
Let v(g) be the first derivative of -g**4/6 + 8*g**3/3 - 9*g**2 - 1105. Factor v(a).
-2*a*(a - 9)*(a - 3)/3
Let s(w) = 11*w**2 + 55*w - 46. Let j(d) = -14*d**2 - 55*d + 44. Let t(a) = -4*j(a) - 5*s(a). Suppose t(c) = 0. Calculate c.
1, 54
Factor -54*l - 4*l**2 - 131*l - 90 + 950*l + 14*l**2 - 85*l**3.
-5*(l - 3)*(l + 3)*(17*l - 2)
Let s(l) = l**2 - 155*l - 470. Let b be s(-3). Factor -6*k**3 + 9/2*k**2 + 0 + 0*k + 3/2*k**b.
3*k**2*(k - 3)*(k - 1)/2
Let i(a) be the first derivative of 2*a**6/9 + 44*a**5/15 + 26*a**4/3 + 64*a**3/9 + 208. Let i(g) = 0. Calculate g.
-8, -2, -1, 0
Let c(k) = k**2 - 5*k**2 - k - 20*k - 8 + 2*k**2. Let q be c(-10). Factor 3 - 80*n - 36*n**3 - 3 - 40*n**q + 31*n**3.
-5*n*(n + 4)**2
Let b = -83 + 83. Suppose 3*s + b*s + 30 = 5*j, -5*j - 5 = 4*s. Factor 15*p + 389*p**4 - 53*p**2 + 12*p**j + 27*p - 382*p**4 - 8.
(p - 1)**2*(p + 4)*(7*p - 2)
Suppose k + 2 - 6 = 0. Suppose 120*o = 119*o + k. Factor -12*r**3 + 8*r**2 - 2*r + 8*r**o + 19*r**4 - 2*r**5 - 19*r**4.
-2*r*(r - 1)**4
Let r be ((-18)/(-12))/(3/4). Suppose -t + 298 + 11 = z, t = -2*z + 311. Factor 305*n - 10 - t*n + 2*n**2 - r.
2*(n - 3)*(n + 2)
Let x(n) be the second derivative of n**8/10080 + n**7/378 + 23*n**6/1080 + 7*n**5/90 - n**4/6 - n - 3. Let k(t) be the third derivative of x(t). Factor k(v).
2*(v + 1)*(v + 2)*(v + 7)/3
Let r(b) be the third derivative of b**5/12 + 265*b**4/24 - 140*b**3 + 790*b**2. Factor r(w).
5*(w - 3)*(w + 56)
Suppose -3*v + 285 = 3*s - 0*v, -2*v - 350 = -4*s. Let p be s/(-18)*(-2)/70. Find q such that 1/7*q**3 + 0 + 0*q**2 + 0*q + p*q**4 = 0.
-1, 0
Let i(u) be the second derivative of -23*u**4/6 + 91*u**3/6 + u**2 - u + 339. Factor i(o).
-(o - 2)*(46*o + 1)
Let w(t) be the second derivative of t**5/100 + 59*t**4/12 + 10804*t**3/15 - 10952*t**2/5 + 15*t + 119. Let w(y) = 0. What is y?
-148, 1
Let c = 445751/2 + -222865. Factor -1/2*k**4 + 23*k - 12*k**3 + 0 - c*k**2.
-k*(k - 1)*(k + 2)*(k + 23)/2
Let q = -54 - -56. Suppose 4 - q = g. Find d such that -32*d - 9*d**4 + 16 - 7*d**4 + 28*d**3 + 4*d**5 + 4*d**g - 4*d**4 = 0.
-1, 1, 2
Let o be (56/(-42))/((-96)/18 + 5). Factor 2/3*k**2 - 10/3*k - o.
2*(k - 6)*(k + 1)/3
Let a(q) = 10*q**2 - 181*q + 18. Let j be a(18). Let t(n) be the first derivative of -6 + 0*n - 9/5*n**5 - 1/2*n**6 - 3/2*n**4 + 0*n**2 + j*n**3. Factor t(z).
-3*z**3*(z + 1)*(z + 2)
Let n be -8*7/((-147)/6)*(-2282)/(-2608). Factor 2/9*v + 0 - 7/9*v**n.
-v*(7*v - 2)/9
Factor 32*o**2 + 465544*o**3 + 130 - 465542*o**3 + 166*o + 6*o**2.
2*(o + 1)*(o + 5)*(o + 13)
Suppose 2395*y = 2687*y. Factor 3/2*r + 3/8*r**2 + y.
3*r*(r + 4)/8
Suppose 22*n - 89 = 87. Let t be (n/6)/((1440/(-9))/(-16)). Solve 0 + 2/5*w + 8/15*w**2 + t*w**3 = 0 for w.
-3, -1, 0
Suppose -2*y + 53 = -0*y - 5*v, 47 = 2*y + v. Let 34*i**2 - 1051 + 3*i**4 + 1059 + y*i + 4*i + 17*i**3 = 0. What is i?
-2, -1, -2/3
Let k = -4 - -3. Let d(f) = -2*f**3 - 2*f - 2. Let u be d(k). Factor u*i**4 - 113*i**2 - i**3 - 2*i**5 + 111*i**2 + 3*i**5.
i**2*(i - 1)*(i + 1)*(i + 2)
Let z(q) be the third derivative of 0 - 8/13*q**3 - 1/780*q**6 + 1/78*q**4 - 71*q**2 + 1/78*q**5 + 0*q. Factor z(x).
-2*(x - 4)*(x - 3)*(x + 2)/13
Suppose 15 = -10*z + 135. Suppose -118*u = -124*u + z. Factor 3/2*h**u + 3*h**3 - 3/2*h**4 - 3*h + 0.
-3*h*(h - 2)*(h - 1)*(h + 1)/2
Let y(h) be the second derivative of -h**4/108 - 92*h**3/27 + 185*h**2/18 + 3*h - 2492. Let y(s) = 0. What is s?
-185, 1
Let o(s) = -s**2 - 17*s - 69. Let y be o(-10). Determine m so that -28*m + 0*m**3 - 6*m**2 - y - 1 + 2*m**3 + 34*m = 0.
1
Let f(l) be the second derivative of l**4/54 + 38*l**3/9 - 232*l**2/9 + 4124*l - 2. Find i such that f(i) = 0.
-116, 2
Suppose 18*g - 4 = 32. Solve -18 + 19 + 17 + 2*w**2 + 2*w**g - 38*w = 0 for w.
1/2, 9
Suppose 5*f - 31 = -3*l, 0 = -5*l + f - 4*f + 25. Let u = -52229 + 52231. Determine r so that -1/3*r**u - l*r - 3 = 0.
-3
Let u(r) be the second derivative of r**5/40 + 17*r**4/8 - r**3/12 - 51*r**2/4 + 2547*r - 1. Let u(h) = 0. Calculate h.
-51, -1, 1
Suppose -25*h - 4*f + 681 = -24*h, 0 = 5*f. Let z = h - 681. Solve 0 - 1/5*g**3 + 0*g**2 + z*g - 4/5*g**4 = 0 for g.
-1/4, 0
Let v(i) be the second derivative of 1/160*i**5 + 3/64*i**4 + 11*i + 0*i**3 + 41/2*i**2 + 0. Let g(s) be the first derivative of v(s). Factor g(q).
3*q*(q + 3)/8
Let i(n) be the second derivative of -8/7*n**2 + 1/10*n**5 + 1/21*n**4 - 4*n + 0 - 4/3*n**3. Suppose i(a) = 0. What is a?
-2, -2/7, 2
Let k = 9/10 + -17/30. Let s(o) = -10*o**2 + 343*o - 97. Let q be s(34). Factor 3*a**3 + 0*a**2 + 2*a**4 + 0*a + 0 + k*a**q.
a**3*(a + 3)**2/3
Suppose 226*l = -343*l + 34*l - 699*l. Solve 1/4*g**2 - 9/4 + l*g = 0.
-3, 3
Let w(p) be the third derivative of -1/336*p**8 + 0*p**7 + 0*p**5 + 72*p**2 + 0 + 0*p**4 + 0*p**3 + 0*p + 0*p**6. Factor w(q).
-q**5
Let -132*t + 19*t**2 + 168*t + 19*t**3 + 44*t - 2*t**4 + t**4 - 117*t**2 = 0. What is t?
0, 1, 8, 10
Let b(m) = -12*m**2. Let n(x) = 83*x**2 + 2508*x - 1572516. Let t(f) = -7*b(f) - n(f). Factor t(g).
(g - 1254)**2
Suppose -37*c = 46*c - 121275 + 121109. Factor -1/7*o**c - 60/7*o - 900/7.
-(o + 30)**2/7
Let h(d) be the first derivative of -4*d**3/3 - 100*d**2 - 1344*d - 1357. Factor h(f).
-4*(f + 8)*(f + 42)
Let j be (18880/1770)/(10 + -2). Let 0 - 2/3*z**3 + 4/3*z**2 - j*z**4 + 2/3*z**5 + 0*z = 0. Calculate z.
-1, 0, 1, 2
Let v be (-6)/10 + (-964)/(-90). Let h = 464/45 - v. Factor 4/5*o**3 + 0 + h*o - 4/5*o**2.
o*(2*o - 1)**2/5
Let n(c) be the second derivative of -c**4/3 + 17*c**3/6 - 6*c**2 + 59*c. Let o be n(3). Factor 10/3 - 25/3*j + 20/3*j**2 - 5/3*j**o.
-5*(j - 2)*(j - 1)**2/3
Let y be (-3)/(-4)*4*6/9. Let -16 + 88/3*t - 17*t**y + 4*t**3 - 1/3*t**4 = 0. Calculate t.
1, 3, 4
Factor 121/6*t - 61/3 + 1/6*t**2.
(t - 1)*(t + 122)/6
Let r(w) = 2*w**3 - w**2. Let v(u) = 69*u**3 + 4 + 4*u - u**2 + 54*u**3 - 129*u**3 + u**4. Let i(z) = 6*r(z) + 3*v(z). Factor i(x).
3*(x - 2)**2*(x + 1)**2
Let i(p) be the first derivative of p**4/10 + 74*p**3/5 - 45*p**2 + 226*p/5 + 3010. Factor i(r).
2*(r - 1)**2*(r + 113)/5
Let o(a) be the second derivative of a**6/30 + 4*a**5/5 + 61*a**4/12 + 11*a**3 + 101*a. Let o(s) = 0. Calculate s.
-11, -3, -2, 0
Let g(q) be the first derivative of q**6/90 + q**5/15 + q**4/6 + 2*q**3/9 + q**2/6 - 72*q + 56. Let w(z) be the first derivative of g(z). Factor w(x).
(x + 1)**4/3
Let f(s) = -s**3 + 10*s**2 + 5*s - 25. Let n(w) = -w**2 - 9*w - 1. Let r(h) = f(h) - n(h). Suppose r(l) = 0. What is l?
-2, 1, 12
Let r(y) be the third derivative of -y**5/60 + 11*y**4/24 + 8*y**3/3 + 2*y**2. Let n be r(12). Factor -2*h**2 - 3*h**3 - 10*h + n*h**2 + 11*h.
-h*(h - 1)*(3*h + 1)
Let k be (2/3)/(17/1020). Let k + 5*r**3 - 19*r**2 + 119*r - 11*r**2 - 139*r + 4*r**4 + r**4 = 0. What is r?
-2, 1, 2
Let w(c) = -17*c - 14. Let k be w(-1). Let -3*h + 0*h**2 + 18*h - 12 - 3*h**3 + k*h**2 - 3*h = 0. Calculate h.
-2, 1, 2
Let n(k) be the first derivative of -k**3/6 - 49*k**2/2 + 303*k/2 + 8921. Let n(o) = 0. What is o?
-101, 3
Let h = 1576414/1970505 + -2/394101. Suppose -5*s = -4*s. Factor -4/5*q**4 + s*q - h*q**2 + 0 - 8/5*q**3.
-4*q**2*(q + 1)**2/5
Let l = -88 - -92. Factor 13*j**3 + 18*j**2 + 17*j**4 + j**5 + 4*j - 8*j**l - 3*j**4 - 6*j**2.
j*(j + 1)**2*(j + 2)**2
Let p(k) be the first derivative of 1/9*k**4 + 4 + 1/30*k**5 - 24*k - 2/3*k**2 - 1/9*k**3. Let t(r) be the first derivative of p(r). Solve t(y) = 0 for y.
-2, -1, 1
Let s(k) = k**3 - 19*k - 15. Let z(f) = -36*f**2 + 16 + 20*f + 96*f**2 - f**3 - 31*f**2 - 30*f**2. Let w(g) = 4*s(g) + 3*z(g). Factor w(j).
(j - 6)*(j + 1)*(j + 2)
Find j, given that 2/3*j**5 - 2/3*j**3 + 14/3*j**2 - 8/3 + 0*j - 2*j**4 = 0.
-1, 1, 2
Suppose 19671 = -10*l + 5531. Let r = -1402 - l. Let 48 - r*p + 3/4*p**2 = 0. Calculate p.
8
Let u(i) be the second derivative of 8/3*i**4 + 7/6*i**6 + 0*i**2 + 6*i**3 + 5*i - 2 - 319/20*i**5. Let u(h) = 0. Calculate h.
-2/7, 0, 2/5, 9
Let l = -2/3048253 - -5127161564/27434277. Let -l - 2/9*p**2 + 116/9*p = 0. Calculate p.
29
Find y such that -1/8*y**5 - 19/8*y**4 - 301/8*y**2 - 161/4*y - 117/8*y**3 - 15 = 0.
-10, -4, -3, -1
Suppose 48*c - 785 = 43*c. Factor 74*j**5 + 12*j**2 - 24*j**3 + 80*j**5 - c*j**5 + 12*j**4 + 6*j**3 - 3*j.
-3*j*(j - 1)**4
Let w(r) be the third derivative of -r**5/60 + 169*r**4/24 - 644*r**3/3 + 