c(a) be the first derivative of -2*a**3/15 - 3854*a**2/5 - 7426658*a/5 + 6992. Determine j so that c(j) = 0.
-1927
Let a = -46 + 598. Let j = -2757/5 + a. Factor i**2 + 1/5*i**3 + j + 7/5*i.
(i + 1)**2*(i + 3)/5
Let r(m) be the third derivative of 1/540*m**6 + 0*m - 11/2*m**3 + 1/90*m**5 - 2/9*m**4 + 31*m**2 + 0. Let f(k) be the first derivative of r(k). Factor f(j).
2*(j - 2)*(j + 4)/3
Let r(x) be the second derivative of -643/4*x**5 + 755/2*x**4 + 29*x**6 + 102*x + 0 + 300*x**2 - 1370/3*x**3 - 15/14*x**7. Find m such that r(m) = 0.
2/3, 1, 2, 15
Let c be (266/(-26) - -1)/((-1)/144). Let l = 1330 - c. Factor 36/13*q**2 + 24/13*q + l*q**3 - 16/13.
2*(q + 2)**2*(5*q - 2)/13
Let i(f) = f**3 - 161*f**2 + 942*f - 1860. Let p be i(155). Factor 5/3*w**2 + 1/3*w**3 + 2*w + p.
w*(w + 2)*(w + 3)/3
Let f = -3572 + 3574. Let m(o) be the first derivative of 2/5*o**5 + o**4 - 2*o - 22 - f*o**2 + 0*o**3. What is u in m(u) = 0?
-1, 1
Let t(g) be the first derivative of -106 + 45*g**2 + 1/4*g**3 + 2700*g. Factor t(k).
3*(k + 60)**2/4
Factor 3044*f + 5606067 + 810*f + 4126*f + 3*f**2 + 222*f.
3*(f + 1367)**2
Let f(a) = -3*a**2 + 2*a. Let x(v) = -5*v**2 - 550*v - 1096. Let q(y) = 2*f(y) - 2*x(y). Factor q(s).
4*(s + 2)*(s + 274)
Let n be 186/38 + (-10)/(-95). Let r be (12550/14)/n + (-4)/14. Suppose 178*m**2 - 5*m - 352*m**2 + r*m**2 - 10 = 0. What is m?
-1, 2
Let n(h) be the second derivative of -5*h**4/12 - 5*h**3/2 + 45*h**2 - 2622*h. Factor n(d).
-5*(d - 3)*(d + 6)
Let q(d) be the first derivative of d**3 - 144*d**2 + 1150. Factor q(s).
3*s*(s - 96)
Let c(b) = -b**2 + 4*b - 5. Let y be c(2). Let h be ((-14)/21)/(2/(-21)) - y. Factor -6*f**3 + 5*f**5 - 9*f**4 + 0*f**4 - h*f**5.
-3*f**3*(f + 1)*(f + 2)
Factor 27*d**2 - 429*d - 101*d**2 + 84 + 28*d**2 + 90 + 31*d**2.
-3*(d + 29)*(5*d - 2)
Let h(c) = -c**3 - 23*c**2 + 14*c + 76. Let a be h(-25). Let o = a + -974. Suppose -1728/7*r**3 - 576/7*r**o - 84*r**5 - 272*r**4 + 0 - 64/7*r = 0. What is r?
-2, -2/3, -2/7, 0
Let r(c) = 2*c**2 - 20*c - 4. Let p be r(-6). What is h in -p*h**3 + 4*h**4 - 7*h + 23*h + 64 - 8*h**5 - 176*h**2 - 35*h**4 - 37*h**4 = 0?
-4, -2, -1, 1/2
Let p(o) be the third derivative of o**5/48 - 5*o**4/16 + 5*o**3/3 - 2*o**2 + 10*o. Suppose p(q) = 0. Calculate q.
2, 4
Suppose 2385*f**2 - 72*f**3 + 864 + 912*f + 2377*f**2 + 2*f**4 - 4788*f**2 = 0. Calculate f.
-3, -1, 4, 36
Let p = -16 + 18. Find i, given that 5*i**p - 30 - 15 - 17*i - 9*i + 66*i = 0.
-9, 1
Let n = -1775628 - -1775630. Factor 275/4*z**n + 0 - 15/4*z**3 - 45/2*z.
-5*z*(z - 18)*(3*z - 1)/4
What is h in -16/9*h + 0 - 88/9*h**2 - 4*h**3 + 10/9*h**5 + 22/9*h**4 = 0?
-2, -1/5, 0, 2
Let f(p) be the second derivative of 1/48*p**4 + 5/12*p**3 + 53 - p - 11/8*p**2. Factor f(w).
(w - 1)*(w + 11)/4
Let u(g) be the third derivative of -g**8/8400 - g**7/600 - 2*g**6/225 - g**5/50 + 23*g**3/2 + 43*g**2. Let r(a) be the first derivative of u(a). Factor r(j).
-j*(j + 2)**2*(j + 3)/5
Let s be 1*(-8)/52 - (-134551)/(-247). Let f = 545 + s. Factor f*u**2 + 0 + 0*u.
2*u**2/19
What is t in 0 + 2/9*t**2 - 34/9*t = 0?
0, 17
Let n(w) be the second derivative of 1/6*w**4 - 46*w + 13/3*w**3 + 0 - 14*w**2. Find b such that n(b) = 0.
-14, 1
Let y be (-1)/2 - (-33)/2. Let m(r) = -r**2 + 26*r + 37. Let c be m(27). Factor 10*w - y + 2*w**2 - 6*w**2 + c.
-2*(w - 1)*(2*w - 3)
Let m(w) = 4*w**3 - 540*w**2 - 1137*w - 553. Let h(u) = -2*u**3 + 271*u**2 + 566*u + 277. Let n(g) = -15*h(g) - 6*m(g). Factor n(f).
3*(f + 1)**2*(2*f - 279)
Let c(a) = 140*a**2 - 28*a - 148. Let m(y) = 39*y**2 - 8*y - 42. Let w(i) = -5*c(i) + 18*m(i). Suppose w(d) = 0. What is d?
-2, 4
Let s(d) be the second derivative of -1/24*d**4 + d + 3 + 1/60*d**6 + 0*d**3 + 1/120*d**5 - 1/252*d**7 + 0*d**2. Let s(x) = 0. Calculate x.
-1, 0, 1, 3
Suppose 3*u - 90 = -78. Suppose -2 + 412*t**2 - 426*t**2 - 2 - 20*t + t**3 + 4*t**4 - u + t**5 = 0. What is t?
-2, -1, 2
Let w(k) = 81716*k - 653725. Let h be w(8). Factor 0*t + 4/11*t**2 + 0 - 2/11*t**h.
-2*t**2*(t - 2)/11
Let o = 478/229 + 358/1145. Solve -3/5*x**4 - 9/5 - 6/5*x + o*x**2 + 6/5*x**3 = 0 for x.
-1, 1, 3
Suppose 55 - 52 = 3*f. Let y = 11 + f. Factor -y*k + 19 - 55 + 8*k**2 - 9*k**2.
-(k + 6)**2
Let v = -3627/19 + 18819/95. Factor -2/5*a**2 - v + 38/5*a.
-2*(a - 18)*(a - 1)/5
Let i = 11481 - 11479. Let p(b) be the third derivative of 25/6*b**3 + 0*b + 0 - 5/6*b**4 - 2*b**i - 1/12*b**5. Factor p(c).
-5*(c - 1)*(c + 5)
Suppose 146*n - 55*n - 62 = 60*n. Let m(u) be the first derivative of 0*u**3 - 3/16*u**n + 2 + 3/16*u**4 + 0*u**5 - 1/16*u**6 + 0*u. Factor m(q).
-3*q*(q - 1)**2*(q + 1)**2/8
Suppose 3*s - 29 + 5 = 0. Suppose s*o + 20 = 3*o, 50 = 2*c + 4*o. Factor 80 + 4*j**3 + j**3 - 35*j**2 + 14*j + c*j - 7*j.
5*(j - 4)**2*(j + 1)
Let m = 4163 - 20799/5. Factor -32/5*a - 88/5*a**3 - 4/5*a**5 + 31/5*a**4 + 104/5*a**2 - m.
-(a - 2)**4*(4*a + 1)/5
Suppose 4*j - 2 = 5*j, -4*j + 124 = 3*m. Let 21*y**3 - 12*y**2 - 4 + 5*y**3 - 16*y + 50*y - m*y**2 = 0. Calculate y.
2/13, 1
Let l(m) be the first derivative of 105 + 5/3*m**3 + 0*m + 0*m**2 + 5/4*m**4. Factor l(p).
5*p**2*(p + 1)
Let l be (4/48*34 - 3)*20/(-20). Factor -11/2*p**2 + 16/3*p + l.
-(p - 1)*(33*p + 1)/6
Let u be (-7416)/(-264) + (-2)/22. Suppose -146*c - u = -153*c. Let 3/2*n**2 - 3/2*n**c + 3/2*n**3 - 3/2*n + 0 = 0. Calculate n.
-1, 0, 1
Let t(i) = 4*i**2 + 46*i + 393. Let v(j) = -5*j**2 - 45*j - 404. Let x(d) = 4*t(d) + 3*v(d). Factor x(z).
(z + 9)*(z + 40)
Suppose 0 = -4*m - 8, 49*m - 50*m - 11 = -3*y. Let s(o) be the third derivative of -1/24*o**4 - 1/60*o**5 + 0*o**y + 0 + 21*o**2 + 0*o. Solve s(j) = 0 for j.
-1, 0
Let y(n) be the second derivative of -n**5/20 + 6*n**4 + 74*n**3/3 - 721*n. Factor y(z).
-z*(z - 74)*(z + 2)
Let k(s) be the third derivative of 1/48*s**6 + 1/3*s**4 + 0*s + 12 - 8*s**2 + 1/840*s**7 + 1/2*s**3 + 29/240*s**5. Factor k(m).
(m + 1)**2*(m + 2)*(m + 6)/4
Let t be 92*(-218)/(-2864) - 7. Let d = t - -2855/3222. What is c in d*c**3 + 4/9*c**4 - 16/9*c + 16/9 - 4/3*c**2 = 0?
-2, 1
Let c be 373/(-2611)*(-1 - 9/12). Let v(a) be the first derivative of -c*a**2 + 0*a + 0*a**3 + 3/32*a**4 - 1/40*a**5 - 6. Factor v(y).
-y*(y - 2)**2*(y + 1)/8
Factor 8*o**2 + 4*o**4 - 32*o + 10*o**3 + 17*o**3 + 30*o - 7*o**3 - 30*o.
4*o*(o - 1)*(o + 2)*(o + 4)
Find c such that -c**2 + 0 - 5/4*c**5 + 0*c + 1/4*c**4 + 5*c**3 = 0.
-2, 0, 1/5, 2
Let p = 745205 + -744693. Determine n, given that -1/8*n**5 - 38*n**3 - 200*n**2 - p*n - 7/2*n**4 - 512 = 0.
-8, -4
Let k(g) be the second derivative of -88*g**6/45 - 34*g**5/15 - 35*g**4/36 - g**3/6 + 2*g + 16. Factor k(a).
-a*(4*a + 1)**2*(11*a + 3)/3
Let f(s) be the first derivative of -s**5/35 + 17*s**4/21 - 19*s + 24. Let x(u) be the first derivative of f(u). Factor x(r).
-4*r**2*(r - 17)/7
Suppose 4*u + 30 = -u. Let j(s) = s**4 + 1. Let i(q) = q**3 + 3 - 5 - 7 - q + q**2 + 11 + q**4 + 0*q. Let p(k) = u*j(k) + 3*i(k). Solve p(r) = 0.
-1, 0, 1
Suppose 2*x = -2*o - 108, -x + 5*x + 218 = -3*o. Let v be x/35*50/(-12) - 5. Factor 0 + 5/3*i**2 - v*i.
5*i*(i - 1)/3
Let r be ((-220)/(-5))/4*1. Suppose -l + 3*v - r = -1, -4*l + 28 = 5*v. Factor 1/2*c**3 + 13/8*c**l - 1/2 - 13/8*c.
(c - 1)*(c + 4)*(4*c + 1)/8
Let f(a) be the third derivative of -a**6/840 - 4*a**5/105 - 5*a**4/56 + a**2 - 82*a. Factor f(j).
-j*(j + 1)*(j + 15)/7
Let s(v) be the first derivative of v**6/36 - 41*v**5/30 + 355*v**4/24 + 1321*v**3/18 + 352*v**2/3 + 242*v/3 + 238. Let s(f) = 0. What is f?
-1, 22
Suppose -4*c - 5*j + 3 = 0, -14 = -5*c - 5*j + 9*j. Suppose -5*z - 24 = 2*u - 38, -4*z + 3*u = -c. Factor 12/5*p + 8/5 + 1/5*p**3 + 6/5*p**z.
(p + 2)**3/5
Let k(r) be the second derivative of 459*r**4/4 - 229*r**3 - 3*r**2/2 - r - 1165. What is s in k(s) = 0?
-1/459, 1
Let o = 816699 + -816695. Determine v so that 8/7*v - 2/7*v**o - 4/7*v**3 + 6/7*v**2 - 8/7 = 0.
-2, 1
Suppose 4*s = -4*a - 3324, -2*s - a = -541 + 2202. Let n = s + 830. Factor 0*c**2 + n*c + 0*c**4 + 0 - 1/2*c**5 + 1/2*c**3.
-c**3*(c - 1)*(c + 1)/2
Suppose 0 = p + 2*y - 12 - 0, 20 = 5*p + 2*y. Let f(a) be the second derivative of 25/16*a**p + 1/96*a**4 + 5/24*a**3 - 9*a + 0. Let f(s) = 0. Calculate s.
-5
Let g(j) be the second derivative of 0*j**2 - 2*j + 1/3*j**4 - 164 + 1/10*j**5 - j**3. Find m, given that g(m) = 0.
-3, 0