be the second derivative of v**4/3 - 44*v**3/3 - 480*v**2 - v - 73. Factor n(k).
4*(k - 30)*(k + 8)
Let t(v) be the first derivative of v**3/21 - 347*v**2/14 - 981. Determine y, given that t(y) = 0.
0, 347
Let d(s) be the third derivative of s**5/390 - 5*s**4/39 + 17*s**3/13 + 638*s**2. Factor d(k).
2*(k - 17)*(k - 3)/13
Let z(a) be the first derivative of -80/13*a**2 - 43 + 238/39*a**3 + 1/39*a**6 + 79/26*a**4 - 38/65*a**5 - 200/13*a. Let z(n) = 0. What is n?
-1, 1, 10
Let c(z) = 5*z**3 + 3*z**2 - 5*z + 3. Let x be 20/(-10) + 1 + 2. Let p(b) = b**3 + b**2 - b. Let d(w) = x*c(w) - 6*p(w). Factor d(o).
-(o - 1)*(o + 1)*(o + 3)
Let g(s) = -s**4 + s**3 - 2*s + 1. Suppose -5 = 18*c - 23. Let a(i) = -21*i**3 - 33*i**2 - 12*i - 3. Let t(x) = c*a(x) + 3*g(x). Suppose t(m) = 0. Calculate m.
-3, -2, -1, 0
Let p be 11 + 194*(-255)/4500. Let l(u) be the second derivative of 10*u + 0 + 8/15*u**2 + 4/15*u**3 + p*u**5 + 1/15*u**4. Let l(f) = 0. What is f?
-2
Let s(g) be the first derivative of g**6/2 + 153*g**5 + 256995*g**4/16 + 1140145*g**3/2 - 5574735*g**2/2 + 4293378*g - 1454. Find d, given that s(d) = 0.
-86, 3/2
Let h be (-23)/(-92) + 23/4. Suppose o**2 + 4*o**2 - 3*o**2 + 5*o - o**2 + h = 0. Calculate o.
-3, -2
Let y(b) = 2*b**3 - 13*b**2 + 16*b - 31. Let a be y(6). Suppose a*d + 8 = 33*d. Suppose 0 - 1/3*g**d + 2/3*g - 1/3*g**3 = 0. What is g?
-2, 0, 1
Let w(f) be the first derivative of -4*f**3/3 + 250*f**2 + 504*f - 7248. Solve w(j) = 0.
-1, 126
Let l(r) be the third derivative of 7*r**6/720 + 61*r**5/120 + 181*r**4/72 + 4*r**3/3 + 2*r**2 - 807*r. What is n in l(n) = 0?
-24, -2, -1/7
Let l be 7/2 + (-28 - -25). Let g(q) be the second derivative of -l*q**3 + q**2 + 0 - 2*q + 1/12*q**4. What is z in g(z) = 0?
1, 2
Let y = -6/18595 + 130261/297520. Let m(v) be the third derivative of -7/80*v**6 - 9*v**2 + 0*v - 1/2*v**3 + y*v**4 + 0 + 1/20*v**5. Factor m(b).
-3*(b - 1)*(b + 1)*(7*b - 2)/2
Let c(g) = -150*g**3 - 3060*g**2 + 5905*g + 979995. Let a(d) = 13*d**3 + 255*d**2 - 492*d - 81666. Let o(h) = 35*a(h) + 3*c(h). Solve o(v) = 0.
-15, 33
Determine r, given that 9/2*r**4 + 0*r + 0 + 183*r**2 + 555/2*r**3 = 0.
-61, -2/3, 0
Let x(o) be the second derivative of o**6/360 + 11*o**5/60 - 23*o**4/24 - o**3/6 - o**2 + 58*o. Let p(t) be the second derivative of x(t). Factor p(w).
(w - 1)*(w + 23)
Suppose -54*b - 51*b = -51*b - 119 - 97. Factor 3/2*r**b + 0 + 0*r + 0*r**2 - 27/2*r**3.
3*r**3*(r - 9)/2
Let c be ((-82)/123)/(((-2450)/(-60))/(-35)). Find u, given that 8/7*u**2 + 0*u**3 - c*u**4 - 4/7 + 0*u = 0.
-1, 1
Let r(z) = 5*z - 6. Let q = 47 - 45. Let t be r(q). Suppose -5*g**4 + 1 - 45*g**3 - 30*g**2 - 15*g**t - 5*g - 1 = 0. Calculate g.
-1, -1/4, 0
Let w(d) be the third derivative of 0 + 3/140*d**5 + 2*d**2 - 1/840*d**6 - 1/28*d**4 - 8/21*d**3 + 9*d. Factor w(q).
-(q - 8)*(q - 2)*(q + 1)/7
Suppose r + 1 = 0, 0 = -2*a - 3*r - 29 - 16. Let t be 7 + (0 - 203/a). Suppose -t + 2/3*q**4 + 20/3*q - 20/3*q**3 + 16*q**2 = 0. What is q?
-1, 1, 5
Let b(x) be the third derivative of -x**5/15 + 83*x**4 - 41334*x**3 - 111*x**2 + 2*x. Factor b(d).
-4*(d - 249)**2
Find p, given that 516/5*p**3 + 992/5*p**2 + 88/5*p**4 + 0 + 4/5*p**5 + 112*p = 0.
-14, -5, -2, -1, 0
Determine l so that 119/2*l + l**2 - 1/2*l**3 - 294 = 0.
-12, 7
Find t such that 188/7*t - 1800/7 + 16/7*t**2 = 0.
-18, 25/4
Factor -716/3*r**2 - 1/3 + 239*r.
-(r - 1)*(716*r - 1)/3
Solve 26640*l + 37816/3*l**2 + 2/3*l**5 - 202/3*l**4 + 4348/3*l**3 + 15552 = 0.
-4, -2, -1, 54
Suppose -3*g + 3*b = -6645, -2*g + 4*b + 1988 = -2452. Let m = -15455/7 + g. Factor -m*i + 12/7 + 3/7*i**2.
3*(i - 4)*(i - 1)/7
Let y = 497 - -1130. Let z = y + -4880/3. Determine t, given that t + z*t**2 + 0 = 0.
-3, 0
Suppose m = 10*m - 18. Factor -1496*n**2 - m*n**3 + 1476*n**2 - 2*n**3 - 24*n.
-4*n*(n + 2)*(n + 3)
Suppose -10*c = -1056 + 1016. Factor 3*d**3 + 0 - 11/3*d**c + 0*d + 2/3*d**2.
-d**2*(d - 1)*(11*d + 2)/3
Suppose -o - 3*o + 40 = 0. Suppose -6*u = -o*u + 4. Let z(t) = -t**3 + t**2 + t. Let g(f) = -6*f**2 - 5*f. Let c(k) = u*g(k) + z(k). Factor c(h).
-h*(h + 1)*(h + 4)
Let k(c) = 3*c - 242 + 0*c + 225. Let q be k(6). Factor -b**2 - 3 + 2*b - q + 3 + 4.
-(b - 3)*(b + 1)
Let u(t) be the second derivative of t**4/6 + 139*t**3/3 + 1170*t**2 - 6556*t. What is j in u(j) = 0?
-130, -9
Let a(x) be the third derivative of x**6/120 + 257*x**5/80 - 1115*x**4/32 + 197*x**3/6 - 48*x**2 - 2*x - 20. Factor a(b).
(b - 4)*(b + 197)*(4*b - 1)/4
Let r(t) = t**4 + 12*t**3 - 3*t**2 - 10*t + 2. Let s = 84 + -91. Let q(j) = -j**4 - 37*j**3 + 8*j**2 + 30*j - 7. Let k(a) = s*r(a) - 2*q(a). Solve k(u) = 0.
-2, -1, 0, 1
Suppose 11226*i = 11224*i + 16, 0 = -q + 3*i - 24. Let z(c) = -c**3 - 5*c**2 + c + 7. Let m be z(-5). Find b such that 2/17*b**3 + 8/17*b - 10/17*b**m + q = 0.
0, 1, 4
Let l(m) = -m**3 + 34*m**2 + m - 40. Let p be l(34). Let q be 16 + -6 - (-42)/p. Factor 2/5*s**4 - s**2 + 0 + 1/5*s**q + 2/5*s.
s*(s - 1)*(s + 2)*(2*s - 1)/5
Let s = -469961/6 - -78327. Factor -1/6*n**3 + s*n - 41/6*n**2 + 41/6.
-(n - 1)*(n + 1)*(n + 41)/6
Let r(m) be the first derivative of -m**4/6 + 5*m**3 + 145*m + 33. Let w(g) be the first derivative of r(g). Factor w(s).
-2*s*(s - 15)
Suppose -6*h + 25 - 1 = 0. Suppose h*x = 3*o - 22, 4*o = -0*o - 3*x - 4. Factor 6*m - 20*m + 2*m**3 + 3*m**o + 5*m**2 + 12 - 8*m.
2*(m - 1)**2*(m + 6)
Let g = 34034 + -34030. Let q(h) be the second derivative of -22/27*h**3 + 36*h - 16/9*h**2 - 1/18*h**5 + 0 + 43/54*h**g. Factor q(u).
-2*(u - 8)*(u - 1)*(5*u + 2)/9
Let s = -420 + 426. Let h = 6 - s. Factor 0*k + h - 10/7*k**3 + 4/7*k**2 - 2*k**4.
-2*k**2*(k + 1)*(7*k - 2)/7
Let g(s) = -268*s**2 - 6431*s + 38. Let m be g(-24). Suppose -8/5 + 56/5*x - m*x**4 - 176/5*x**3 - 42/5*x**2 = 0. Calculate x.
-2, -1, 1/5, 2/7
Let r(m) = -m**3 + 37*m**2 + 257*m + 48. Let l be r(43). Factor 16/3 + 100*a**2 - 40*a - 290/3*a**3 - 6*a**l + 40*a**4.
-2*(a - 2)**3*(3*a - 1)**2/3
Find s such that -1013673 - 1265288 - 7426 - 5238*s - 3*s**2 = 0.
-873
Let f(i) be the third derivative of 0*i - 4/39*i**3 + 5/156*i**4 - 28*i**2 - 2 - 1/390*i**5. What is o in f(o) = 0?
1, 4
Let k(y) be the second derivative of 3*y**5/20 - 7*y**4/4 - 27*y**3 - 108*y**2 - 868*y. Let k(a) = 0. What is a?
-3, -2, 12
Suppose -4*p + 17 = -23. Suppose 2*k = k + p. Suppose -k - 14*q**2 + 9*q**2 - 16*q + q = 0. What is q?
-2, -1
Let f(n) be the first derivative of n**5/36 - 25*n**4/18 + 95*n**3/18 + 239*n**2/2 - 215. Let h(z) be the second derivative of f(z). Solve h(r) = 0 for r.
1, 19
Suppose 0 = 2*k + 2, -4*s - 10*k = -8*k - 46. Factor s*d**2 - 61*d**4 - 18*d**3 + 85*d**4 - 27*d**4 + 72*d.
-3*d*(d - 2)*(d + 2)*(d + 6)
Suppose -10 = -2*k, -26 + 2 = -2*i - 4*k. Factor 5*x**5 + 24663*x - 24693*x + 55*x**i - 15*x**3 - 2*x**4 - 13*x**4.
5*x*(x - 3)*(x - 1)**2*(x + 2)
Let r(k) be the second derivative of -1/6*k**6 + 77 + k + 0*k**5 + 0*k**3 + 25/12*k**4 - 10*k**2. Let r(s) = 0. What is s?
-2, -1, 1, 2
Suppose 5*d + 27 = -j, -145 + 55 = 2*j - 2*d. Let c be (360/j - -6)/((-2)/14). Factor c - z**2 - 4*z**3 - 5*z**2 - 6 + 4*z - 6*z**2.
-4*(z - 1)*(z + 1)*(z + 3)
Let b be (-7)/(-1 - 0/(-21)). Let f(g) be the third derivative of 0*g**4 - 1/210*g**b + 0 + 0*g**3 + 0*g**5 - 8*g**2 + 0*g - 1/336*g**8 + 0*g**6. Factor f(d).
-d**4*(d + 1)
Let n be (1 - -893) + (9 - (11 + -5)). Let g = n - 6255/7. What is w in g*w**2 + 16/7*w**3 + 16/7*w + 4/7 + 4/7*w**4 = 0?
-1
Let k(z) be the third derivative of 0 - 1/84*z**6 + 32/21*z**3 - 19/105*z**5 + 0*z - 16/21*z**4 + 34*z**2. Factor k(g).
-2*(g + 4)**2*(5*g - 2)/7
Let y = 6194 + -6190. Let o(l) be the first derivative of -1/3*l + 7/12*l**2 - 20 - 3/10*l**5 - 7/24*l**y + 11/18*l**3. Suppose o(k) = 0. Calculate k.
-1, 2/9, 1
Let s(a) be the third derivative of a**6/180 + 7*a**5/45 + 8*a**4/9 - 128*a**3/9 + 400*a**2. Factor s(n).
2*(n - 2)*(n + 8)**2/3
Let m = -138604 + 66114142/477. Let u = m - -8/53. Factor -8/9 + 8/9*s**3 + u*s**4 - 8/9*s + 2/3*s**2.
2*(s - 1)*(s + 1)*(s + 2)**2/9
Let r = 196549 - 196546. Factor 6/5 + 12/5*a**2 + 3/5*a**3 + r*a.
3*(a + 1)**2*(a + 2)/5
Let p be (-6)/((-30)/10)*(-2)/(-22). Let h = 859 + -854. Find m, given that -4/11*m**4 - p*m**h + 4/11*m**2 + 0*m**3 + 2/11*m + 0 = 0.
-1, 0, 1
Factor 24/5 - 8*g + 18/5*g**2 - 2/5*g**3.
-2*(g