 10*k**2 - 2. Let j(q) be the second derivative of a(q). Factor j(u).
(u - 1)**2*(u + 1)**2/6
Let p be ((-127)/35)/((-1320)/625). Let z = -1/264 + p. Determine f so that -4/7*f**2 - 16/7*f - z = 0.
-3, -1
Let c(n) = 4*n**2 + 2. Let i = -108 + 106. Let x(d) = 5 - 2 - 3 + 17*d**2 + 9. Let s(y) = i*x(y) + 9*c(y). Factor s(z).
2*z**2
Let h = -257 + 260. Suppose -h*r = -34 + 28. Find c, given that 2/11*c**3 - 6/11*c + 0*c**r + 4/11 = 0.
-2, 1
Let x = -943/14 + 8515/126. Let q(l) be the third derivative of -x*l**4 - 1/3*l**3 + 0*l + 1/30*l**5 - 10*l**2 + 0. Determine p, given that q(p) = 0.
-1/3, 3
Suppose 178 - 295 = 12*v - 165. Let -1/2*i**2 + 5*i - v - 1/2*i**3 = 0. What is i?
-4, 1, 2
Let a(z) be the third derivative of 1/42*z**7 - 1/8*z**6 + 0*z + 5/8*z**4 + 7*z**2 - 3 - 5/3*z**3 + 1/12*z**5. Let a(y) = 0. Calculate y.
-1, 1, 2
Let a(y) be the second derivative of 0*y**3 - 3/14*y**4 + 1/21*y**6 - 35*y + 0 + 3/70*y**5 + 0*y**2 + 1/147*y**7. Determine s so that a(s) = 0.
-3, 0, 1
Suppose -1366 = -288*p - 214. Suppose 2/7*b**p + 0*b**3 + 16/7*b - 6/7 - 12/7*b**2 = 0. Calculate b.
-3, 1
Let x(m) be the third derivative of m**7/1890 + m**6/60 + 7*m**5/45 - m**4/12 - 29*m**3/3 + 46*m**2 - 1. Let i(g) be the second derivative of x(g). Factor i(n).
4*(n + 2)*(n + 7)/3
Let b(z) = -1077*z - 98005. Let r be b(-91). Let q = 1/463 + 1847/2315. Factor 0*n - 4*n**r - q*n**3 + 0.
-4*n**2*(n + 5)/5
Let h(z) be the third derivative of z**6/10 - 73*z**5/4 + 2443*z**4/8 - 294*z**3 - 10378*z**2. Determine c so that h(c) = 0.
1/4, 7, 84
Let d be (-50838)/3893 - 4/8*-28. Factor -2/17*q**3 + d + 12/17*q - 6/17*q**2.
-2*(q - 2)*(q + 1)*(q + 4)/17
Let a(t) be the first derivative of -3*t**5/5 - 289*t**4/2 + 193*t**3/3 + 2707. Factor a(j).
-j**2*(j + 193)*(3*j - 1)
Let i(q) be the second derivative of -q**4/16 - 19*q**3/2 - 111*q**2/2 + 845*q. Factor i(v).
-3*(v + 2)*(v + 74)/4
Solve -25/6*w**4 - 2*w**5 + 1/3*w + 0 + 5/3*w**3 + 25/6*w**2 = 0.
-2, -1, -1/12, 0, 1
Let l(x) = -9*x**2 + 1425*x + 9120. Let s(o) = -7*o**2 + 1140*o + 7297. Let p(m) = -19*l(m) + 24*s(m). Factor p(b).
3*(b + 7)*(b + 88)
Let i(g) = -15*g - 84. Let a be i(-7). Factor -25*k - 225*k**2 - a*k**4 + 12*k**3 - 29*k - 108*k**3 - 36*k**3.
-3*k*(k + 3)**2*(7*k + 2)
Factor 1/4*q**2 - 351/4*q + 0.
q*(q - 351)/4
Let n be 12/72 + 70/12. Let t be (39/78)/(n/4). Factor t*u**2 + 1 + 4/3*u.
(u + 1)*(u + 3)/3
Let t(n) be the second derivative of 234*n + 8/3*n**3 + 0 - 8/3*n**4 + 0*n**2 - 2/15*n**6 + n**5. Factor t(z).
-4*z*(z - 2)**2*(z - 1)
Let d be 164362/47740 + 99/(-30) + 3 + 0. Factor d*j**3 + 46/7*j**2 + 26/7*j + 2/7.
2*(j + 1)**2*(11*j + 1)/7
Let z(c) be the second derivative of c**4/4 + 11*c**3/6 - 12*c**2 + 70*c. Let i(l) = 2*l**2 - l - 1. Let o(p) = -2*i(p) + z(p). Factor o(a).
-(a - 11)*(a - 2)
Let l be 4 - (5/((-20)/8) + -15). Suppose 6*p = -9 + l. Factor -4/3*x - 2/3 + 2*x**p.
2*(x - 1)*(3*x + 1)/3
Suppose -2*r = 4*q + 10, -2*q - 5 = -5*r - 6. Let n be (5/(-5))/(q - -5)*-6. Factor -52/7*y**3 + 0*y + 169/7*y**4 + 4/7*y**n + 0.
y**2*(13*y - 2)**2/7
Let d = -537284 - -537286. Find y, given that -288 + 144*y - 24*y**d + 4/3*y**3 = 0.
6
Let x(h) = h**3 + 16*h**2 - 15*h + 39. Let u be x(-17). Suppose u*c + 3 = -4*b, 4*b - 13*c = -11*c + 18. Solve -6/7*z**b + 0*z + 0 - 2/7*z**4 - 4/7*z**2 = 0.
-2, -1, 0
Suppose -k + 2*l + 20 = 0, -3*l - 12 = -253*k + 256*k. Factor -8/3*r + 11/3*r**3 - 2/3*r**k + 0 - 10/3*r**2.
-r*(r - 4)*(r - 2)*(2*r + 1)/3
Solve -323/5*z**2 - 1/5*z**4 + 0 - 289/5*z - 7*z**3 = 0 for z.
-17, -1, 0
Let x = -1/265 - -563/8745. Let p(k) be the first derivative of 4/11*k**2 - x*k**3 - 6/11*k + 2. Suppose p(r) = 0. Calculate r.
1, 3
Suppose 0 = -118*o + 114*o + 16. Suppose -78*g**3 - 538*g**4 + 295*g**4 - 3 + 276*g**o - 36 + 6*g**2 + 3*g**5 + 75*g = 0. Calculate g.
-13, -1, 1
Let t(p) be the second derivative of p**7/3780 + p**6/1080 - p**5/30 + 47*p**4/12 - 2*p - 1. Let i(j) be the third derivative of t(j). Factor i(z).
2*(z - 2)*(z + 3)/3
Let a(q) be the first derivative of q**3/5 + 63*q**2/5 - 129*q/5 + 9114. Let a(y) = 0. What is y?
-43, 1
Let q(y) be the first derivative of -3*y**5/25 - 11*y**4/5 - 58*y**3/5 - 18*y**2 + 81*y/5 - 143. Solve q(g) = 0 for g.
-9, -3, 1/3
Find m, given that 42*m - 3648/5 - 3/5*m**2 = 0.
32, 38
Let a(n) = 10*n + 16*n - 30*n - 17 + 11*n. Let p be a(3). Solve -3*q**3 + 6*q - 3/2*q**p - 6 + 9/2*q**2 = 0.
-2, 1
Let w(s) be the third derivative of s**5/240 + 515*s**4/48 + 265225*s**3/24 - 5*s**2 + 196. Suppose w(j) = 0. Calculate j.
-515
Let l be (-2083)/694 - 420/(-168). Let z = -1/694 - l. Factor z*b**3 + 0 - 1/2*b + 0*b**2.
b*(b - 1)*(b + 1)/2
Suppose -6 = -3*h, 2*s + 6*h - 162 = 5*h. Factor -s*z**2 + 6*z + 98*z**2 - 4 + 0*z + 8*z.
2*(z + 1)*(9*z - 2)
Suppose j + 1298*g - 42 = 1299*g, 9*g = -j - 98. Factor 0 - 8/5*n - j*n**2.
-4*n*(35*n + 2)/5
Let m(b) be the third derivative of 0 + 1/200*b**6 + 0*b**3 + 3/350*b**7 - 1/20*b**4 - 3/100*b**5 + 170*b**2 + 0*b + 1/560*b**8. Solve m(n) = 0.
-2, -1, 0, 1
Let n = 3316296 + -3316292. Let i = -4 + 6. Suppose -n*p**i + 3/4*p**4 - 7/2*p - 1/2*p**3 - 3/4 = 0. What is p?
-1, -1/3, 3
Suppose 62*r - 1 = -21 + 1012. Let f(u) be the first derivative of -2*u**2 + 0*u + 1/3*u**6 - 2*u**3 + 1/2*u**4 + 6/5*u**5 + r. What is i in f(i) = 0?
-2, -1, 0, 1
Let v(q) be the third derivative of -q**5/300 + 151*q**4/10 - 136806*q**3/5 + 65*q**2 + 26*q. Find f, given that v(f) = 0.
906
Let x = -24479 + 73438/3. Let c(g) be the first derivative of -1/18*g**3 + x*g**2 - 1/2*g + 4. Let c(j) = 0. Calculate j.
1, 3
Let g(d) = -72*d**3 + 66*d**3 + 7*d**2 - 7*d + 7 - 53*d**4 - 3*d**4. Let l(x) = -57*x**4 - 6*x**3 + 6*x**2 - 6*x + 6. Let a(m) = -6*g(m) + 7*l(m). Factor a(u).
-3*u**3*(21*u + 2)
Let c(l) = l**3 + 27. Let t be c(0). Suppose 2*u + t = 109. Factor -2*i**3 + 5*i**3 - 5*i + 24 + u*i + 13*i**2 + 5*i**2.
3*(i + 2)**3
Let t(u) = 4*u**5 + u**4 + 3*u**2 + 3. Let h(g) = -14*g**2 + g**5 + 9*g**2 + 6*g**2 + 4 - 3 - g**4. Let y(l) = 12*h(l) - 4*t(l). Solve y(v) = 0 for v.
-4, 0
Let s(g) = -108*g**2 - 16816*g - 17673592. Let k(n) = -13*n**2 + 3. Let j(i) = -8*k(i) + s(i). Suppose j(d) = 0. Calculate d.
-2102
Factor -25 + 5/4*x**2 + 121/4*x.
(x + 25)*(5*x - 4)/4
Let y(n) = 14*n**2 - 5748*n + 6044. Let p(t) = 15*t**2 - 5720*t + 6046. Let l(r) = -10*p(r) + 11*y(r). Suppose l(f) = 0. Calculate f.
1, 1506
Suppose -11 = -j + 3*w - 2, 0 = -2*w + 6. Let d be 3*3/j - (-84)/24. Factor 0 + 1/4*f**3 - 1/4*f**d + 1/4*f**2 - 1/4*f.
-f*(f - 1)**2*(f + 1)/4
Let y(g) = -g**2 - 1. Let v(s) = -s**3 + 15*s**2 - 48*s + 2. Let u = -20 - -17. Let t(q) = u*y(q) - v(q). Let l(o) be the first derivative of t(o). Factor l(c).
3*(c - 4)**2
Let h(u) be the third derivative of u**7/490 - 3*u**6/40 - 3*u**5/140 + 61*u**4/56 + 3*u**3 + 7*u**2 - 2*u + 24. Let h(a) = 0. What is a?
-1, 2, 21
Let x(b) be the third derivative of -2*b**7/105 - 9*b**6/5 - 203*b**5/5 + 1682*b**4/3 - 3272*b**2. Determine j so that x(j) = 0.
-29, 0, 4
Let t be (-5)/280*-554 - (6 - 3)/21. Let q(r) be the first derivative of -34 - 21/2*r + t*r**2 - 3/8*r**4 - 5/2*r**3. Factor q(y).
-3*(y - 1)**2*(y + 7)/2
Let h(r) = -5*r**2 + 8996*r - 14. Let y(k) = -7*k - 2. Let t(d) = -h(d) + 7*y(d). Solve t(l) = 0 for l.
0, 1809
Let q(c) be the third derivative of c**7/56 - 2*c**6/9 - c**5/2 - 61*c**3/6 - 41*c**2 + 1. Let r(o) be the first derivative of q(o). Let r(s) = 0. What is s?
-2/3, 0, 6
Solve -146/3*a - 64/3 - 6*a**3 - 100/3*a**2 = 0 for a.
-32/9, -1
Solve 1/3*r**3 - 6 - 2*r**2 - 25/3*r = 0 for r.
-2, -1, 9
Let z(q) be the first derivative of 0*q + 13/15*q**2 - 1/30*q**4 + 91 + 8/15*q**3. Suppose z(u) = 0. Calculate u.
-1, 0, 13
Let n = -1660015/8 + 207503. Factor 1/8*w**3 + n*w**2 + 0 + w.
w*(w + 1)*(w + 8)/8
Let u be (-11 - -7) + 70/17. Let r be -11*4/(-11)*(-1)/(-34)*8. Factor -24/17*t + r + 12/17*t**2 - u*t**3.
-2*(t - 2)**3/17
Let y(p) = p**2 - 5*p + 6. Let r be y(4). Let a = -186 + 190. Factor 7*j**r - 14*j**3 - 4*j**a - j - 15*j**2 + 9*j.
-2*j*(j + 2)**2*(2*j - 1)
Let r(u) be the second derivative of 1/5*u**6 + u**2 - 102*u + 7/10*u**5 + 4/3*u**4 + 3/2*u**3 + 1/42*u**7 + 0. Let r(m) = 0. What is m?
-2, -1
Let j(r) = r**4 - 33*r**3 - 68*r**2 - 63*r - 19. Let q = -70 + 75. Let o(m) = 32*m**3 + 68*m**2 + 64*m + 20