 490423/3. Suppose -h*o**2 + 10/3*o - 4 = 0. What is o?
2, 3
Let h be 7*6*(-90)/(-27). Let v be 928/h - 3 - 16/(-28). Suppose 6/5 + 27/5*o**2 + 3*o**3 + v*o + 3/5*o**4 = 0. What is o?
-2, -1
Let a(z) = -3 - z**4 + 278*z + 13*z**2 - 566*z + 285*z. Let m(c) = -12*c**2 + 4*c + 4. Let g = 10 + -7. Let w(i) = g*m(i) + 4*a(i). Factor w(x).
-4*x**2*(x - 2)*(x + 2)
Let o be (-10 + 3)*2 - 26080/(-978). Factor 28/3 - 2*f**2 + 2/3*f**4 - o*f + 14/3*f**3.
2*(f - 1)**2*(f + 2)*(f + 7)/3
Let o be 1*-2*((-1070)/(-60) + -18). Let u(h) be the first derivative of -h - o*h**3 - 11 - h**2. Factor u(z).
-(z + 1)**2
Suppose -17*t - 9564 + 9632 = 0. Let b(q) be the second derivative of 1/70*q**5 + 4/21*q**3 + 0 + 0*q**2 + 2/21*q**t - 22*q. Factor b(f).
2*f*(f + 2)**2/7
Let y = -182872/13 - -14080. Let z = 1202/91 - y. Determine v so that z - 4/7*v - 6/7*v**2 = 0.
-1, 1/3
Let p(u) be the second derivative of -68*u - 4*u**2 + 2*u**3 + 0 - 1/3*u**4. Solve p(h) = 0 for h.
1, 2
Suppose 17 = -5*i + 5*k - 38, -2*i = k + 22. Let u = i + 14. Suppose -3*c**2 - c**4 + 4 + 33*c - c**3 - u*c**3 - 29*c = 0. Calculate c.
-2, -1, 1
Factor 0 - 144/5*w - 39/5*w**2 + 3/5*w**3.
3*w*(w - 16)*(w + 3)/5
Let x(u) be the second derivative of 1/12*u**2 + 0*u**3 + 0 - 1/72*u**4 + 57*u. Factor x(h).
-(h - 1)*(h + 1)/6
Suppose 2*o + 23 = 17. Let g be 5 + (o - -2) + 4. Let m(q) = 11*q**2 + q. Let k(l) = -7*l**2 - l. Let d(x) = g*k(x) + 5*m(x). Solve d(a) = 0 for a.
-3, 0
Let c = -195 + 199. What is k in -25*k**c - 4*k**2 + 29*k**4 - 7*k**5 - 8*k - 53*k**5 + 68*k**3 = 0?
-1, -1/3, 0, 2/5, 1
Let l(s) = -95*s - 377. Let h be l(-4). Let n(d) be the first derivative of 3/4*d**4 + 3/10*d**5 + 6*d - 3/2*d**3 - h - 3*d**2. Factor n(j).
3*(j - 1)**2*(j + 2)**2/2
Let z(b) = -2*b**4 - b**2 + 2*b + 1. Let q(i) = 5*i**4 + i**3 + 19*i**2 - 22*i - 3. Let d(p) = q(p) + 3*z(p). Factor d(s).
-s*(s - 4)*(s - 1)*(s + 4)
Suppose 83*p - 8 = 87*p + 3*k, -3*p - 4*k = 20. Let y(t) be the third derivative of 1/40*t**5 + 0 - 9/8*t**p + 81/4*t**3 + 0*t - 6*t**2. Factor y(i).
3*(i - 9)**2/2
Let z = 23 - -570. Let u = 8899/15 - z. Factor -2/5*j + u + 2/15*j**3 + 0*j**2.
2*(j - 1)**2*(j + 2)/15
Suppose r + 1 = -2*f, 3*r + 1 = -f - 4*f. Factor -6*s**r + 3*s**4 - 3*s**2 + 5*s + 2*s**2 - 2*s**2 + s.
3*s*(s - 2)*(s - 1)*(s + 1)
Let r(w) be the first 