0.
-1, 0, 1
Let a(i) be the first derivative of 4/3*i**3 - 6*i**2 + 68 - 16*i. Determine c, given that a(c) = 0.
-1, 4
Let r(v) be the second derivative of -v**4/3 - 430*v**3/3 - 852*v**2 - 8713*v. Factor r(u).
-4*(u + 2)*(u + 213)
Let d(i) = -39 - i + 106 - 56. Let n be d(7). Solve -n*a**3 + 20*a**2 + 11 + 8 - 3 - 32*a = 0 for a.
1, 2
Let q(p) be the first derivative of 33*p**2 - 129 + 43*p**3 + 0*p - 3/2*p**4. Factor q(w).
-3*w*(w - 22)*(2*w + 1)
Let a(g) be the first derivative of 24*g + 7 + 5*g**2 + 1/4*g**5 + 25/6*g**3 + 5/3*g**4. Let p(u) be the first derivative of a(u). Suppose p(s) = 0. What is s?
-2, -1
Let o(k) be the third derivative of k**9/70560 + 17*k**8/23520 + 33*k**5/20 - 2*k**2 + 41*k. Let b(m) be the third derivative of o(m). Factor b(l).
6*l**2*(l + 17)/7
Factor -9*w**3 + 339*w**2 + 1 + 812*w + 496*w + 12*w**3 - 1.
3*w*(w + 4)*(w + 109)
Let w(k) = -k**3 + 33*k**2 - 18*k - 220. Let m(y) = 30*y**2 - 18*y - 222. Let o(a) = -2*m(a) + 3*w(a). What is t in o(t) = 0?
-2, 3, 12
Let c(w) be the first derivative of w**6/3 + 72*w**5/5 - 155*w**4/2 + 132*w**3 - 80*w**2 - 728. Suppose c(h) = 0. What is h?
-40, 0, 1, 2
Let m = 136486 - 136486. Find t, given that 8/11*t + 2/11*t**4 + m - 2/11*t**3 - 8/11*t**2 = 0.
-2, 0, 1, 2
Let a(o) be the first derivative of -3*o**4/28 + 2*o**3/7 + 3*o**2/14 - 6*o/7 - 1399. What is g in a(g) = 0?
-1, 1, 2
Factor 105*y + 0 + 1/3*y**2.
y*(y + 315)/3
Let g = -462460 - -462464. Determine x, given that -24/5 + 34/5*x - 2/5*x**3 - 26/15*x**2 + 2/15*x**g = 0.
-4, 1, 3
Let w be (10 - 17 - (-434)/63)*-27. Determine q so that 18/7*q - 24/7*q**4 - 8/7*q**w - 10/7*q**5 + 20/7*q**2 + 4/7 = 0.
-1, -2/5, 1
Let n(t) = 2*t**2 + 5*t + 4. Let l be n(-7). Let c = 90 - l. Factor 5*v**2 - 3*v - 29*v + c*v - 16*v.
5*v*(v - 5)
Solve -45/4*w**2 - 3/8*w**3 + 0 - 87/8*w = 0 for w.
-29, -1, 0
Suppose -n - 13*n = 6*n + 29*n. Suppose 1/5*d**3 - 1/5*d**2 - 1/5*d**5 + n + 1/5*d**4 + 0*d = 0. What is d?
-1, 0, 1
Let y = -481 - -521. Let w be ((-12)/(-16))/(15/y). Factor 0*h**w - 2/5*h**3 - 4/5 + 6/5*h.
-2*(h - 1)**2*(h + 2)/5
Let u(a) = -a**2 + a - 2. Let g(i) = -4*i**3 + 152*i**2 - 708*i + 544. Let v(p) = -g(p) + 8*u(p). Determine w so that v(w) = 0.
1, 4, 35
Let u = -75219 + 75221. Factor -2/3*q**3 + 2/3*q**4 + 0 + 2/9*q**u - 2/9*q**5 + 0*q.
-2*q**2*(q - 1)**3/9
Let c(q) be the first derivative of -q**5/10 + q**4/3 + q**3 + 41*q + 45. Let j(m) be the first derivative of c(m). What is i in j(i) = 0?
-1, 0, 3
Suppose -40*f + 10*f + 64 = 2*f. Factor -2/3*x**3 + 0*x + 0 - 2/9*x**5 - 2*x**f + 10/9*x**4.
-2*x**2*(x - 3)**2*(x + 1)/9
Let v(d) = 6*d - 5. Let u be v(3). Suppose 4*l = -1 + u. Let r(y) = 8*y**2 - 13*y + 8. Let w(k) = 15*k**2 - 25*k + 15. Let c(p) = l*w(p) - 5*r(p). Factor c(q).
5*(q - 1)**2
Let p(h) be the second derivative of h**5/30 + 5*h**4/12 + 4*h**3/3 + 225*h**2/2 - 166*h. Let b(v) be the first derivative of p(v). Factor b(t).
2*(t + 1)*(t + 4)
Let j = -1223 + 1225. Let c(d) be the first derivative of 2/7*d**3 - 9/7*d + 15/14*d**j + 15. Factor c(q).
3*(q + 3)*(2*q - 1)/7
Let m be (-1)/(-2)*774 - 3. Let i = -382 + m. Solve 3/2*d**3 + 3 + 6*d**i + 15/2*d = 0.
-2, -1
Let y(a) = 2*a**4 - 13*a**3 + 36*a**2 + 639*a + 1728. Let h(j) = -11*j**4 + 77*j**3 - 216*j**2 - 3837*j - 10368. Let i(p) = -6*h(p) - 34*y(p). Factor i(x).
-2*(x - 8)*(x + 6)**3
Let i = -10143 - -10146. Let x(b) be the first derivative of 1/4*b**2 - 6 + 0*b - 1/8*b**i - 1/32*b**4. Factor x(m).
-m*(m - 1)*(m + 4)/8
Suppose 5*l - 4*l = 4*l. Suppose l = -12*d + 7*d + 115. Solve -4*n + d*n**4 - 22*n**4 - n**5 + 4*n = 0.
0, 1
Let y be 4/18 - ((-336)/(-54) - 6). Let l be (y - 2)*(-19 - -18). Factor 4*r**3 - 3*r - l*r**2 + 3*r**4 - r + 3 - 4*r**4 + 0*r.
-(r - 3)*(r - 1)**2*(r + 1)
Suppose -g + 3*g = g. Suppose 5*k - h = 10, g = k + 2*h + 1 - 3. What is m in 0*m**2 + 2*m - 5*m**2 + 3*m**2 + 0*m + 2*m**4 - k*m**3 = 0?
-1, 0, 1
Let a(u) be the second derivative of -u**7/420 + u**6/80 - u**5/60 + 35*u**2/2 - 10*u. Let x(r) be the first derivative of a(r). Let x(t) = 0. What is t?
0, 1, 2
Let j(o) = o**2 - 9794*o + 2673225. Let y(p) = 3264*p - 891075. Let z(s) = -3*j(s) - 8*y(s). What is c in z(c) = 0?
545
Let i(r) be the first derivative of -446631/5*r + 160 + 25281/10*r**2 - 159/5*r**3 + 3/20*r**4. Determine t so that i(t) = 0.
53
Let t be (-33)/(-88) - ((-110)/(-64) + -2). Let y = t + -15/608. Suppose y*b**2 + 24/19*b + 16/19 + 2/19*b**3 = 0. What is b?
-2
Let h(m) = -m**4 + 311*m**3 + 23*m**2 - 311*m + 55. Let p(r) = 104*r**3 + 8*r**2 - 104*r + 20. Let v(n) = -4*h(n) + 11*p(n). Factor v(z).
4*z*(z - 25)*(z - 1)*(z + 1)
Let u be (-3 - (-24)/20)*50/(-6). Let p(f) be the first derivative of -1/45*f**5 - 2/9*f**2 - 5/36*f**4 - 8/27*f**3 + 0*f - u. Suppose p(j) = 0. Calculate j.
-2, -1, 0
Let p be (3/2 + -2)*(-16 + -3 + 19). Let t(n) be the third derivative of -1/40*n**6 + p*n + 3/20*n**5 + 0 - 22*n**2 + 1/2*n**4 + 0*n**3. Factor t(w).
-3*w*(w - 4)*(w + 1)
Let t(n) be the second derivative of n**7/84 - 7*n**6/10 + 69*n**5/5 - 298*n**4/3 + 348*n**3 - 648*n**2 - 2*n - 596. Factor t(b).
(b - 18)**2*(b - 2)**3/2
Let o(a) be the third derivative of 17*a**5/60 + a**4/24 - a**3 + 15*a**2 - 2*a. Let i(g) = 37*g**2 + 3*g - 12. Let b(r) = -6*i(r) + 13*o(r). Factor b(x).
-(x + 2)*(x + 3)
Let z be 22950/3366 + ((-2)/11)/(-1). Suppose a - 5*o = -z*o + 12, -a - 3 = -o. Factor 2/15*t + 2/15*t**4 + 2/15 - 4/15*t**3 + 2/15*t**5 - 4/15*t**a.
2*(t - 1)**2*(t + 1)**3/15
Suppose p - 2*o - 10 = 0, 3*o - 3 + 13 = -p. Suppose -4*m = -p*m - 4. Let -65*x**m + 61*x**2 + 2*x**3 + 0*x**3 = 0. Calculate x.
0, 2
Suppose 5*j - 12*r + 1130 = -13*r, j = 2*r - 215. Let t be (j/35 - -6)/(-3) - 0. Solve -t*v**2 + 0 + 1/7*v = 0 for v.
0, 1
Let r(z) be the first derivative of -z**4/12 + 206*z**3/9 - 10609*z**2/6 + 531. Factor r(g).
-g*(g - 103)**2/3
Let m = -281 + 344. Let v be ((-6)/m)/((-18)/84). Determine k, given that 0 - 2/9*k**2 + v*k = 0.
0, 2
Let h(k) be the second derivative of k**4/24 - 11*k**3/6 - 42*k**2 + 958*k. Find q such that h(q) = 0.
-6, 28
Let z(g) be the third derivative of -17/42*g**7 + 3/2*g**5 + 2*g**2 - 5/24*g**4 + 0 + 25/112*g**8 - 7/12*g**6 - 5/6*g**3 - g. Determine t, given that z(t) = 0.
-1, -1/5, 1/3, 1
Let y(x) = -173*x**3 - 3*x**2 + x + 3. Let s be y(-1). Factor -l**3 + 190 + 128*l + 432 + 32*l**2 + 2*l**3 - s + 157*l.
(l + 2)*(l + 15)**2
Find p such that 72 + 2*p**3 + 106*p**2 - 263*p**2 + 145*p**2 - 62*p = 0.
-4, 1, 9
Factor -332*z**2 - 96 + 2*z**3 - 88*z + 716*z**2 - 400*z**2.
2*(z - 12)*(z + 2)**2
Let s(m) be the first derivative of -5*m**9/2016 + 3*m**8/280 - m**7/80 + 25*m**3 - 68. Let w(v) be the third derivative of s(v). Suppose w(u) = 0. What is u?
0, 1, 7/5
Let s be -22 + 19/((-31350)/(-36322)). Let g(v) be the third derivative of -s*v**5 + 0 - 20*v**2 + 0*v + 0*v**3 + 1/30*v**4. Let g(c) = 0. What is c?
0, 1
Suppose -7*g - 15 = -2*g. Let h be -2 + (-1 - g - (-3 + 0)). Factor -7*f**3 - 3*f**3 + 9*f**h.
-f**3
Let h be 13 - 13/((-13)/(-7)). Let p be (h/(-91))/((-54)/126). Factor p*t - 2/13 + 2/13*t**2 - 2/13*t**3.
-2*(t - 1)**2*(t + 1)/13
Suppose 4*d + 2*u + 28 = 0, -100 = 1304*u - 1299*u. Factor 68/7*k + 48/7 + 30/7*k**2 + 4/7*k**d.
2*(k + 2)*(k + 4)*(2*k + 3)/7
Let n(b) be the first derivative of b**6/360 - b**5/20 - 7*b**4/24 + 158*b**3/3 - 158. Let r(w) be the third derivative of n(w). Factor r(j).
(j - 7)*(j + 1)
Let m(a) = -10*a**2 + 132*a + 272. Let r be m(15). Factor 3/4*u + 0 - 3/4*u**r.
-3*u*(u - 1)/4
Let u = 305/292 + 17/438. Let m(n) be the first derivative of -11 - u*n**3 + 7/4*n - 1/8*n**4 + n**2. Factor m(q).
-(q - 1)*(q + 7)*(2*q + 1)/4
What is d in -8*d + 111*d**3 - 9 + 20*d - 20*d**2 - 109*d**3 + 31*d**2 = 0?
-3, 1/2
Let r(v) = -40*v**4 + 1124*v**3 - 2364*v**2 - 1964*v - 340. Let g(h) = -h**4 - h**3 + h**2 - h + 2. Let x(z) = 4*g(z) - r(z). Suppose x(d) = 0. Calculate d.
-1/3, 3, 29
Let h(w) be the first derivative of -w**4/6 + 112*w**3/3 - 1980*w**2 - 64800*w + 2223. Find m, given that h(m) = 0.
-12, 90
Let t be 4/6 + ((-3650)/(-375) - 8). Suppose -t*o**2 + 3/5*o**3 + 3/5*o + 18/5 = 0. Calculate o.
-1, 2, 3
Let g = 51291539 + -191573896676/3735. Let k = 1/747 + g. Factor 16/5*w + k*w**2 + 0.
2*w*(w + 8)/5
Let i = 130127 + -906215/7. Let s = 670 - i. 