 - 5*k**3/12 + 72*k. Factor n(p).
p*(p - 5)*(p - 1)**2*(p + 1)/2
Suppose 2*p + 4*g = 12, -p - 2*p - g = -3. Let c(r) be the second derivative of 0 + p*r**3 + 0*r**2 - r + 1/18*r**4. Factor c(l).
2*l**2/3
Factor 4*s**3 + 180*s**2 - 95 + 283 + 868117*s - 868489*s.
4*(s - 1)**2*(s + 47)
Let f = 1513/8 - 189. Let h(p) be the first derivative of f*p**4 + 2/3*p**3 + 5/4*p**2 + p + 5. Determine o, given that h(o) = 0.
-2, -1
Let -128/9 - 34/9*w**2 + 160/9*w + 2/9*w**3 = 0. What is w?
1, 8
Factor 59*z**3 + 25*z**4 - 24*z**3 - 60*z - 176*z**2 + 36*z**2.
5*z*(z - 2)*(z + 3)*(5*z + 2)
Let j be (-21)/(-12)*((-4)/(-36) + (-22)/1386). Factor -j*s - 1/3*s**2 + 1/6.
-(s + 1)*(2*s - 1)/6
Find v such that 7/8*v**3 + 3/8*v**5 + 1/2*v**2 - 5/4*v**4 + 0 - 1/2*v = 0.
-2/3, 0, 1, 2
Let w be 23/35 - 52/91. Let f = w - -27/35. Find u, given that -4/7 - f*u**2 + 2*u = 0.
1/3, 2
Let x(f) be the second derivative of -15*f + 5/4*f**4 + 5/3*f**3 + 0 + 0*f**2 + 1/4*f**5. Factor x(l).
5*l*(l + 1)*(l + 2)
Let r = 379 + -25013/66. Let y = r - -389/462. Solve -2/7*l**3 - 4/7*l - y*l**2 + 0 = 0 for l.
-2, -1, 0
Let g = 6/19 - -46/95. Let i(x) be the first derivative of -1/4*x**4 + g*x**5 + 1/2*x**2 - 4/3*x**3 + 6 + 0*x. Factor i(t).
t*(t - 1)*(t + 1)*(4*t - 1)
Let s(k) = -18*k**3 + 87*k**2 - 39*k - 156. Let o(z) = z**3 - z**2 + z + 4. Let y(h) = 12*o(h) + s(h). Factor y(d).
-3*(d - 12)*(d + 1)*(2*d - 3)
Factor -1/2*g**5 - g**4 + 0 + g**2 + 1/2*g + 0*g**3.
-g*(g - 1)*(g + 1)**3/2
Let s(l) be the first derivative of 5*l**6/6 + 3*l**5/4 - 3*l**4/4 + l**3/6 - 16*l - 1. Let v(m) be the first derivative of s(m). Factor v(j).
j*(j + 1)*(5*j - 1)**2
Let o(s) = -s**3 + 6*s**2 + 2*s - 10. Suppose 0 = -y + 6*y - 30. Let z be o(y). Suppose -6/7 - 4/7*g + 2/7*g**z = 0. What is g?
-1, 3
Let k(q) be the third derivative of -1/448*q**8 - 1/70*q**7 + 3*q**2 - 1/40*q**6 + 0*q**4 + 0*q**5 + 0 + 0*q + 0*q**3. Let k(f) = 0. What is f?
-2, 0
Let w(h) be the first derivative of 2*h**3/3 - 19*h**2 + 119. Factor w(v).
2*v*(v - 19)
Determine p so that -8*p**5 - 20*p - 34686*p**3 + 3*p**5 - 30*p**4 + 34621*p**3 - 60*p**2 = 0.
-2, -1, 0
Let l(b) be the third derivative of -b**6/120 - 7*b**5/30 + 31*b**4/24 - 8*b**3/3 - 104*b**2. Let l(t) = 0. What is t?
-16, 1
Let g = 49 - 50. Let r = g + 6/5. Factor -1/5*d**4 + 3/5*d**2 - 2/5 + 1/5*d - r*d**3.
-(d - 1)**2*(d + 1)*(d + 2)/5
Let r(d) = -d**2 + d. Suppose -19 = c - 3*w + 8, -145 = 5*c - 5*w. Let y(n) = -7*n**2 + 2*n - 4. Let h(s) = c*r(s) + 5*y(s). Determine u, given that h(u) = 0.
-2
Determine x, given that -1922/3 - 124/3*x - 2/3*x**2 = 0.
-31
Suppose -5*n + w - 21 = 0, -4*n - n = -2*w + 22. Let q be 3*n*(-3)/12. Factor 3*d**3 + d**2 - d**q + d**2.
2*d**2*(d + 1)
Let d(c) be the third derivative of -c**6/24 + c**5/6 + 35*c**4/24 + 10*c**3/3 - 114*c**2. Determine y, given that d(y) = 0.
-1, 4
Let v be (7 + -7)/(5 + -6). Let n(f) be the second derivative of 1/20*f**6 - 2*f - 3/20*f**5 + 0 + 0*f**3 + v*f**2 + 1/8*f**4. Let n(r) = 0. Calculate r.
0, 1
Let x = 17 - 11. Suppose 0*a + x = 3*a. Solve 1/2*c**5 + 0*c**3 - 1/2*c**4 + 0*c**a + 0*c + 0 = 0.
0, 1
Let w = -37 - -39. Suppose -400*d**2 + 396*d**w + d + 4 - d = 0. What is d?
-1, 1
Let 24/7*x + 3/7*x**2 + 45/7 = 0. What is x?
-5, -3
Solve -12/5*c + 0 + 24/5*c**3 + 26*c**2 - 22/5*c**4 = 0.
-2, 0, 1/11, 3
Let t(o) be the first derivative of -2*o**5 - 5*o**4 - 25*o**3/6 - 5*o**2/4 - 4. Factor t(l).
-5*l*(l + 1)*(2*l + 1)**2/2
Let d(m) be the third derivative of m**5/390 + m**4/26 - 16*m**3/39 + 73*m**2. Factor d(g).
2*(g - 2)*(g + 8)/13
Suppose 6*q + 12 - 36 = 0. What is o in 12*o**3 + 9*o**2 + 6*o**4 + 0*o**4 - 3*o**q = 0?
-3, -1, 0
Let s(z) be the third derivative of -z**8/420 - 8*z**7/525 + 11*z**6/150 - 2*z**5/25 + 10*z**2 + 3. Suppose s(q) = 0. Calculate q.
-6, 0, 1
Suppose 606/7*z**4 + 850/7*z**3 + 90/7*z**5 + 20/7*z + 354/7*z**2 + 0 = 0. Calculate z.
-5, -1, -2/3, -1/15, 0
Let t(k) be the third derivative of -k**6/204 - k**5/85 - k**4/204 + 86*k**2. Let t(h) = 0. What is h?
-1, -1/5, 0
Let c be (-1)/2 + 65/10 + -4. Let x(g) be the third derivative of -1/210*g**5 + 0 + 4*g**c - 1/21*g**3 - 1/42*g**4 + 0*g. Determine y so that x(y) = 0.
-1
Let f(b) = 3*b**2 + 3*b**2 - 18*b - 5*b**2 - 3*b**2 + 2. Let r be f(-9). Determine s, given that 2/15*s + 4/15*s**r - 2/15 = 0.
-1, 1/2
Suppose -2*m**3 + 16*m + 8*m**2 + 8 - 5/2*m**4 - 1/2*m**5 = 0. Calculate m.
-2, -1, 2
Suppose 5*v = -3*v + 648. Suppose 3*y = -v + 81. Factor 4/9*s**4 + 0*s**3 + 2/9*s**5 + 0 + y*s**2 + 0*s.
2*s**4*(s + 2)/9
Let l = 164 - 160. Let x(f) be the third derivative of 0*f - 1/20*f**5 - 5*f**2 + 1/4*f**l + 0 + 0*f**3. Factor x(h).
-3*h*(h - 2)
Let z(g) = -g**4 + g**3 - g**2 - g + 1. Let f = -23 - -22. Let t(y) = -6*y**4 + 10*y**3 - 2*y**2 - 10*y + 6. Let o(l) = f*t(l) + 2*z(l). Factor o(x).
4*(x - 1)**3*(x + 1)
Factor -64/5 - 76/5*l**3 - 4/5*l**4 - 204/5*l**2 - 196/5*l.
-4*(l + 1)**3*(l + 16)/5
Let u(o) be the third derivative of 0 - 2/51*o**3 - 7*o**2 + 1/510*o**5 + 0*o - 1/204*o**4. Let u(w) = 0. Calculate w.
-1, 2
Let f(h) be the second derivative of h**4/36 - 16*h**3/9 + 128*h**2/3 + 149*h. Let f(d) = 0. Calculate d.
16
Let j = 34 + -28. Determine p, given that p**3 + 21*p**4 + 12*p**3 + j*p**2 + 14*p**3 = 0.
-1, -2/7, 0
Suppose 2 = 5*s + 2*x, -3*s + 7*s - 2*x + 2 = 0. Let j(u) be the second derivative of 0*u**3 + 1/72*u**4 + u - 1/12*u**2 + s. What is n in j(n) = 0?
-1, 1
Suppose -h + 5*n = 3*h - 69, -36 = -h + 5*n. Let b(y) = 4*y**2 - 22*y - 38. Let x(s) = 7*s**2 - 43*s - 75. Let u(l) = h*b(l) - 6*x(l). Factor u(p).
2*(p + 4)**2
Let u = 120 + 144. Let c be 6/4 - (-44)/u. Factor 6*w**2 + c*w - 2/3.
(2*w + 1)*(9*w - 2)/3
Let a be 80/240 - 1/6*-1. Factor 1/2*c**2 + 0 + 0*c**3 - a*c**4 + 0*c.
-c**2*(c - 1)*(c + 1)/2
Let p(i) be the third derivative of -3*i**7/490 + i**6/280 + i**5/10 - i**4/14 - 4*i**3/7 + 12*i**2. Determine h so that p(h) = 0.
-2, -2/3, 1, 2
Let j(o) be the first derivative of o**4/16 + o**3/3 + 3*o**2/8 - 48. Solve j(p) = 0.
-3, -1, 0
Suppose 2*d - 7 = 5. Suppose 8*b - 10 = d. Solve 0*i + 0 - 1/2*i**b - 1/2*i**4 - i**3 = 0.
-1, 0
Let x(f) be the second derivative of -1/70*f**5 - 2/7*f**2 - 2/21*f**4 - 14*f - 5/21*f**3 + 0. Factor x(d).
-2*(d + 1)**2*(d + 2)/7
Factor 2/5*m + 1/5*m**2 + 0.
m*(m + 2)/5
Let n = 1097 - 1091. Let m(p) be the third derivative of 0*p + 0*p**3 - n*p**2 + 1/120*p**5 - 1/24*p**4 + 0. Suppose m(j) = 0. What is j?
0, 2
Let l be 0*((-1)/2 - -1). Let t be (8/140)/((-9)/(-126)). Determine a so that 6/5*a**2 + l + t*a**3 + 2/5*a = 0.
-1, -1/2, 0
Let y(s) = -s**2 + 10*s - 6. Let k be y(9). Factor -3*n + 2*n**2 + 10*n**2 - 5*n + 6*n**3 - 2*n**k + 4*n**5 - 12*n**4.
4*n*(n - 2)*(n - 1)**2*(n + 1)
Suppose 3*x - 2*x + 2 = 0. Let a be 4/(-6)*(x + 1). Let 4/3 + a*d - 4/3*d**2 - 2/3*d**3 = 0. Calculate d.
-2, -1, 1
Let w = -5365/8 - -671. Let g(o) be the first derivative of 3 - w*o**4 - 1/2*o**3 + 0*o + 0*o**2. Suppose g(q) = 0. Calculate q.
-1, 0
Let z be ((-135)/18 + 7)*20/(-1). Let a(n) be the first derivative of 15/4*n**4 + 0*n + 2 + n**5 - z*n**2 + 0*n**3. Factor a(w).
5*w*(w - 1)*(w + 2)**2
Let d = 675/4 + -135. What is l in -45/4*l**2 - d - 135/4*l - 5/4*l**3 = 0?
-3
Factor 468*o - 7*o**2 - 23 - 139*o - 119 + 170*o.
-(o - 71)*(7*o - 2)
Let v(x) be the third derivative of -x**10/151200 - x**9/60480 + x**8/10080 + x**5/15 - 4*x**2. Let s(d) be the third derivative of v(d). What is n in s(n) = 0?
-2, 0, 1
Let a be 78/3*(-1)/(-6). Let s be 4/(-18) + (174/(-81))/((-2)/3). Factor 4/3 + 5/3*w**s + 4/3*w - a*w**2.
(w - 2)*(w - 1)*(5*w + 2)/3
Suppose -9*b + 336 = -13*b. Let h = 87 + b. Factor 2/3*d**h + 0 + 0*d - 2/3*d**2.
2*d**2*(d - 1)/3
Let q(c) be the second derivative of -2*c**4 + 1/5*c**5 + 10/3*c**3 + 0*c**2 + 43*c + 0. Factor q(p).
4*p*(p - 5)*(p - 1)
Let p = 28 + -25. Factor 12*t**2 + 5*t**3 + t - 10*t**2 - 4*t**p.
t*(t + 1)**2
Let o(a) be the second derivative of -2*a**7/49 - 4*a**6/15 + a**5/35 + 16*a**4/7 + 104*a**3/21 + 32*a**2/7 + 3*a - 1. Let o(y) = 0. What is y?
-4, -1, -2/3, 2
Let d(o) = -o**5 + o**4 + o**3 - o. Let i(v) = 3*v**5 + 2*v**4 + 4*v**3 + 4*v**2 + 3*v. Let u(l) = -10*d(l) - 5*i(l). Factor u(n).
-5*n*(n + 1)**4
Let y(k) = 3*k**2 - 7 - 6*k + 4 - 3 - k**3. Let q(f) = f + 1. Let l(r) = 6*q