**4 + 5. Let x(p) = c*a(p) + 4*q(p). Factor x(j).
j**4
Let b = 12 - 24. Let l be 1 + (-32)/b + 2/6. Factor -8/3*r - 4/3*r**2 + l.
-4*(r - 1)*(r + 3)/3
Suppose 0 = -3*l - 9, 0 = -3*n - 2*l - 0*l + 57. Let q(j) = j**3 - 3 - 1 + 4*j**2 - 3 + 0*j**2 + 4*j. Let c(r) = -1. Let z(o) = n*c(o) - 3*q(o). Factor z(h).
-3*h*(h + 2)**2
Let x(g) be the third derivative of g**6/960 + g**5/240 - g**4/192 - g**3/24 - 146*g**2. Factor x(k).
(k - 1)*(k + 1)*(k + 2)/8
Suppose -i + 122 = 22. Let y = i + -96. Factor -1/7*g**y - 1/7*g**3 + 1/7*g**2 + 0 + 1/7*g.
-g*(g - 1)*(g + 1)**2/7
Let a be 385/(-770)*(-1 - 3). Factor -1/2*q + 0 + 1/4*q**3 + 1/4*q**a.
q*(q - 1)*(q + 2)/4
Suppose -196 - 140 = -6*u. Let w = 3 - 0. Suppose -63*k**4 - 2*k**5 - 12*k**2 - u*k**5 + 72*k**w - 89*k**5 = 0. What is k?
-1, 0, 2/7
Factor 1/3 + 4/3*j**2 - 5/3*j.
(j - 1)*(4*j - 1)/3
Let x(s) be the third derivative of 11*s**2 - 1/30*s**6 + 2/15*s**5 + 0*s**3 + 0*s + 0 + 1/2*s**4. Factor x(y).
-4*y*(y - 3)*(y + 1)
Let i(v) be the second derivative of -8*v - 5/6*v**3 + 0 + 1/3*v**6 + 0*v**2 - 5/4*v**5 + 5/3*v**4. Factor i(w).
5*w*(w - 1)**2*(2*w - 1)
Suppose -4/5*h**2 + 2/5*h**5 + 0 + 4/5*h**4 + 0*h - 2/5*h**3 = 0. Calculate h.
-2, -1, 0, 1
Factor 6 - 2/3*c**2 + 16/3*c.
-2*(c - 9)*(c + 1)/3
Let d(a) be the second derivative of -a**7/7560 + a**6/720 + a**5/90 + 7*a**4/12 + 9*a. Let x(l) be the third derivative of d(l). Suppose x(k) = 0. Calculate k.
-1, 4
Let o(h) = h**3 - 9*h**2 + 2*h - 18. Let s be o(9). Let g(j) be the second derivative of s*j**2 - 1/2*j**3 - 1/12*j**4 + 0 - 3*j. Find y, given that g(y) = 0.
-3, 0
Let j = 844 + -845. Let q(r) = 11*r - 3*r + 8*r**3 - 4*r**2 + 3 + 3. Let x(c) = -c**3 - c - 1. Let g(l) = j*q(l) - 6*x(l). Factor g(v).
-2*v*(v - 1)**2
What is t in 18/23*t - 6/23*t**2 + 0 - 10/23*t**3 - 2/23*t**4 = 0?
-3, 0, 1
Let t(g) be the third derivative of -g**5/30 + g**4/2 - 8*g**3/3 - g**2 + 15. Let t(h) = 0. What is h?
2, 4
Suppose -6 = 3*q - 0*q. Let z be 2*(-12)/(-8) + q. What is t in -z - 4*t + 5*t + 4*t**2 + t**2 + 2*t**3 + t**3 = 0?
-1, 1/3
Let c(t) = -2*t**3 + 7*t**2 + 9*t. Suppose -2*b + o + 11 = -4*b, -3*b - 3*o = 15. Let q(v) = v**3 - 7*v**2 - 8*v. Let a(d) = b*q(d) - 5*c(d). Factor a(n).
n*(n + 1)*(4*n + 3)
Let -145 + 160/3*p - 5/3*p**2 = 0. Calculate p.
3, 29
Let z(t) = -57*t**4 + 39*t**3 + 147*t**2 + 45*t - 42. Let j(i) = 23*i**4 - 16*i**3 - 59*i**2 - 18*i + 17. Let g(c) = 12*j(c) + 5*z(c). Let g(p) = 0. What is p?
-1, 1/3, 2
Let d(n) be the first derivative of -2*n**5/55 - 3*n**4/22 + 4*n**2/11 - 51. Solve d(p) = 0.
-2, 0, 1
Let c(r) be the second derivative of r**7/42 - 59*r**6/30 + 229*r**5/80 + 11*r**4/3 - 115*r**3/24 - 29*r**2/4 + 30*r - 2. What is a in c(a) = 0?
-1/2, 1, 58
Factor -29/8*f - 15/4 + 1/8*f**2.
(f - 30)*(f + 1)/8
Let x(g) be the second derivative of -g**6/60 + 3*g**5/40 - g**4/12 - 3*g - 24. Factor x(t).
-t**2*(t - 2)*(t - 1)/2
Suppose -3 = 4*p - 9728*u + 9725*u, 0 = p + 3*u - 18. Find l such that -32/5*l**p - 77/5*l**4 - 4/5*l**2 - 49/5*l**5 + 0 + 0*l = 0.
-1, -2/7, 0
Let c(u) be the first derivative of 8/65*u**5 - 1/13*u**2 + 0*u + 1/26*u**4 - 8/39*u**3 - 16. Suppose c(s) = 0. What is s?
-1, -1/4, 0, 1
Let g(n) be the second derivative of 1/4*n**4 + 0 + 0*n**2 - 10*n + n**3. Solve g(x) = 0 for x.
-2, 0
Let n(j) be the second derivative of -j**7/280 - j**6/40 - j**5/20 + 5*j**3/3 + 10*j. Let f(g) be the second derivative of n(g). Factor f(i).
-3*i*(i + 1)*(i + 2)
Suppose -145*a - 54*a = -398. Factor -1/3*b**3 + b**4 - 3*b**a - 2/3 + 3*b.
(b - 1)**2*(b + 2)*(3*b - 1)/3
Let x(i) = i**5 - i**3 + i. Let v(f) = 10*f**5 - 10*f**4 + 9*f. Let a(q) = -2*v(q) + 18*x(q). Factor a(j).
-2*j**3*(j - 9)*(j - 1)
Suppose 13*z = 8*z - 5*d + 40, d = 5. Factor -m**2 - 7/2*m - 2 + 1/2*m**z.
(m - 4)*(m + 1)**2/2
Let a be 8/28*(-6 - (-180)/16). Suppose 0 - a*q**3 + 9/2*q**2 - 3*q = 0. What is q?
0, 1, 2
Factor 99*n + 127*n - 250*n - 3*n**2.
-3*n*(n + 8)
Solve 1/2*t**2 - 32 + 15*t = 0.
-32, 2
Factor a**3 + 225*a**2 - 36*a**2 - 2839 + 2843 + 9024*a + 8832.
(a + 1)*(a + 94)**2
Let l(m) be the third derivative of -m**7/70 + m**6/4 - 6*m**5/5 - 4*m**4 + 64*m**3 - 11*m**2 + 10*m. Solve l(d) = 0.
-2, 4
Let a(w) = 3*w**3 - w**2 - 4*w + 3. Let n be 1*4*(-10)/(-20). Let u be a(n). Factor 5*t**3 - 2*t**3 + 6*t + 6 - u*t.
3*(t - 1)**2*(t + 2)
Let f(r) be the third derivative of r**10/15120 + r**9/3780 - r**7/630 - r**6/360 - r**4/24 - 3*r**2. Let p(x) be the second derivative of f(x). Factor p(k).
2*k*(k - 1)*(k + 1)**3
Suppose 3*c = -2*n - 18, 13*n + c = -0*c + 31. Factor 0*k - 3/2*k**4 - 3*k**n + 0*k**2 + 0.
-3*k**3*(k + 2)/2
Let a = -6188 + 6190. What is d in -2/5*d + 0 + 2/5*d**a + 2/5*d**3 - 2/5*d**4 = 0?
-1, 0, 1
Suppose 0 = 5*v + 6*v - 33. Let -5*o**v + 39*o**2 + 105*o + 8*o**3 - 71 - 76 = 0. Calculate o.
-7, 1
Suppose -7 + 3 = -2*o. Let v be 36/21 + o/7. Solve -2*w**3 - w**4 + 0*w**4 + v*w - 2*w - w**2 = 0 for w.
-1, 0
Let i be (0 + 1)/((-3)/(-72)). Let m(q) be the first derivative of 10*q**4 - i*q**2 + 5 + 12*q**3 - 26*q**4 + 16*q + 14*q**4. Find o, given that m(o) = 0.
1/2, 2
Let w(l) be the first derivative of 5*l**2 + 2/5*l**5 - 1/2*l**4 - 2*l**3 + 13 - 4*l. Factor w(h).
2*(h - 1)**3*(h + 2)
Let j(d) be the third derivative of -d**9/151200 + d**8/16800 + d**7/12600 - d**6/600 + d**5/4 - 16*d**2. Let l(c) be the third derivative of j(c). Factor l(r).
-2*(r - 3)*(r - 1)*(r + 1)/5
Let o(y) = -9*y**3 + 43*y**2 + 2*y - 22. Let p(n) = -4*n**3 + 21*n**2 + n - 12. Let l(m) = -3*o(m) + 7*p(m). What is w in l(w) = 0?
-1, 1, 18
Let i(g) be the third derivative of -g**7/70 + g**6/40 + g**5/5 - g**4/2 - 2*g**2 + 106. Factor i(l).
-3*l*(l - 2)*(l - 1)*(l + 2)
Suppose 28 = -3*i + 4*z, 2*z - 20 = 2*i - 4. Let f be -5 + 3 + 0 - i. Suppose 0*o**2 - o**2 + 0*o + f*o + 2*o**2 = 0. Calculate o.
-2, 0
Let y(i) be the third derivative of -i**6/24 - 13*i**5/12 - 25*i**4/12 + 20*i**3 + 3*i**2 + 24*i. Factor y(j).
-5*(j - 1)*(j + 2)*(j + 12)
Let a(i) be the third derivative of i**8/112 - 2*i**7/35 - i**6/40 + i**5/5 - 129*i**2. Solve a(h) = 0 for h.
-1, 0, 1, 4
Factor -7*d - 2*d**2 - 144 - 19*d + 122 + 5*d + 3*d**2.
(d - 22)*(d + 1)
Let m(f) be the first derivative of 9*f**4/4 - 11*f**3/3 - 8*f**2 + 4*f - 175. Factor m(p).
(p - 2)*(p + 1)*(9*p - 2)
Factor 2/11*o**5 + 0*o + 722/11*o**3 + 0*o**2 + 0 + 76/11*o**4.
2*o**3*(o + 19)**2/11
Let x(a) = a**3 + 3*a**2 + 6*a + 1. Let z be x(-2). Let i be 5 - 6 - 4/(24/z). Factor 1/6*f**4 + 0 - 1/6*f**2 - 1/6*f**3 + 0*f + i*f**5.
f**2*(f - 1)*(f + 1)**2/6
Let -10*h**5 + 10*h**2 - 26*h**3 - 5*h**5 + 6*h**3 - 10*h**4 + 22*h**5 + 15*h - 2*h**5 = 0. What is h?
-1, 0, 1, 3
Let h(y) be the first derivative of 64*y**3/9 - 8*y**2/3 - y + 348. Solve h(f) = 0 for f.
-1/8, 3/8
What is s in 658*s**4 - 903*s**4 + 1382*s**2 - 120 - 145*s**3 - 120 + 1578*s**2 + 390*s**3 - 20*s = 0?
-3, -2/7, 2/7, 4
Let j(o) be the second derivative of o**7/231 - 18*o**6/55 + 103*o**5/55 - 152*o**4/33 + 67*o**3/11 - 50*o**2/11 + 355*o. Factor j(n).
2*(n - 50)*(n - 1)**4/11
Let j(a) be the first derivative of -4*a**4 - 16*a**3 - 32*a**2 - 2/5*a**5 - 32*a - 10. Factor j(g).
-2*(g + 2)**4
Let d(a) be the second derivative of a**5/10 - 3*a**4/2 - a**3/3 + 9*a**2 + 99*a + 3. Factor d(p).
2*(p - 9)*(p - 1)*(p + 1)
Suppose 2*i + 116 - 112 = 4*u, -2*u + 2 = 3*i. Suppose i*d + 0 + 1/3*d**2 - 1/3*d**3 - 1/3*d**4 + 1/3*d**5 = 0. Calculate d.
-1, 0, 1
Let o(d) be the first derivative of d**4/6 - 22*d**3/3 + 57*d**2 - 162*d + 414. Solve o(y) = 0.
3, 27
Let f(i) = -i**3 - 12*i**2 + 26*i + 314. Let z be f(-12). Factor 9/5*h**z - 6/5*h**3 + 1/5*h**4 + 4/5*h - 12/5.
(h - 3)*(h - 2)**2*(h + 1)/5
Let r(o) be the second derivative of o**8/6720 - o**7/1260 - o**6/720 + o**5/60 + 5*o**4/4 + 21*o. Let w(u) be the third derivative of r(u). Factor w(f).
(f - 2)*(f - 1)*(f + 1)
Let y(k) be the second derivative of 8/21*k**3 + 0 - 2*k - 4/35*k**5 + 2/21*k**4 + 2/105*k**6 - 6/7*k**2. Determine g, given that y(g) = 0.
-1, 1, 3
Let q(t) be the first derivative of -t**6/720 - t**5/360 + 3*t**2 + 7. Let b(p) be the second derivative of q(p). Suppose b(o) = 0. What is o?
-1, 0
Factor -157512*l - 180704*l - 43593*l - 126587*l + 25992*l**2 - 150068*l + 3*l**4 + 6255408 - 456*l**3.
3*(l - 38)**4
Let j(n) be the firs