 o(u) = 4*u**4 - 3*u**3 - 8*u**2 + 21. Let i(n) = -2*n**4 + n**3 + 4*n**2 - 9. Let z(q) = x*i(q) - 3*o(q). Factor z(r).
2*r**2*(r - 1)*(r + 2)
Let f(n) = -5*n**4 - 290*n**3 - 850*n**2 - 842*n - 279. Let x(u) = -6*u**4 - 291*u**3 - 852*u**2 - 843*u - 279. Let b(m) = -3*f(m) + 2*x(m). Factor b(o).
3*(o + 1)**3*(o + 93)
Let a(i) be the first derivative of -i**6/10 + 9*i**5/25 - 3*i**4/10 - 2*i**3/5 + 9*i**2/10 - 3*i/5 + 908. Factor a(h).
-3*(h - 1)**4*(h + 1)/5
Let s(p) be the first derivative of -p**4/3 + 1220*p**3/9 - 49136*p**2/3 + 262848*p + 4685. Solve s(z) = 0.
9, 148
Factor -1376/7 - 720/7*f - 2/7*f**3 - 102/7*f**2.
-2*(f + 4)**2*(f + 43)/7
Let j(h) be the second derivative of 2*h**6/75 - 33*h**5/25 + 272*h**4/15 + 4276*h. Let j(k) = 0. Calculate k.
0, 16, 17
Let n(p) = 38*p + 50. Let h be n(23). Let b = h - 922. Let 7/4*f + 1/4*f**3 + 5/4*f**b + 3/4 = 0. Calculate f.
-3, -1
Let q(w) = -48*w - 66. Let z(l) = 17*l + 22. Let s(b) = -4*q(b) - 11*z(b). Let a be s(-4). Let -2/3*g - 1/3 - 1/3*g**a = 0. Calculate g.
-1
Let c(h) be the second derivative of 2*h**6/15 - 400*h**5 + 500000*h**4 - 1000000000*h**3/3 + 125000000000*h**2 - 1165*h. Suppose c(i) = 0. What is i?
500
Let j(t) be the first derivative of 5/6*t**3 - 27*t - 15/2*t**2 - 1/4*t**5 - 27 + 5/4*t**4. Let m(s) be the first derivative of j(s). Factor m(q).
-5*(q - 3)*(q - 1)*(q + 1)
Let h(u) = u - 1. Let i be (3 - 34/6)*(-12)/16. Let a(f) = 4*f**i + 12 - 8*f - 6 - 4*f**2 + 2*f**2. Let n(r) = -a(r) - 6*h(r). Solve n(b) = 0 for b.
0, 1
Let a be (-6)/8 + (-42)/4*(-13)/182. Let n(w) be the third derivative of 1/15*w**3 + a*w + 28*w**2 - 1/150*w**5 + 1/120*w**4 - 1/600*w**6 + 0. Factor n(b).
-(b - 1)*(b + 1)*(b + 2)/5
Suppose -20*z - 77 = -65*z - 33*z + 79. Let p be ((-4)/(-10))/((-6)/(-80)). Factor -3 - 5*c + 8/3*c**z + p*c**3.
(c - 1)*(4*c + 3)**2/3
Let l be -3*(-12)/441*(-49 - -70). Factor 2/7*x**3 + l + 22/7*x + 12/7*x**2.
2*(x + 1)*(x + 2)*(x + 3)/7
Let i(k) be the second derivative of k**6/25 + 771*k**5/100 + 857*k**4/2 + 20097*k**3/10 + 11907*k**2/5 - 415*k - 1. What is u in i(u) = 0?
-63, -2, -1/2
Determine w, given that -11*w + 30 + 11*w**3 - 89/3*w**2 - 1/3*w**4 = 0.
-1, 1, 3, 30
Let i(u) be the second derivative of -u**7/14 + 13*u**6/10 + 189*u**5/20 + 83*u**4/4 + 17*u**3 - u + 107. Determine c, given that i(c) = 0.
-2, -1, 0, 17
Let p be (-14)/((-126)/(-27)) - -10. Suppose -p*s - 6*s = -3*s. Factor s*f + 0 + 4/3*f**4 - 4/3*f**3 - 8/3*f**2.
4*f**2*(f - 2)*(f + 1)/3
Let j = 315 - 39. Let x be 1/8 + j/736. Suppose r**2 - 1/2*r**5 + 0 - r**4 + 0*r**3 + x*r = 0. Calculate r.
-1, 0, 1
Let j(s) be the second derivative of -s**7/126 + s**6/18 - s**5/10 - 6*s - 154. Find a such that j(a) = 0.
0, 2, 3
Suppose -4*b + 516 = 2*u, -5 = 3*b - 17. Suppose 11500*v + 549*v**2 + 0*v**4 + 945*v**2 + 0*v**4 + 2091*v**2 + u*v**3 + 10580 + 5*v**4 = 0. Calculate v.
-23, -2
Find d such that 4 + 4 - 26 + d + 6*d + 10 + d**2 = 0.
-8, 1
Suppose -16*j + 226 + 430 = 0. Suppose -j*v = -0*v. Suppose -2/11*l**2 + 4/11*l + v = 0. Calculate l.
0, 2
Let c(s) be the second derivative of -s**4/18 + 226*s**3/9 - 75*s**2 + 2*s + 2454. Factor c(u).
-2*(u - 225)*(u - 1)/3
Let f(k) be the third derivative of -k**4/6 - 3*k**3/2 - 4*k**2. Let s be f(-3). Factor -11*g**5 - 2*g**2 + 20 - 2*g**s + 13*g**5 + 2*g**4 - 20.
2*g**2*(g - 1)*(g + 1)**2
Factor 3/7*r**3 + 369/7*r + 75/7*r**2 + 513/7.
3*(r + 3)**2*(r + 19)/7
Let c(y) be the first derivative of 4/3*y - 329 + 8/3*y**2 + 7/9*y**3. Factor c(o).
(o + 2)*(7*o + 2)/3
Let r(g) be the second derivative of 0*g**4 - 87*g + 0 + 5/2*g**3 - 5*g**2 - 1/4*g**5. Factor r(k).
-5*(k - 1)**2*(k + 2)
Let c(t) = -t**2 + 63*t - 180. Suppose 11*a - 1 - 32 = 0. Let d be c(a). Factor -34/9*q**3 - 2*q**5 + 0 - 8/9*q**2 + d*q - 44/9*q**4.
-2*q**2*(q + 1)**2*(9*q + 4)/9
Suppose 2*o = 8, -3*m - 3*o = 2*m - 37. Suppose m*i + 15 = 10*i. Factor -10*c**3 + 14*c**3 + 14*c**2 + 5*c**4 - 10*c + 11*c**2 - 24*c**i.
5*c*(c - 2)*(c - 1)**2
Suppose f + 3 = 95. Let j = f - 88. Factor j*u**5 - 20*u**2 + 5*u + 6*u**3 - 13*u - 18*u**3 + 3*u**4 + u**4.
4*u*(u - 2)*(u + 1)**3
Let d = 641665 - 10908273/17. What is w in -104/17*w - 64/17*w**2 - d - 10/17*w**3 = 0?
-4, -2, -2/5
Let n be 7/63 - (-638)/9. Suppose 0 = 9*u - 37 - n. Suppose s + 17*s**2 + 3*s - u*s**2 - 29*s = 0. What is s?
0, 5
Let k(c) = -c**3 - 4*c**2 + 4*c - 5. Let g be k(-5). Suppose 3*b - 5*b + 2*s + 6 = 0, -b - 4*s + 28 = g. Factor -6 - y**2 + 5 + b*y - 6*y.
-(y - 1)**2
Let d(l) = 8*l**3 + 1. Let x be d(1). Suppose 3*v + 3 - x = 0. Suppose 1 + 328*i**v - 1 - 316*i**2 + 3*i**3 = 0. Calculate i.
-4, 0
Let s(d) = -1378*d + 4. Let g be s(0). Let f(x) be the first derivative of -27 + 0*x**2 + x**3 + 1/4*x**g + 0*x. Factor f(l).
l**2*(l + 3)
Let b = 1737 - 2765. Let p = -1026 - b. Factor -4/7*c**3 + 2/7*c**4 + 4/7*c - 2/7*c**p + 0.
2*c*(c - 2)*(c - 1)*(c + 1)/7
Let t(j) be the third derivative of j**9/211680 + j**8/35280 + 7*j**5/6 + 38*j**2. Let k(d) be the third derivative of t(d). Factor k(m).
2*m**2*(m + 2)/7
Suppose 0 = -7*m + 18*m - 110. Factor 0*d**2 + 20*d + 15 - 3*d**2 - m*d - 2*d**2.
-5*(d - 3)*(d + 1)
Let h = -617947/5 - -122940. Let n = h + 651. Factor 1/5*r**4 + 4*r**2 + 0 + n*r**3 + 16/5*r.
r*(r + 2)**2*(r + 4)/5
Let t(o) be the first derivative of o**5/30 - o**4/8 - 2*o**3/3 + 5*o**2/3 + 8*o + 2430. Suppose t(c) = 0. Calculate c.
-2, 3, 4
Let f(h) be the first derivative of 3468*h**2 + 1/2*h**4 - 78608*h - 68*h**3 - 95. Factor f(a).
2*(a - 34)**3
Let c = 248 + -128. Find g, given that c*g**2 + 7764*g**5 + 132*g + 66 + 33*g**3 - 6*g**4 - 7767*g**5 - 18 = 0.
-2, -1, 4
Let v(h) be the first derivative of h**7/252 - h**6/216 - h**5/72 + 9*h**3 + 22. Let r(a) be the third derivative of v(a). Find k such that r(k) = 0.
-1/2, 0, 1
Let o be -4 - -7 - (-7 - 10 - -15). Let j(y) be the first derivative of -20*y - y**o + 0*y**4 + 0*y**2 - 10 + 25/3*y**3. Find g, given that j(g) = 0.
-2, -1, 1, 2
Let i(o) = -202*o**3 - 60*o**2 - 309*o - 491. Let v(m) = 90*m**3 + 30*m**2 + 154*m + 246. Let q(k) = -4*i(k) - 9*v(k). Factor q(g).
-2*(g + 5)**3
Let c be (8/4 + (-1 - -556))/1. Let m = -1670/3 + c. What is z in m*z**3 + 0*z**2 - 1/6*z**5 - 1/6*z + 0*z**4 + 0 = 0?
-1, 0, 1
Let w(j) be the second derivative of 5/2*j**3 - 1/4*j**5 + 5*j**2 + 0 - 146*j + 0*j**4. Let w(a) = 0. Calculate a.
-1, 2
Find t such that 121 + 224*t**2 + 270*t + 27 + 170*t - 458*t**2 + 222*t**2 = 0.
-1/3, 37
Let u(a) = -5*a**2 - 629*a + 764. Let c be u(-127). Factor -6*p**c - 2/3*p**4 - 10/3*p**3 - 4/3 - 14/3*p.
-2*(p + 1)**3*(p + 2)/3
Factor 70 - 5*s**2 + 142*s + 2*s**3 - 4*s**2 - 37*s**2 + 46 + 74.
2*(s - 19)*(s - 5)*(s + 1)
Let g be (231/66)/7*0/1. What is x in -1/11*x**3 + g + 0*x - 2/11*x**2 = 0?
-2, 0
Let a(d) be the third derivative of -d**5/160 + 99*d**4/64 + 4*d**2 - 18. Factor a(z).
-3*z*(z - 99)/8
Let h = 4554 + -68309/15. Let p(t) be the second derivative of 0*t**3 + 0 + 0*t**2 + h*t**6 + 0*t**4 + 4*t - 1/10*t**5. Suppose p(y) = 0. Calculate y.
0, 1
Suppose -4*b - 4*p = -116, 8977*b - 8980*b + 2*p + 92 = 0. Let -3/4*w**2 - 300 + b*w = 0. What is w?
20
Let b(p) be the second derivative of -p**6/315 - 3*p**5/14 - 39*p**4/14 - 111*p**3/7 - 324*p**2/7 - 30*p + 103. Factor b(c).
-2*(c + 3)**3*(c + 36)/21
Let y be (30952/48)/53 + 24/(-2). Let x(d) be the second derivative of y*d**3 + 1/6*d**4 + 0 - 3/20*d**5 + 0*d**2 + 33*d. Factor x(g).
-g*(g - 1)*(3*g + 1)
Let y = 123 - 129. Let d be (y/(-5))/((-4)/(-10)). Find r such that 9 + 2 + 3*r**d - 26 - 21*r**2 + 33*r = 0.
1, 5
Suppose 4*o + 48 = -2*d, -21 = 525*d - 529*d + o. Factor 1/5*z**d + 3364/5 + 116/5*z.
(z + 58)**2/5
Let m(t) be the second derivative of t**5/30 - 95*t**4/2 + 1136*t**3/3 - 3404*t**2/3 - 948*t + 7. Suppose m(p) = 0. Calculate p.
2, 851
Let g = -8114 - -17631/2. Let z = g - 700. Suppose 1/2*s**2 + z*s + 1 = 0. Calculate s.
-2, -1
Let p(x) be the second derivative of -5*x**4/36 - 230*x**3/9 - 880*x**2/3 - 627*x. Let p(r) = 0. Calculate r.
-88, -4
Let d(f) be the second derivative of -1/80*f**5 - 4/3*f**3 + 78*f + 0 + 5/24*f**4 + 4*f**2. What is g in d(g) = 0?
2, 4
Let l = -69 + 63. Let b be ((-16)/(-10))/(l/(-45)*3). Let -316*q**2 - 6*q**b + 4*q**4 + 310*q**2 - 8*q + 0*q**4 + 8*q**3 + 8 = 0. Calculate q.
-1, 1, 2
Let 