 146*r**3 - 70*r**2 + r**4 + 46 + 21*r = 0.
-2, -1, 1, 23
Let n(t) be the third derivative of -t**6/1260 + t**5/420 + t**4/14 - 151*t**3/3 - 3*t**2 + 68. Let k(v) be the first derivative of n(v). Factor k(z).
-2*(z - 3)*(z + 2)/7
Let n(o) be the second derivative of 1331*o**5/10 + 121*o**4 + 44*o**3 + 8*o**2 + 3*o + 163. What is g in n(g) = 0?
-2/11
Let j(b) be the second derivative of 31*b**5/2 - 205*b**4/12 + 25*b**3/6 + 198*b + 1. Factor j(z).
5*z*(2*z - 1)*(31*z - 5)
Solve 80/3*x**2 + 2/3*x**3 + 226/3*x + 148/3 = 0.
-37, -2, -1
Let o(t) be the second derivative of -t**4/8 + 203*t**3/24 + 17*t**2/4 + 2259*t. Solve o(c) = 0.
-1/6, 34
Let l(w) be the first derivative of -w**8/840 + w**7/175 - w**6/150 - w**5/75 + w**4/20 - 31*w**3/3 - 20. Let k(n) be the third derivative of l(n). Factor k(i).
-2*(i - 1)**3*(5*i + 3)/5
Suppose 0 = -78*z + 92*z - 1456. Solve 40*b**2 + 3*b**3 + b**3 + 38*b + z - 92*b - 94*b = 0 for b.
-13, 1, 2
Let j(y) be the third derivative of -y**5/30 - 359*y**4/12 + 67*y**2. Let j(k) = 0. What is k?
-359, 0
Let j be (-21)/14 + 54/4. Let b be (j/20)/(2/30) - 6. Factor -12/7*y**2 + 0*y + 2*y**b + 0 - 2/7*y**4.
-2*y**2*(y - 6)*(y - 1)/7
Let p(u) be the first derivative of -7*u**4/3 - 212*u**3/3 - 576*u**2 + 1040*u/3 + 2830. What is n in p(n) = 0?
-13, -10, 2/7
Let t = -3233 + 3233. Let k(w) be the third derivative of 1/33*w**3 + t*w**6 + 0*w**4 - 4*w**2 + 0*w + 0 + 1/1155*w**7 - 1/165*w**5. Solve k(l) = 0 for l.
-1, 1
Let v(k) = k**2 - 13*k + 8. Let g be v(0). Factor -g*n**2 + 30*n + 13*n**2 + 40 - 5*n**3 - 11*n**2 - 9*n**2.
-5*(n - 2)*(n + 1)*(n + 4)
Let v(n) be the second derivative of -n**6/200 - n**5/25 - n**4/8 - n**3/5 - 4*n**2 + 78*n. Let q(z) be the first derivative of v(z). Factor q(f).
-3*(f + 1)**2*(f + 2)/5
Let l(z) be the first derivative of 5*z**4/4 + 165*z**3 - 5325*z**2/2 + 13625*z - 7572. Factor l(j).
5*(j - 5)**2*(j + 109)
Determine d, given that 0 + 11/2*d**4 - 31/2*d**2 + 11*d - 3/2*d**3 + 1/2*d**5 = 0.
-11, -2, 0, 1
Factor 216*z**2 - 198*z**3 + 167*z**4 - 21*z**2 + 161*z**4 + 161*z**4 - 486*z**4.
3*z**2*(z - 65)*(z - 1)
Let y = 97 + -81. Let i(d) = d**3 - 15*d**2 - 13*d + 8. Let o be i(y). Let -o*n + 102*n - n**2 - 7 - 54*n = 0. What is n?
-7, -1
Let -45*y**3 - 116*y**2 + 189*y - 7/2*y**4 - 49/2 = 0. Calculate y.
-7, 1/7, 1
Let x(y) be the first derivative of 173 + 4/5*y**5 - 9*y**4 + 24*y**3 + 8*y**2 - 96*y. Suppose x(n) = 0. Calculate n.
-1, 2, 6
Let w = 13235487/740 + -17886. Let m = -1/148 - w. Factor -1/10*c + 1/10*c**3 + m*c**2 - 1/5.
(c - 1)*(c + 1)*(c + 2)/10
Factor 14 + 17/2*j**2 + 1/2*j**3 + 22*j.
(j + 1)*(j + 2)*(j + 14)/2
Let y(j) be the second derivative of 3/10*j**2 - 2*j + 1/60*j**4 - 31 - 2/15*j**3. Factor y(n).
(n - 3)*(n - 1)/5
Let i be (-1 + 2*1/8*-20)*41616/(-540). Factor 136/5*w + 2/5*w**2 + i.
2*(w + 34)**2/5
Let v(s) be the second derivative of -1/42*s**4 + s + 0*s**2 - 1/42*s**3 + 0*s**5 - 58 + 1/294*s**7 + 1/105*s**6. What is i in v(i) = 0?
-1, 0, 1
Let f(u) be the first derivative of 23/12*u**4 - 5*u**3 + 1/60*u**6 - 3/10*u**5 + 42 - 40*u + 25/4*u**2. Let j(x) be the first derivative of f(x). Factor j(r).
(r - 5)**2*(r - 1)**2/2
Let w = 373 + 3165. Factor -8681 - 3693 - 72*s**2 - 376*s + w + 68*s**2.
-4*(s + 47)**2
Let v(f) be the first derivative of -f**3 + 2013*f**2/2 - 6148. Factor v(t).
-3*t*(t - 671)
Let w(b) be the third derivative of b**6/540 + 4*b**5/135 - 11*b**4/27 + 16*b**3/9 - 2*b**2 + 2765*b - 1. Let w(g) = 0. What is g?
-12, 2
Let j(m) be the second derivative of m**7/14 + 3*m**6/5 + 6*m**5/5 - 3*m**4/2 - 9*m**3/2 + 824*m. Find v such that j(v) = 0.
-3, -1, 0, 1
Let k(o) be the second derivative of o**6/180 - 4*o**5/15 - 17*o**4/12 + 43*o**3/6 + 137*o. Let x(t) be the second derivative of k(t). Factor x(f).
2*(f - 17)*(f + 1)
Let h(x) be the second derivative of -3*x**3 - 3/2*x**2 - 9/4*x**4 + 0 - 3/5*x**5 - 91*x. Factor h(w).
-3*(w + 1)**2*(4*w + 1)
Solve 12*u**5 - 732*u - 200*u**2 + 380 - 616*u**2 + 1019*u**3 + 1632*u**4 + 100*u**5 + 417*u**3 - 380*u**2 = 0.
-95/7, -1, 1/2
Suppose 0 = 6*u + 55 + 5. Let i = 19 + u. Factor -i*n**3 + 0*n**3 + 9*n**4 + 3*n**5 - 6*n**5 + 3*n**2.
-3*n**2*(n - 1)**3
Let z(l) be the second derivative of l**7/126 - 83*l**6/45 + 470*l**5/3 - 5364*l**4 + 36936*l**3 - 104976*l**2 - 11523*l. Factor z(m).
(m - 54)**3*(m - 2)**2/3
Let r(x) = 15*x**2 + x. Let y(g) = -3*g**3 - 426*g**2 - 381*g. Let u(n) = -3*r(n) - y(n). Find o such that u(o) = 0.
-126, -1, 0
Factor 11/4 - 1/4*g**4 - 3*g + 3*g**3 - 5/2*g**2.
-(g - 11)*(g - 1)**2*(g + 1)/4
Let u(f) = f**3 - 7*f**2 - 9*f + 10. Let m be u(8). Determine p, given that -252*p**m - p**3 - 26340 - 17366 - 2*p**3 - 7056*p - 22150 = 0.
-28
Let n be (3*1 - (-112)/(-28)) + -11. Let q(d) = -d**4 - d**2 + d. Let b(t) = 24*t**4 + 15*t**3 - 27*t. Let h(a) = n*q(a) - b(a). Factor h(g).
-3*g*(g - 1)*(g + 1)*(4*g + 5)
Suppose -87 + 24 = -21*w. Suppose -3*y - 23 + 83 = 0. Factor -y*a + 44*a**2 + 58*a**2 - 12*a**3 - 22*a**2 - 13*a**w - 35*a**4.
-5*a*(a - 1)*(a + 2)*(7*a - 2)
Suppose 5*c - 21 = c - 3*z, 3*z - 9 = 0. Let b be (92/(-184))/((-3)/27). Determine f so that 2 - 1/2*f**3 + c*f**2 - b*f = 0.
1, 4
Factor 423/2*w**2 - 3/2*w**4 + 0 + 0*w + 210*w**3.
-3*w**2*(w - 141)*(w + 1)/2
Let y(d) be the second derivative of 0*d**2 - d + 8/15*d**4 + 28/15*d**3 + 29 + 1/50*d**5. Determine j so that y(j) = 0.
-14, -2, 0
Let x(y) be the second derivative of y**4/4 - 13*y**3 + 459*y**2/2 + 1078*y. Factor x(j).
3*(j - 17)*(j - 9)
Let o(a) = -44*a - 167. Let p be o(-2). Let s(w) = 2*w**2 + 151*w - 553. Let z be s(p). Factor 0*c + 0*c**3 + z - 1/4*c**4 + 1/4*c**2.
-c**2*(c - 1)*(c + 1)/4
What is g in -2/17*g**5 + 644/17*g - 642/17*g**3 + 326/17*g**2 + 0 - 326/17*g**4 = 0?
-161, -2, -1, 0, 1
Solve -15/8*u**3 + 1/2*u**4 + 0 - 5*u + 1/8*u**5 - 29/4*u**2 = 0.
-5, -2, -1, 0, 4
Find r, given that 224 - 17/9*r**3 + 1/9*r**4 - 58/9*r**2 + 608/9*r = 0.
-4, 7, 18
Suppose 11*g = 7*g + 8. Let c = -23 - -25. What is r in -2*r + 8 - 3 - 4*r**g + r**4 + 0 - 2 + c*r**3 = 0?
-3, -1, 1
Let g(x) = 8*x**4 + 9*x**3 + x**2 - 9*x - 6. Let d(a) = 46*a - 6*a**2 - 36*a**4 + 32 + 2*a**3 - 6*a**4 - 48*a**3. Let t(j) = -3*d(j) - 16*g(j). Factor t(s).
-2*s*(s - 1)*(s + 1)*(s + 3)
Let f be (1*-1 - -61) + (-19)/(-19). Let i = -35 + f. Factor 5 + 115*y**2 + 15 + 9*y**3 + 100*y + i*y**3.
5*(y + 1)*(y + 2)*(7*y + 2)
Factor -2251*k**3 + 48*k**2 + 0*k**4 - 7 - 46*k + 2233*k**3 + k**4 + 22.
(k - 15)*(k - 1)**3
Let p = -200/51 + 3008/663. Factor 6/13*a**2 - 14/13 + p*a.
2*(a - 1)*(3*a + 7)/13
Let m = -5422 + 5427. Let r(k) be the first derivative of 8 + 0*k**2 + k**m + 5/3*k**3 + 5/2*k**4 + 0*k. Factor r(x).
5*x**2*(x + 1)**2
Let a = -17 + 19. Suppose -d + 5*d - 8 = -5*z, -a*z + 20 = -4*d. Factor 3*f**2 - 4*f + 0*f - z + f - 2.
3*(f - 2)*(f + 1)
Let p = 2 - -2. Factor 20*v**2 - 11*v**p + 504*v**3 + 3*v**5 + 568*v**2 - 70*v**4.
3*v**2*(v - 14)**2*(v + 1)
Let d be -290*12/(-360) - 5/(10/16). Factor 50/3 - 95/3*x + 40/3*x**2 + d*x**3.
5*(x - 1)**2*(x + 10)/3
Suppose -r + 4 = -4*a, 0 = r - 4*a - a - 5. Suppose r = 41*g + 32 - 114. What is n in 0 - 7/4*n**4 + 1/2*n**g + 0*n - 5/4*n**3 = 0?
-1, 0, 2/7
Let j(q) = q**4 - q**2 - 1. Let y(k) = 7*k**4 - 594*k**3 + 585*k**2 + 594*k - 597. Let b(z) = -5*j(z) + y(z). What is v in b(v) = 0?
-1, 1, 296
Let p = -301210 - -301226. Determine r so that -8 + 2/3*r**5 - 8*r**4 + 2/3*r - 4/3*r**3 + p*r**2 = 0.
-1, 1, 12
Let p be 0*(-1 + -1)/(-6) - (-532)/114. Find j such that 2/3*j**3 - 16/3*j**2 + 0 + p*j = 0.
0, 1, 7
Let x(a) be the first derivative of 2*a**3 + 1/40*a**5 + 0*a + 1/120*a**6 - 9 + 0*a**4 + 0*a**2. Let k(i) be the third derivative of x(i). Factor k(g).
3*g*(g + 1)
Let -240*l - 5*l**2 + 11*l**3 + 14*l**3 - 23*l**2 - 22*l**3 - 86*l**2 = 0. Calculate l.
-2, 0, 40
Let j(l) be the second derivative of -l**4/6 - 92*l**3/3 + 93*l**2 + l + 1093. Factor j(y).
-2*(y - 1)*(y + 93)
Let x(u) be the third derivative of u**5/330 + 31*u**4/12 + 1348*u**3/33 - 4*u**2 - 419*u. Solve x(q) = 0 for q.
-337, -4
Let u(b) = 0*b + 388*b**2 + b - 390*b**2. Let t(q) = q**3 + 14*q**2 - 5*q. Let y(s) = t(s) + 6*u(s). Determine f, given that y(f) = 0.
-1, 0
Suppose 24*i = 36626 - 36530. Let h = -633 + 1915/3. Let 26/3*n + 2/3*n**3 - h*n**2 - i = 0. What