*(j - 1)**3*(j + 1)
Let c(g) be the first derivative of -g**4/3 - 43*g**3/3 + 22*g**2 - 240*g - 283. Let o(p) be the first derivative of c(p). Factor o(r).
-2*(r + 22)*(2*r - 1)
Let f(u) = -2*u - 566 - 3*u + 561. Let d be f(0). Let g(p) = p**2 - p + 1. Let c(k) = -7*k**2 + 4*k - 3. Let v(t) = d*c(t) - 30*g(t). Factor v(s).
5*(s - 1)*(s + 3)
Let d(n) be the third derivative of 0 - 59*n**2 + 0*n + 0*n**3 + 0*n**4 - 1/180*n**6 + 0*n**5. Factor d(m).
-2*m**3/3
Let p = -4/65849 - -1712086/197547. Let 4/3*o + 0 - p*o**2 - 34/3*o**3 + 290/3*o**4 + 50*o**5 = 0. What is o?
-2, -1/3, 0, 1/5
Let t(o) = 2082*o + 4168. Let f be t(-2). Factor 9*s**5 + 640/3*s - 1160/3*s**2 - 128/3 - 90*s**f + 300*s**3.
(s - 4)**2*(3*s - 2)**3/3
Let d(o) = -o**5 - 7*o**3 - 22*o**2 - 12*o + 2. Let v(h) = -h**5 - h**4 - h**2 + 1. Let j = -54 - -53. Let g(z) = j*d(z) + 2*v(z). Factor g(u).
-u*(u - 3)*(u + 1)*(u + 2)**2
Factor 82*l**4 + 82*l**4 + 16*l - 294*l**2 - 40*l**3 - 1080 - 952*l - 240*l**4 + 74*l**4.
-2*(l + 3)*(l + 5)*(l + 6)**2
Let f be 0 + -5 - (-1)/(432/(-112) - -4). Let 3/7*h**f + 3/7 - 6/7*h = 0. What is h?
1
Let x(f) be the third derivative of f**7/1050 - f**6/75 - f**5/6 - 3*f**4/5 - 19*f**3/6 + 7*f**2 + 3*f. Let m(b) be the first derivative of x(b). Factor m(z).
4*(z - 9)*(z + 1)*(z + 2)/5
Let t(f) be the second derivative of f**8/140 - f**7/40 - 17*f**6/60 - f**5/5 + 23*f**3/6 - f**2 - 32*f. Let m(d) be the second derivative of t(d). Factor m(n).
3*n*(n - 4)*(n + 2)*(4*n + 1)
Suppose 0 = -2*v + 24 - 22. Let -56*j**3 - 5*j**2 + 6 - v + 5*j + 51*j**3 = 0. What is j?
-1, 1
Let i = -191271/4 - -47818. Determine j, given that 1 + 5*j**2 - 5/2*j**3 + i*j**5 - 15/4*j + 0*j**4 = 0.
-4, 1
Let v(p) = -2*p**3 - 41*p**2 - 22*p - 33. Let r be v(-20). Factor -236*z**2 + r*z + 24 + 7*z + 2*z + 238*z**2.
2*(z + 2)*(z + 6)
Factor 16*o**2 + 4*o**3 + 75*o**4 + 716*o - 352 - 19*o**4 - 388*o**2 - 52*o**4.
4*(o - 8)*(o - 1)**2*(o + 11)
Suppose 4*i = -4*u - 4, 5*u + 1 = 10*u + 3*i. Factor 33*q - 39*q + 2*q**3 + q + 5*q**u + 11*q**2 + 29*q.
2*q*(q + 2)*(q + 6)
Let l = -442 + 445. Suppose l*b + 25 = -5*n, -3*n - 15 = 5*b - 7*b. Factor -4/5*j**3 + 8/5*j**5 + 0 + b*j**2 + 0*j + 14/5*j**4.
2*j**3*(j + 2)*(4*j - 1)/5
Factor -36*s**2 + 15*s**4 - 27*s - 50*s**4 + 47*s**4 - 3*s**5 + 6*s**3.
-3*s*(s - 3)**2*(s + 1)**2
Suppose 0 = 2*d + 3*p - 15, -p + 12 - 77 = -4*d. Suppose d = -2*y + 15. Factor y*g + 1/3*g**5 + 1/3*g**2 - 1/3*g**3 - 1/3*g**4 + 0.
g**2*(g - 1)**2*(g + 1)/3
Let j(y) = 52*y - 2597. Let w be j(50). Let c(k) be the first derivative of -35/8*k**4 + 0*k**2 + 0*k - 5/3*k**w + 32. Factor c(s).
-5*s**2*(7*s + 2)/2
Let x be 88/110 - 282/15. Let z be (x/(-15))/((-9)/(-15)). Let -1/5*w**3 + 0*w**z + 1/5*w + 0 = 0. Calculate w.
-1, 0, 1
Find m such that -17487*m**2 + 19*m**4 + 16782*m**2 + 1071*m - 22*m**4 - 363*m**3 = 0.
-119, -3, 0, 1
Let u(x) be the first derivative of -192*x**3/7 + 1200*x**2/7 - 2500*x/7 - 490. Factor u(q).
-4*(12*q - 25)**2/7
Let z(c) be the first derivative of -c**5 - 25*c**4/4 + 20*c**3 + 90*c**2 - 4169. Factor z(o).
-5*o*(o - 3)*(o + 2)*(o + 6)
Determine q so that 4/13*q + 302/13*q**2 + 0 = 0.
-2/151, 0
Let w(y) be the first derivative of 3*y**5/20 + 315*y**4/8 + 10813*y**3/4 - 16695*y**2/2 + 8427*y + 4187. Factor w(b).
3*(b - 1)**2*(b + 106)**2/4
Let b(h) be the first derivative of -h**4/20 + 2*h**3 - 72*h**2/5 + 485. Factor b(o).
-o*(o - 24)*(o - 6)/5
Factor 0 - 62/5*s**3 - 2/5*s**4 - 90*s - 102*s**2.
-2*s*(s + 1)*(s + 15)**2/5
Let o be 22 - 2*(-1365)/(-126). Factor 1/3*l**5 - o*l**3 + 0 + 0*l**2 + 0*l + 0*l**4.
l**3*(l - 1)*(l + 1)/3
Let a(t) be the third derivative of 1/36*t**5 + 3*t**2 + 0*t + 5/9*t**3 - 5/24*t**4 + 0. Factor a(p).
5*(p - 2)*(p - 1)/3
Let d(r) be the second derivative of 19/6*r**3 - 1/3*r**4 + 1/90*r**5 + 22*r + 1/270*r**6 + 0*r**2 + 0. Let f(v) be the second derivative of d(v). Factor f(n).
4*(n - 2)*(n + 3)/3
Suppose -4*u + 12 = -3*q - 3, 0 = u + 2*q - 1. Let 0*a**u - 2*a**2 - 3821 - 17*a**2 + 8*a + 12*a**3 + 3820 = 0. Calculate a.
1/4, 1/3, 1
Let n = 165 + -160. Suppose -3*x + 10 = -j, -4*x + n*j + 12 = 4*j. Solve -2/13*g**x + 4/13 + 2/13*g = 0.
-1, 2
Let -175*r**2 + 88*r**2 + 11*r**3 - 10*r + 83*r**2 - 9*r**3 + 12 = 0. Calculate r.
-2, 1, 3
Let n(i) be the second derivative of -20*i**3/3 - 677*i**2/2 - 228*i. Let f be n(-17). Let -2*c**f + 19/2*c - 11/2*c**2 - 2 = 0. What is c?
-4, 1/4, 1
Suppose -47 + 5 = -4*d - 2*s, 2*d = s + 31. Find v such that -v**2 - 2*v**2 + 22 + 13 + 18*v + d = 0.
-2, 8
Let f(p) be the third derivative of 0*p**3 + 0*p + 1/120*p**5 + p**2 - 13/48*p**4 + 0. Factor f(o).
o*(o - 13)/2
Let m(l) be the first derivative of l**4/26 - 2078*l**3/39 + 2075*l**2/13 - 2074*l/13 - 3320. Determine a so that m(a) = 0.
1, 1037
Factor 0 + 22/3*m**2 - 24*m - 1/3*m**3.
-m*(m - 18)*(m - 4)/3
Let g(v) be the second derivative of 0 + 99*v + 1/12*v**4 + 1/200*v**5 + 3/20*v**3 + 0*v**2. Factor g(y).
y*(y + 1)*(y + 9)/10
Let v = 516 + -509. Let d be v + (-13)/((-546)/(-288)). Factor -d*w**3 + 1/7*w + 1/7 - 1/7*w**2.
-(w - 1)*(w + 1)**2/7
Factor 96 - 96*l + 9193*l**3 - 18384*l**3 + 9188*l**3 + 30*l**2.
-3*(l - 4)**2*(l - 2)
Factor -2/9*o**3 - 4694/9 + 9386/9*o - 4690/9*o**2.
-2*(o - 1)**2*(o + 2347)/9
Suppose 49*u = 44*u + 15. Let q(j) be the third derivative of 0*j**5 + 1/144*j**6 - 1/126*j**7 + 5/2016*j**8 + 0 - j**2 + 0*j + 0*j**4 + 0*j**u. Factor q(w).
5*w**3*(w - 1)**2/6
Let o(c) = -3*c**4 + 413*c**3 - 9555*c**2 + 38029*c + 8. Let p(x) = -5*x**4 + 825*x**3 - 19110*x**2 + 76060*x + 20. Let j(g) = -5*o(g) + 2*p(g). Factor j(h).
5*h*(h - 39)**2*(h - 5)
Let b(j) = -j**3 + 8*j**2 - 4*j + 6. Let q be b(7). Let k be (-9842)/(-63) + (-3)/(q/2). Factor 3*d**5 - d**5 - k*d**2 - 6*d**3 + 154*d**2 + 2*d**4 + 4*d.
2*d*(d - 1)**2*(d + 1)*(d + 2)
Let l(o) be the first derivative of -2*o**3/57 + 2084*o**2/19 - 2171528*o/19 + 11011. Suppose l(d) = 0. What is d?
1042
Suppose -17992*c = -17972*c. What is s in c + 3*s**4 + 3*s**3 - 3*s**2 - 18/5*s + 3/5*s**5 = 0?
-3, -2, -1, 0, 1
Let l(q) = 6 + 5*q - 10*q + 3 - q**2. Let r(g) = g**2 + 4*g - 9. Let f(n) = 4*l(n) + 3*r(n). Let f(k) = 0. Calculate k.
-9, 1
Let a = 3767/3 + -1254. Let u(l) be the first derivative of 4/3*l - 45 - a*l**2 - 14/9*l**3. Factor u(m).
-2*(m + 1)*(7*m - 2)/3
Let s(g) = 8*g**3 - 50*g**2 - 254*g + 121. Let k(r) = 39*r**3 - 216*r**2 - 1269*r + 606. Let m(x) = -5*k(x) + 24*s(x). Factor m(b).
-3*(b - 1)**2*(b + 42)
Let k(h) be the second derivative of -1/3*h**3 + 0 - 1/60*h**6 + 0*h**4 + 0*h**2 + 3/40*h**5 + 166*h. Factor k(g).
-g*(g - 2)**2*(g + 1)/2
Let v be (-3)/((-126)/(-4)) - (-14 + 15/((-28350)/(-23445))). Solve 41/4*s**3 - 89/4*s**2 + 3 + 14*s - v*s**4 = 0.
-1/6, 2, 3
Let o(f) be the second derivative of -1/3*f**6 - 21/10*f**5 - 7*f + 0*f**2 - 19/6*f**4 + 0 - f**3. Solve o(q) = 0.
-3, -1, -1/5, 0
Let t be 11*(286/20)/13 + 24/(-2). Factor t*v**4 + 0 - 4/5*v - v**3 + 17/10*v**2.
v*(v - 8)*(v - 1)**2/10
Let o(p) be the first derivative of 58 + 3/11*p**2 + 0*p + 2/33*p**3. Solve o(x) = 0.
-3, 0
Suppose -80*g - 1/4*g**4 - 9/2*g**3 - 117/4*g**2 - 75 = 0. What is g?
-6, -5, -2
Let i(u) be the first derivative of -5*u**4/4 - 3390*u**3 - 3447630*u**2 - 1558328760*u - 1436. Factor i(q).
-5*(q + 678)**3
Let g(o) be the first derivative of -35*o**3/3 - 405*o**2/2 - 220*o - 2508. Factor g(u).
-5*(u + 11)*(7*u + 4)
Let t be 0 + -2 + (0 - -3). Suppose -2*d - 5*p + t = -23, d - p = 5. Factor d*b**4 + 0*b**3 - 3*b**3 - 4*b**4 - b**5 + b**2.
-b**2*(b - 1)**3
Let n(g) be the third derivative of -8/21*g**7 - 15/8*g**4 + 0*g - 5/3*g**6 - 329*g**2 + 0 + 0*g**3 - 11/4*g**5. Determine t so that n(t) = 0.
-1, -3/4, 0
Suppose 32 = 10*f + 122. Let q be (3 - (-33)/f)*18/(-24). Factor q + 1/2*b**2 - b.
(b - 1)**2/2
Suppose 459 - 39 = 35*a. Let k be (-3 - a/(-18))/(-1). Find y, given that -3/2*y - 1/6*y**2 - k = 0.
-7, -2
Let i be (-2 - -3)*(-2)/(-5). Let o = -6555/14 - -32971/70. Factor i*t**2 - o*t + 12/5.
2*(t - 6)*(t - 1)/5
Let y(f) be the second derivative of -9/7*f**2 - 44*f + 0*f**3 + 1/42*f**4 + 0. Factor y(s).
2*(s - 3)*(s + 3)/7
Suppose -v + 94 = 2*v + 4*w, 3*v + 5*w - 89 = 0. Factor v*q**2 + 14*q**2 + 6*q - 24 + 18*q**2 - 67*q**2.
3*(q - 2)*(q + 4)
Let w(c) be the first derivative of -1/25*c**5 -