 - 1)**3/3
Let v be (-35)/(-14)*(-1 + -1)/(-1). Factor -3570*l**4 + 3565*l**4 - 45 + 20*l + 5 - v*l**3 + 30*l**2.
-5*(l - 2)*(l - 1)*(l + 2)**2
Factor -975 - 134*y - 3888*y**2 - 36*y + 7788*y**2 - 3895*y**2.
5*(y - 39)*(y + 5)
Suppose x - 3*x + 4 = 0, o - 4*x - 7 = 0. Suppose 20 = z + o. Determine d, given that -5*d**2 - 2*d**z + d**2 + 4*d**4 - 2*d**3 + 4*d**5 + 0*d**2 = 0.
-2, -1, 0, 1
Let x(p) be the third derivative of -p**6/360 + 7*p**5/120 + 31*p**3/6 + 19*p**2. Let j(z) be the first derivative of x(z). Suppose j(b) = 0. Calculate b.
0, 7
Let l be (3/7)/(2/6). Let w = 556362/7 - 79479. Suppose -66/7*i**3 - l*i**2 + 0 + 60/7*i**5 + w*i**4 + 6/7*i = 0. Calculate i.
-1, -2/5, 0, 1/4, 1
Suppose -8 - 2 = -5*o. Let n be (9 + (-21)/14*6)/(-3). Determine v so that 7/2*v**3 + 1/2*v**o + 0 + n*v = 0.
-1/7, 0
Let d(b) = b**2 - 3*b - 2. Suppose -4*h + 1954 = 1958. Let y(f) = f**2 - 2*f - 2. Let j(k) = h*d(k) + 2*y(k). Factor j(u).
(u - 2)*(u + 1)
Let n be (-1)/(-23) - 33/759. Let y(d) be the third derivative of 0*d - 2*d**2 + 0*d**3 - 1/210*d**5 + n + 0*d**4 - 1/420*d**6. Factor y(u).
-2*u**2*(u + 1)/7
Let o = -1698552 + 1698602. Suppose -304/3*b**3 - 2*b**5 + 76/3*b**4 + 0 + 340/3*b**2 + o*b = 0. What is b?
-1/3, 0, 3, 5
Factor -51*a - 108 + 5/2*a**2 + 1/2*a**3.
(a - 9)*(a + 2)*(a + 12)/2
Suppose 0 = -m + 4*p + 2 - 9, -4*p + 12 = 0. Suppose -5*q = -m*k + 15, 2*q + 9 = 16*k - 13*k. Factor 0 + q*t + 1/5*t**4 + 1/5*t**2 + 2/5*t**3.
t**2*(t + 1)**2/5
Let i be (-6)/(-33) + (-2294)/(-814). Let m(d) be the second derivative of 0 + 3*d - 1/5*d**i + 1/20*d**4 - 9/10*d**2. Find g, given that m(g) = 0.
-1, 3
Solve -59/2*z**3 + 0 + 1/2*z**4 - 325/2*z - 385/2*z**2 = 0.
-5, -1, 0, 65
Let h be (-17252)/(-41314) - (-10)/7. Determine b so that 4/13*b**2 + h*b + 16/13 - 2/13*b**4 - 6/13*b**3 = 0.
-2, -1, 2
Suppose 0*r = -4*r - 44. Let c(z) = -26*z**3 - 304*z**2 - 2205*z - 5145. Let o(f) = -5*f**3 - 61*f**2 - 441*f - 1029. Let n(q) = r*o(q) + 2*c(q). Factor n(t).
3*(t + 7)**3
Let b be (6/5)/(((-49)/105)/(-7)). Suppose -66 = 12*w - b*w. Factor -w + 43 - r**3 + 5*r**2 - 11*r**2.
-(r - 2)*(r + 4)**2
Let s(g) = g**2 - 26*g + 10. Suppose 3*w + 8*x - 3*x = 43, 3*w - x - 13 = 0. Let n(b) = -27*b + 9. Let m(q) = w*s(q) - 5*n(q). Factor m(t).
3*(t - 1)*(2*t - 5)
Suppose d**3 + 208177*d**4 - 416433*d**4 - 4*d**2 - d**5 + 44*d**2 + 208216*d**4 = 0. What is d?
-40, -1, 0, 1
Let o(w) be the third derivative of -1/1680*w**7 - 5/96*w**6 - 25/4*w**4 + 0 + 0*w - 95*w**2 - 12*w**3 - 673/480*w**5. Factor o(p).
-(p + 1)**2*(p + 24)**2/8
Let x = -300 - -303. Factor 2 + 9*v**4 + 6 - 11*v**4 + v**x + 6*v**2 - 5*v**3 + 16*v.
-2*(v - 2)*(v + 1)**2*(v + 2)
Let p(r) be the first derivative of -r**3/4 - 1107*r**2/8 - 2642. Factor p(s).
-3*s*(s + 369)/4
Let t(l) be the third derivative of -l**6/24 - 77*l**5/12 + 5*l**4/24 + 385*l**3/6 - 425*l**2. Determine h so that t(h) = 0.
-77, -1, 1
Suppose -401 + 2*d**4 - 375*d**2 - 87*d**2 - 1476*d**2 + 642*d**3 + 1942*d - 247 + 0*d**4 = 0. What is d?
-324, 1
Suppose -2*b = -8, 12*x - 5*b = 14*x + 10. Let i(m) = 2*m + 33. Let v be i(x). Factor -14*k**3 - 90*k + 69*k**2 - 22 - k**3 + v*k**3 - 5.
-3*(k - 3)**2*(4*k + 1)
Suppose -7 = -2*a - 2*h + 5, 21 = a - 4*h. Suppose -14 - 16 = -6*k. Factor 56*w + 196 + w**2 - k*w**2 + a*w**2 - w**2.
4*(w + 7)**2
Let k(u) be the third derivative of 9*u + 0 + 1/70*u**5 + 6/7*u**3 + 2*u**2 - 25/56*u**4. Factor k(y).
3*(y - 12)*(2*y - 1)/7
Let h(c) = 35498750*c**2 - 33668*c + 16. Let x(w) = -35498753*w**2 + 33659*w - 18. Let z(y) = 5*h(y) + 4*x(y). Factor z(g).
2*(4213*g - 2)**2
Let u(l) be the first derivative of 3*l**4/4 + 68*l**3 + 1920*l**2 + 12288*l - 1149. Factor u(a).
3*(a + 4)*(a + 32)**2
Let r(j) = -6*j + 4. Let t be r(-5). Let q = t - 29. Solve 2*n**2 + 5 - 7 - 5*n + q*n**3 + 7 - 7*n**2 = 0 for n.
-1, 1
Suppose 25/3*v**3 - 10/3*v**4 - 8*v + 0 - 1/3*v**5 + 10/3*v**2 = 0. What is v?
-12, -1, 0, 1, 2
Let o be (-36)/16*36/(-27). Find f such that -16*f - o*f**2 - 23*f**2 - 2*f**3 + 14*f**2 = 0.
-4, -2, 0
Let w(m) = -17*m**3 - 80*m**2 - 1355*m - 6755. Let u(z) = 10*z**3 + 39*z**2 + 678*z + 3378. Let j(h) = -5*u(h) - 3*w(h). Suppose j(s) = 0. What is s?
-15
Suppose -2*g + n + 10 = 0, 6*n + 25 = 5*g + 7*n. Suppose 102*p**4 + 758*p**3 - 1071*p**2 - 27*p**4 + 610*p**3 - 373*p**2 + p**g = 0. Calculate p.
-38, 0, 1
Let a = -424474 + 424476. Find w, given that 2760*w - 1350 - 2/3*w**4 + 184/3*w**3 - 4412/3*w**a = 0.
1, 45
Factor -4/5*c**2 + 864/5 - 12*c.
-4*(c - 9)*(c + 24)/5
Let q(t) be the third derivative of t**6/30 - 9*t**5/5 - 44*t**4/3 - 40*t**3 - 2*t**2 - 455*t. Factor q(w).
4*(w - 30)*(w + 1)*(w + 2)
Factor 20*x + x + 49 + 3*x + 0*x + 1071 - 4*x**2.
-4*(x - 20)*(x + 14)
Suppose -12*g = 2394 - 186. Let i be (g/4508)/(1/(-56)). Suppose 24/7*h**2 + 2/7*h**4 + 12/7*h**3 + 0 + i*h = 0. Calculate h.
-2, 0
Let n(g) = -27*g - 165. Let c be n(-15). Solve c*a - 7*a**3 - 42 - 33*a**3 + 0*a**3 + 8*a**3 - 22*a - 192*a**2 = 0.
-7, 1/4, 3/4
Let c = 337 - 337. Suppose -208*p + 211*p - 6 = c. Factor 2/9*g**p + 8 - 8/3*g.
2*(g - 6)**2/9
Let m(l) be the second derivative of 280*l**4 - 325*l**3/3 - 15*l**2/2 + l - 754. Factor m(p).
5*(14*p - 3)*(48*p + 1)
Let k = 30830/369 + -9484/123. Solve 2/9*p**3 + k - 2/9*p - 58/9*p**2 = 0 for p.
-1, 1, 29
Let l(q) be the third derivative of 0 + 0*q + 3*q**2 + 1/20*q**4 + 1/10*q**3 + 1/100*q**5. Factor l(x).
3*(x + 1)**2/5
Solve -10/7*j**4 - 60/7*j**2 - 54/7*j**3 - 16/7*j + 0 = 0.
-4, -1, -2/5, 0
Factor 35/3*u**2 - 25/3*u**3 - 5*u + 0 + 5/3*u**4.
5*u*(u - 3)*(u - 1)**2/3
Let h be ((-162)/(-25515))/((-24)/(-21) - 1)*140. Factor 58/9 - h*n - 2/9*n**2.
-2*(n - 1)*(n + 29)/9
Determine s so that 31104/11 - 4320/11*s - 2/11*s**3 + 168/11*s**2 = 0.
12, 36
Let z = -35 - -40. Suppose 4*k - m - 12 = 0, k + 4*k + 10 = -z*m. Solve 71 - 71 + 2*r**2 + 2*r**k - 20*r = 0 for r.
0, 5
Let q(i) = -29*i + 754. Let y be q(26). Let g(v) be the second derivative of y + 2/21*v**4 - 1/35*v**5 - 2/21*v**3 + 0*v**2 + 18*v. Let g(w) = 0. What is w?
0, 1
Let z(c) = c**5 + c**4 - c**3 - 1. Let o(g) = 8*g**5 + 120*g**4 - 216*g**3 + 100*g**2 - 12. Let h(a) = o(a) - 12*z(a). Factor h(d).
-4*d**2*(d - 25)*(d - 1)**2
Let n be (2 + -3)*-2 + -5. Let r(p) = -2*p**3 - 21*p**2 + 27*p - 18. Let b(v) = v**3 + 10*v**2 - 14*v + 9. Let a(h) = n*r(h) - 7*b(h). Factor a(k).
-(k - 1)**2*(k + 9)
Let n(p) = p**2 + 16*p + 31. Let r be n(-14). Suppose 19 = -r*h + 25. Determine l so that -319*l + 321*l - 5*l**h - l**4 - l**3 + 5*l**3 = 0.
0, 1, 2
Let a(t) be the second derivative of t**4/6 - 40*t**3/3 + 2*t + 1322. Factor a(g).
2*g*(g - 40)
Let h = 17/5603 - -27964/16809. Factor h*n**2 + 2/3*n**3 - 2*n - 1/3*n**4 + 0.
-n*(n - 3)*(n - 1)*(n + 2)/3
Let f(i) be the first derivative of -2/9*i**3 + 2*i + 11/6*i**2 + 18. Suppose f(t) = 0. Calculate t.
-1/2, 6
Suppose -3*x = 3*c - 51, 91 = -x + 6*x + 3*c. Suppose -n - 27 = 5*w - 47, -2*n - 5*w + x = 0. Let -1/7*u**3 + n - 1/7*u**2 + 0*u = 0. What is u?
-1, 0
Let t(q) = -3*q**2 + 30*q - 19. Let n be t(9). Factor -4*h + 40*h + 57*h**2 - 161*h**2 - n + 76*h**2.
-4*(h - 1)*(7*h - 2)
Suppose -3*q + 592 + 625 = -2*h, -3*q + 601 = -h. Let u = 1849/3 + h. Factor -u*b**2 + 0 - 1/3*b**3 + 0*b.
-b**2*(b + 1)/3
Let b(l) = -2*l - 67. Let q be b(-36). Factor q*w - 4*w**2 + 4*w + 2*w**2 + w - 12.
-2*(w - 3)*(w - 2)
Suppose 345*n + 343*n - 24 = 680*n. Let s(z) be the first derivative of 19 + 5*z + 5/4*z**2 - 5/6*z**n. Suppose s(h) = 0. Calculate h.
-1, 2
Let v be (44/(-352))/(3/(-8)). Let j(d) be the second derivative of 10*d + 16*d**2 + 8/3*d**4 + 2/5*d**5 + 0 - v*d**6 + 1/21*d**7 - 32/3*d**3. Factor j(n).
2*(n - 2)**3*(n - 1)*(n + 2)
Let a(n) be the third derivative of n**6/120 - 11*n**5/20 - 14*n**3/3 - 13*n**2 + n. Let g(y) be the first derivative of a(y). Determine r so that g(r) = 0.
0, 22
Let d(k) be the second derivative of -k + 12*k**2 + 11/20*k**5 - 2/15*k**6 - 22/3*k**3 - 16 + 5/6*k**4. Factor d(x).
-(x - 2)**2*(x + 2)*(4*x - 3)
Let q(k) be the second derivative of -3*k**5/20 + 9*k**3/2 - 2851*k. Determine h so that q(h) = 0.
-3, 0, 3
Factor 48669*f + 341*f**2 - 9877*f + f**3 + 28900 - 9552*f.
(f + 1)*(f + 170)**2
Let l = -326 - -354. Let -3*n**3 + l*n + n + 54 - 13*n**2 + 16*n + 0*n**2 + n**2 = 0. What is n?
