*d**2 - 180*d**3 + 144 - 9*d**5 - 6*d**4 = 0.
1, 2, 6
Let z(x) be the third derivative of 1/336*x**8 + 0*x + 0 + 178*x**2 + 0*x**3 + 1/240*x**5 - 1/840*x**7 + 7/48*x**4 - 3/80*x**6. Find h, given that z(h) = 0.
-7/4, -1, 0, 1, 2
Suppose i - 11*i + 40 = 0. Suppose 4*a + q - i*q = 115, -4*q - 112 = -4*a. Factor -4*p - a + 4*p**2 + 8 + 15.
4*(p - 2)*(p + 1)
Let v be (260/(-208))/((-10)/4). Let z(r) be the first derivative of r + 7/4*r**2 + v*r**3 - 15. Find g, given that z(g) = 0.
-2, -1/3
Let -60*z**2 - 2*z**3 - 101 - 193 + 0*z**3 - 366*z - 14 = 0. Calculate z.
-22, -7, -1
Let n = 860 - 858. Suppose 63*k**2 + k**4 - 33*k**2 - 31*k**n = 0. What is k?
-1, 0, 1
Suppose 14*b + 8*b - 6864 = 0. Factor 35*l**2 + 7 + 55*l + b*l**3 + 18 - 307*l**3.
5*(l + 1)**2*(l + 5)
Let l = -355853/5 + 71171. Solve -4*d**2 + l*d**3 + 32/5*d + 0 = 0 for d.
0, 2, 8
Let f(d) be the second derivative of -d**4/66 - 870*d**3/11 - 1703025*d**2/11 - 1757*d. Solve f(n) = 0 for n.
-1305
Let g be 4/6 - 825/9. Let t = -89 - g. Factor 6*c + 6*c**2 + 22*c + 0*c**2 - 2*c**t + 24.
4*(c + 1)*(c + 6)
Let m(o) = o**3 + 351*o**2 + 15792*o - 102. Let r be m(-53). Factor -2/3*f + r - 2/3*f**2.
-2*(f - 2)*(f + 3)/3
Let k(p) be the second derivative of -p**4/18 - 1006*p**3/9 - 253009*p**2/3 + 1883*p. Suppose k(a) = 0. What is a?
-503
Let 77*n + 9*n**3 - 74*n + 9*n**2 + n**2 + 2*n**4 + 0*n**2 = 0. Calculate n.
-3, -1, -1/2, 0
Let z(q) be the third derivative of -q**6/300 - 19*q**5/75 - 23*q**4/3 - 120*q**3 - 341*q**2 - 2. Find s such that z(s) = 0.
-18, -10
Let q(t) = -3*t**2 - 3640*t - 1098077. Let g(o) = -66*o**2 - 80085*o - 24157695. Let z(r) = -2*g(r) + 45*q(r). What is u in z(u) = 0?
-605
Let x(y) = 36*y**3 - 344*y**2 + 740*y - 552. Let c(o) = -o**3 + 2*o**2 + 2*o. Let q(n) = -40*c(n) - x(n). Factor q(z).
4*(z - 2)*(z - 1)*(z + 69)
Let s(y) be the second derivative of 7*y**7/18 - 77*y**6/90 + 8*y**5/15 - y**4/9 - 4*y - 20. Factor s(j).
j**2*(j - 1)*(7*j - 2)**2/3
Let k be 15/5*-2*12. Let m = 74 + k. Factor -m*l**4 + 66*l**3 - 4*l**2 + 2*l**2 - 61*l**3.
-l**2*(l - 2)*(2*l - 1)
Let a(s) be the first derivative of -s**6/72 - s**5/12 + 25*s**4/8 - 2*s**3/3 + 2*s - 24. Let f(c) be the third derivative of a(c). Factor f(r).
-5*(r - 3)*(r + 5)
Suppose -9*z - 10 = -14*z. Determine j so that -3*j**z + 87*j**4 + j**5 - 34*j**4 - 30*j**4 - 28*j**4 + 7*j**3 = 0.
0, 1, 3
Let u(j) be the third derivative of -j**7/70 + j**6/40 + 48*j**5/5 - 152*j**4 + 512*j**3 - 1591*j**2. Factor u(v).
-3*(v - 8)**2*(v - 1)*(v + 16)
Let n be -22*(90/6)/((-3)/4). Let o = n - 2196/5. Factor -o - 6/5*q - 2/5*q**2.
-2*(q + 1)*(q + 2)/5
Let 23/3*h + 55/3*h**3 + 4/3*h**4 + 86/3*h**2 - 4 = 0. Calculate h.
-12, -1, 1/4
Let h(z) = 22*z - 2437. Let p be h(111). Let t(k) be the third derivative of -20*k**2 + 0*k + 0 - 5/12*k**3 + 1/120*k**p + 1/12*k**4. Factor t(f).
(f - 1)*(f + 5)/2
Let 668/3*z**2 - 2684/3*z + 896 + 1/3*z**3 = 0. Calculate z.
-672, 2
Let f(o) be the first derivative of -9*o**4/8 - 311*o**3/2 - 6006*o**2 + 4056*o + 210. Determine g, given that f(g) = 0.
-52, 1/3
Let q(n) be the second derivative of -n**6/20 - 3*n**5/20 + 71*n**4/8 + 18*n**3 + 67*n + 1. Factor q(f).
-3*f*(f - 8)*(f + 1)*(f + 9)/2
Suppose -5*l + 2 = -3*p - 2, 0 = 3*l - 2*p - 2. Let y be l/((-14)/(-35)) - 2 - -2. Suppose -y*b**4 + 0 + 0*b**3 + 5/2*b - 5/2*b**5 + 5*b**2 = 0. Calculate b.
-1, 0, 1
Let l(v) be the second derivative of v**4/42 + 436*v**3/7 + 427716*v**2/7 - 2*v + 146. Factor l(t).
2*(t + 654)**2/7
Suppose -303*o = -305*o - 2*n, -2 = -3*o - 2*n. Solve 2/9*t**3 + 0 + 2/9*t**5 - 2/3*t**4 - 4/9*t + 2/3*t**o = 0.
-1, 0, 1, 2
Let z(l) be the first derivative of -3*l**5/5 + 471*l**4/2 - 23689*l**3 - 226080*l**2 - 691200*l - 9441. Factor z(n).
-3*(n - 160)**2*(n + 3)**2
Factor -3*y**2 - y + 0*y**2 + 0*y**2 - 8*y - 183 + 178 + y**3.
(y - 5)*(y + 1)**2
Let y(o) be the first derivative of 0*o - 33 + 0*o**2 - o**4 + 4/5*o**5 + 2/3*o**6 - 4/3*o**3. Suppose y(p) = 0. What is p?
-1, 0, 1
Factor -25*d**2 + 80*d**2 + 730*d + 2188 + 132.
5*(d + 8)*(11*d + 58)
Suppose -6*v + 5*v + 4*i - 12 = 0, 2*i - 28 = -5*v. Factor -41*c - 788*c**v + 113*c + 32*c**3 - 84*c**2 + 784*c**4.
-4*c*(c - 3)**2*(c - 2)
Let o(k) be the first derivative of -k**6/2 - 8*k**5/5 - 3*k**4/2 + k**2/2 - 2005. Factor o(i).
-i*(i + 1)**3*(3*i - 1)
Let x(j) be the second derivative of -3*j - 9 + 1/6*j**4 + 0*j**2 + 32/3*j**3. Factor x(i).
2*i*(i + 32)
Let l(t) be the first derivative of -t**8/4480 - t**7/560 - t**6/192 - t**5/160 - 12*t**3 + 210. Let n(u) be the third derivative of l(u). Factor n(o).
-3*o*(o + 1)**2*(o + 2)/8
Let y(o) be the second derivative of -o**5/5 - 5*o**4/3 + 22*o**3 - 54*o**2 - 121*o + 15. Factor y(z).
-4*(z - 3)*(z - 1)*(z + 9)
Let v(a) be the first derivative of 31*a**3 + 468*a**2 + 60*a - 910. Factor v(t).
3*(t + 10)*(31*t + 2)
Let q(r) be the third derivative of -r**6/15 - 3*r**5/5 - 5*r**4/3 - 2*r**3 - r**2 + 3977. Factor q(f).
-4*(f + 1)*(f + 3)*(2*f + 1)
Suppose 5*k + 3*h - 10 + 1 = 0, 0 = -4*h + 12. What is y in -5*y - 8927 + k*y**2 - y**2 + 8923 = 0?
-4, -1
Let z(a) be the first derivative of -2/23*a**3 + 1/46*a**4 - 4/23*a**2 + 0*a + 79. Factor z(q).
2*q*(q - 4)*(q + 1)/23
Factor -52/9*m**2 + 50*m - 44 - 2/9*m**3.
-2*(m - 6)*(m - 1)*(m + 33)/9
Let o = -4/879 - -907/6153. Let l(a) be the second derivative of 1/14*a**4 + 1/70*a**5 + 1/7*a**3 + o*a**2 + 0 - 3*a. Factor l(y).
2*(y + 1)**3/7
Let m = -347905 + 347907. Solve 3468/7 + 3/7*l**m + 204/7*l = 0 for l.
-34
Let v(s) be the second derivative of 16 - 2/189*s**7 - 1/45*s**5 + 0*s**2 - 3*s + 0*s**4 + 4/135*s**6 + 0*s**3. Factor v(w).
-4*w**3*(w - 1)**2/9
Let d(z) be the third derivative of 5/8*z**4 - 1/6*z**5 - 31*z**2 + 0 + 0*z + 50/3*z**3. Factor d(s).
-5*(s - 4)*(2*s + 5)
Suppose -10*y + 360 = 30*y. Find t such that 175 - 2*t**2 - 197 + y*t - 33*t = 0.
-11, -1
Let o be (1/8)/((30/50)/((-36)/(-60))). Let i(w) be the second derivative of 0*w**2 + 0 + 12*w - 1/80*w**5 + o*w**3 - 1/24*w**4. Factor i(j).
-j*(j - 1)*(j + 3)/4
Let q(b) be the second derivative of 11/15*b**4 + 8*b + 1/10*b**5 + 2 - 17/15*b**3 - 2*b**2. What is d in q(d) = 0?
-5, -2/5, 1
Let k(a) be the third derivative of -7/72*a**4 - 1/72*a**6 - 1/5*a**5 + 0*a**3 - 145*a**2 + 0*a + 0. Find o such that k(o) = 0.
-7, -1/5, 0
Suppose -n + 0 = 5*t - 20, -2*n + 15 = 5*t. Suppose t*y - 284 = 196. Factor 50 + 30*w**2 + 5*w**3 + 46 + 45*w - y.
5*w*(w + 3)**2
Let p(x) be the second derivative of -89*x + 1/20*x**4 + 1/10*x**2 + 1/100*x**5 + 1/10*x**3 + 0. Factor p(f).
(f + 1)**3/5
Let v(u) be the first derivative of -2/9*u**3 + 3*u**2 + 258 + 0*u. Suppose v(x) = 0. What is x?
0, 9
Factor 0 + 136*r - 4*r**3 + 0 - 12*r**2 + 115*r - 179*r.
-4*r*(r - 3)*(r + 6)
Suppose 37 = 5*g + 4*f, -4*g + 17 = -2*f + f. Let j be -1*2*2/(-1). Suppose 5*i**2 - 10*i**j + 5*i**4 - 5*i**2 + g*i**5 = 0. Calculate i.
0, 1
Let x(k) be the first derivative of -k**6/990 - 7*k**5/660 + k**4/33 + 29*k**3/3 - k**2/2 - 42. Let b(f) be the third derivative of x(f). Factor b(q).
-2*(q + 4)*(2*q - 1)/11
Let l(w) be the second derivative of -3*w**6/50 - 3*w**5/4 - 69*w**4/20 - 63*w**3/10 - 3*w - 9. Factor l(h).
-3*h*(h + 3)**2*(3*h + 7)/5
Let u(v) = v**2 - 14*v + 51. Let q be u(6). Let b(j) = -2*j - 16. Let h be b(-12). Determine m so that h + 5*m**q - 15*m**2 - 7 + 15*m - 6 = 0.
1
Let h be ((-7)/(2625/(-30)) - 86/450)/((-14)/58956). Factor h*n + 850/7*n**3 + 250/21*n**4 + 2890/7*n**2 + 0.
2*n*(5*n + 17)**3/21
Suppose -5*o + 9 = -3*z, 0 = -0*z - 2*z + 4. Factor -3*u**o - 161*u**4 + 80*u**4 + 84*u**4 - 15*u**2 - 9*u.
3*u*(u - 3)*(u + 1)**2
Let a(h) = -12*h**4 - 64*h**2 - 27*h**3 + 7*h**3 + 61*h**2. Let y(b) = 12*b**4 + 20*b**3 + 2*b**2. Let l(x) = -6*a(x) - 5*y(x). Factor l(n).
4*n**2*(n + 1)*(3*n + 2)
Let y(t) be the second derivative of -t**5/100 + 21*t**4/10 + 259*t**3/30 - 192*t**2/5 + 817*t. Solve y(n) = 0.
-3, 1, 128
Let v(d) be the second derivative of 7/10*d**3 + 13/20*d**4 + 0 + 0*d**2 - 1/50*d**6 + 3/20*d**5 + 231*d. Factor v(a).
-3*a*(a - 7)*(a + 1)**2/5
Let d(f) be the second derivative of -f**5/390 - 5*f**4/156 - 2*f**3/13 - 13*f**2/2 + 2*f + 43. Let q(a) be the first derivative of d(a). What is h in q(h) = 0?
-3, -2
Let f(x) = 5*x**4 + 136*x**3 + 625*x**2 + 512*x. Let a