g + 18)
Suppose 34454*h = 34463*h - 288. Factor -8788/5*g + 10816/5*g**2 - 2184/5*g**3 + 0 + h*g**4 - 4/5*g**5.
-4*g*(g - 13)**3*(g - 1)/5
Let b(k) be the second derivative of k**5/90 - 11*k**4/36 - 289*k**2/2 + 9*k - 6. Let n(s) be the first derivative of b(s). Find d, given that n(d) = 0.
0, 11
Let j(z) be the first derivative of -13*z**6/720 - 3*z**5/16 - 3*z**4/8 - 8*z**3/3 + 211. Let b(t) be the third derivative of j(t). Factor b(u).
-(u + 3)*(13*u + 6)/2
Let u = 546109/500610 - -1/45510. Determine l, given that -2*l + u + 12/11*l**2 - 2/11*l**3 = 0.
1, 2, 3
Let f = -449 + 434. Let v(s) = -s**3 - 14*s**2 + 14*s - 13. Let m be v(f). Determine a so that 2/3*a**2 + 4/3 + m*a = 0.
-2, -1
Let t be (8/42 + 0)/(5798/8697). Factor -8/7*n + t*n**2 + 6/7.
2*(n - 3)*(n - 1)/7
Let t(l) be the third derivative of -l**6/280 - 61*l**5/140 - 899*l**4/56 + 961*l**3/14 - l**2 - 317*l - 1. Find z such that t(z) = 0.
-31, 1
Let c(d) be the third derivative of -23/105*d**5 + 0 - 2/735*d**7 + 0*d**3 + d**2 - 11/42*d**4 - 73*d - 13/210*d**6. Solve c(z) = 0 for z.
-11, -1, 0
Let o = -553465 - -553467. Factor 68/15 + 2/15*f**o + 14/3*f.
2*(f + 1)*(f + 34)/15
Suppose -41*w = -40*w - 35. Let y be (-6)/2 - w/(4 + -11). Suppose 1/2*t**5 + t**2 + 3/2*t - 1 - y*t**3 + 0*t**4 = 0. Calculate t.
-2, -1, 1
Let a = 78830 + -78828. What is p in -6/5*p + 3*p**a - 3/5*p**3 - 24/5 = 0?
-1, 2, 4
Let g(q) = -9*q**4 - 130*q**3 - 232*q**2 - 250*q - 76. Let n(f) = -12*f**4 - 171*f**3 - 309*f**2 - 333*f - 102. Let s(a) = -9*g(a) + 7*n(a). Factor s(b).
-3*(b + 1)**2*(b + 2)*(b + 5)
Let x(g) be the first derivative of 20*g**2 + 3/4*g**5 + 50/3*g**3 + 35/6*g**4 + 11 - 10*g. Let d(v) be the first derivative of x(v). Factor d(k).
5*(k + 2)**2*(3*k + 2)
Let n(q) = -22*q**2 + q. Let v(a) = -67*a**2 - 69*a - 207. Let x(z) = -6*n(z) + 2*v(z). What is w in x(w) = 0?
-69, -3
Let v = -29 - -24. Let k(l) = l**2 + 6*l + 7. Let b be k(v). Determine j, given that 9*j**5 + 6*j**3 + 2*j**4 - 15*j**5 - 2*j**b + 0*j**4 = 0.
-1, 0, 1/3, 1
Let y(a) be the first derivative of 2*a**5/55 - 3*a**4/11 - 2*a**3/11 + 16*a**2/11 + 24*a/11 + 2658. Find s such that y(s) = 0.
-1, 2, 6
Suppose 0 = -8*u + 25 + 119. Let -45 + u*k + 4*k**2 + 17 + 6*k = 0. Calculate k.
-7, 1
Suppose 45 = -4*f - 5*j, -f + 3*j - 1450 + 1477 = 0. Let -18/7*t**3 + 18/7*t - 3/7*t**4 + f + 3/7*t**2 = 0. What is t?
-6, -1, 0, 1
Let u(d) be the second derivative of d**6/120 + d**5/4 - 91*d**4/48 + 59*d**3/12 - 6*d**2 - 1174*d. Factor u(p).
(p - 2)*(p - 1)**2*(p + 24)/4
Let u be 112/32*(-48)/(-28). Suppose u*w = 12*w. Solve -2/7*d**3 + 0 + 0*d**2 + 1/7*d**5 + w*d**4 + 1/7*d = 0.
-1, 0, 1
Let n(m) be the third derivative of -5/24*m**4 + 0*m - 26*m**2 + 0 + 1/3*m**5 - 10/3*m**3 + 1/24*m**6. Solve n(b) = 0.
-4, -1, 1
Factor 2/9*r**2 + 112/9*r + 0.
2*r*(r + 56)/9
Factor 0 - 1/2*o**2 - 20*o.
-o*(o + 40)/2
Determine q so that -33767 - 160921 - 89*q**4 - 310*q**4 - 3986*q**2 + 148*q**3 + 46176*q + 397*q**4 = 0.
13, 24
Factor 2/7*d**2 - 1664/7*d + 346112/7.
2*(d - 416)**2/7
Let g = -146 + 162. Let r be (-57)/(-4) - 16/64. Factor 7*k + g*k**3 - 10*k**3 + k + 28*k**2 + r*k**3.
4*k*(k + 1)*(5*k + 2)
Let d = -801247/1885 - 51/377. Let l = 426 + d. Factor -4/5*q**5 - l*q**4 + 8/5*q**2 - 4/5 + 8/5*q**3 - 4/5*q.
-4*(q - 1)**2*(q + 1)**3/5
Let u(x) be the first derivative of -41 - 3/4*x**4 - 3/2*x + 1/9*x**3 + 1/36*x**6 + 17/12*x**2 + 7/30*x**5. What is o in u(o) = 0?
-9, -1, 1
Let q(p) = -950546873*p**3 - 4959371*p**2 - 8623*p - 7. Let a(n) = -3802187491*n**3 - 19837482*n**2 - 34491*n - 29. Let f(b) = 2*a(b) - 9*q(b). Factor f(r).
5*(575*r + 1)**3
Let i(s) = -s**3 - 4*s**2 + 11*s + 4. Let g(m) = 3*m**3 - 14 + 14*m**2 + 21*m - 8*m - 47*m. Let u(w) = 6*g(w) + 21*i(w). Let u(q) = 0. What is q?
-3, 0, 3
Let q(y) be the second derivative of 2*y**7/147 - 2*y**6/15 - y**5/7 + 25*y**4/7 + 753*y. Solve q(m) = 0.
-3, 0, 5
Let k(o) be the first derivative of o**5/15 - 23*o**4/6 - 47*o**3/9 + 501. Factor k(g).
g**2*(g - 47)*(g + 1)/3
Suppose 2*s - 3*k = -2*s - 1, 3*s - 3*k + 3 = 0. Determine c so that -4 + 9*c**2 - 5 + 56*c + 6*c**s - 50*c = 0.
-1, 3/5
Let i be 1/(-2) + (-155)/(-62). Factor -3 - i*z + 19 - 4*z**3 + 2*z**4 + 19*z - z - 3*z**4.
-(z - 2)*(z + 2)**3
Factor 7/4*u - u**4 + 15/4*u**3 + 0 - 9/2*u**2.
-u*(u - 1)**2*(4*u - 7)/4
Let q(n) be the first derivative of n**7/5460 - n**6/180 - 7*n**5/390 - n**3/3 + 18*n**2 - 132. Let g(l) be the third derivative of q(l). Factor g(p).
2*p*(p - 14)*(p + 1)/13
Let h(v) be the second derivative of -5*v**4/12 + 305*v**3/3 + 615*v**2/2 - 1022*v. Factor h(u).
-5*(u - 123)*(u + 1)
Let h(l) be the first derivative of 2*l**3/21 + 32*l**2/7 + 384*l/7 + 1679. Let h(t) = 0. Calculate t.
-24, -8
Let q(m) be the third derivative of 2*m**2 - 1/100*m**5 + 0*m + 2*m**3 - 19/40*m**4 + 5. Find f such that q(f) = 0.
-20, 1
Let x(d) be the second derivative of -d**4/108 + 35*d**3/54 - 11*d**2/3 - 2918*d. Suppose x(u) = 0. What is u?
2, 33
Let j be 3 + (2 - 2) - (1 - 40). Factor 5*g**2 - 5*g - 32 + 20*g + j.
5*(g + 1)*(g + 2)
Let o = 24783/2 + -12384. Factor 3/4*w**3 + 51/4*w + o*w**2 + 6.
3*(w + 1)**2*(w + 8)/4
Let t(a) be the first derivative of 4*a**5/5 - 288*a**4 + 90616*a**3/3 - 552384*a**2 + 3678724*a + 9446. Suppose t(y) = 0. What is y?
7, 137
Let p(v) be the third derivative of v**8/1176 + 11*v**7/735 + 41*v**6/420 + 61*v**5/210 + 5*v**4/14 - 4*v**2 + 48*v. Find y, given that p(y) = 0.
-5, -3, -2, -1, 0
Let q(i) = -i**3 + 23*i**2 - 113*i + 153. Let b(w) = 4*w**3 - 69*w**2 + 451*w - 459. Let t(s) = 4*b(s) + 14*q(s). Let t(d) = 0. What is d?
-17, -3
Let j(f) = f**3 - 13*f**2 + 37*f - 11. Let c be j(9). Let v be 7/((-140)/32) - c. Suppose v - 2/5*b**5 - 2/5*b + 2/5*b**4 - 4/5*b**2 + 4/5*b**3 = 0. What is b?
-1, 1
Let s(t) be the second derivative of -t**5/72 - 5*t**4/18 + 6*t**2 - 8*t - 2. Let r(v) be the first derivative of s(v). Suppose r(z) = 0. What is z?
-8, 0
Let a(q) be the first derivative of -3*q**4/4 + 15*q**3 - 21*q**2 + 803. Factor a(l).
-3*l*(l - 14)*(l - 1)
Let l(v) be the second derivative of -v**4/24 + 310*v**3/3 - 96100*v**2 - 2038*v. Factor l(n).
-(n - 620)**2/2
Let a(c) be the second derivative of -c**5/170 - 37*c**4/102 + 26*c**3/17 + 683*c + 5. Let a(b) = 0. Calculate b.
-39, 0, 2
Let b(d) be the second derivative of d**6/60 + 19*d**5/75 - 4*d**4/15 - 339*d**2/2 - 22*d - 1. Let z(o) be the first derivative of b(o). Factor z(i).
2*i*(i + 8)*(5*i - 2)/5
Let p be 7/2 - (68/(-8) - -9). Let -8*u**3 + 6*u**3 + p*u**3 - 14*u**2 - 11*u**3 + 12*u = 0. What is u?
-2, 0, 3/5
Let x(m) be the second derivative of 26/15*m**3 - 8/5*m**2 - 3 - 3/5*m**4 - 14*m. Suppose x(c) = 0. Calculate c.
4/9, 1
Suppose 3*a - 5*u = -233, 3*u + 2*u + 71 = -a. Let k = a - -80. Factor -31*n**k + 16*n**4 - 6*n**3 - 35*n**5 - 35*n**4 - 9*n**3.
-5*n**3*(n + 1)*(7*n + 3)
Let s(y) = y**2 + y + 1. Let j(p) = 7*p**2 + 23*p - 32. Let g(o) = -j(o) + 6*s(o). Let f be g(-19). Factor f - 1/6*k**4 - 2*k**3 - 6*k**2 + 0*k.
-k**2*(k + 6)**2/6
Let -60*w - 117*w - 171*w - 1475*w**2 + 1472*w**2 + 708 = 0. What is w?
-118, 2
Let d = -1181469 - -10633222/9. Let 176*w**2 - 768 + d*w**5 + 4*w**4 + 428/9*w**3 - 192*w = 0. Calculate w.
-12, -2, 2
Let n be (-160)/(-35) - (-5)/(105/9). Suppose -3 = -4*y - 5*l + 14, -n = -5*l. Factor -v**2 + v**2 - 48*v - v**y - 64 - 12*v**2.
-(v + 4)**3
Let b(v) be the second derivative of -157*v + 1/3*v**2 + 0 - 1/9*v**4 + 5/18*v**3 - 1/20*v**5. Factor b(y).
-(y - 1)*(y + 2)*(3*y + 1)/3
Let f(p) = -9*p**4 - 3*p**3 + 9*p**2 + p - 1. Let r be 3/(-4) + (-6)/(-48)*-2. Let x(a) = -a**4 + a**3 + a**2 + a + 1. Let o(l) = r*f(l) - x(l). Factor o(g).
2*g*(g - 1)*(g + 1)*(5*g + 1)
Let m(t) be the third derivative of -t**7/840 + t**6/80 + t**5/4 - t**4 + 14*t**2 - 1. Let y(c) be the second derivative of m(c). Suppose y(v) = 0. Calculate v.
-2, 5
Let g(h) = h**4 + 4*h**3 - 2*h + 2. Let o(t) = -9*t**4 + 28*t**3 + 60*t**2 - 42*t - 72. Let c(a) = -14*g(a) - 2*o(a). Factor c(y).
4*(y - 29)*(y - 1)*(y + 1)**2
Solve -343*g**5 + 148*g + 114*g**5 + 40*g**4 + 233*g**5 + 136*g**3 + 208*g**2 + 40 = 0 for g.
-5, -2, -1
Let j(x) be the third derivative of x**6/360 + x**5/12 + 3*x**4/4 + 20*x**3/9 - 4*x**2 + 4*x. Factor j(m).
(m + 1)*(m + 4)*(m + 10)/3
Suppose -7*s 