r.
-2*r*(r - 2)*(r - 1)
Let h(z) be the third derivative of -z**5/12 - 55*z**4/24 - 15*z**3 - 2417*z**2. Factor h(l).
-5*(l + 2)*(l + 9)
Let n = 6088/105315 + -2/3009. Let s = n + 1114/105. Factor 4/3*u**2 - s*u + 64/3.
4*(u - 4)**2/3
Find p such that -16*p**2 - 270*p + 986*p + 11*p**2 + 3*p**2 - 64082 = 0.
179
Let m be (2 - (-6)/7)/((-10)/(-35)). Suppose 5*b = 2*s - 4, b + 3*b - 5*s = -m. Find t, given that 3/5*t + b*t**2 - 3/5*t**3 + 0 = 0.
-1, 0, 1
Let i(f) be the first derivative of -3*f**5/5 - 249*f**4/4 - 1680*f**3 + 2646*f**2 - 666. Determine g so that i(g) = 0.
-42, 0, 1
Let x be (20/(-6))/(30/(-45)). Suppose x*m - 190 = -5*m. Determine a, given that -12*a**2 + 3*a - 7*a**3 - 3*a**4 - m*a + 23*a**3 - a**4 + 16 = 0.
-1, 1, 2
Let x(m) be the second derivative of m**6/20 + 399*m**5/40 + 4611*m**4/8 + 12155*m**3/4 - 12675*m**2 + 5045*m. Let x(d) = 0. What is d?
-65, -4, 1
Let g(h) be the third derivative of 5*h**8/336 - 7*h**7/6 + 415*h**6/24 - 325*h**5/4 + 3414*h**2. Factor g(p).
5*p**2*(p - 39)*(p - 5)**2
Let f = -19094 + 19094. Factor 1/3*x**4 - 1/3*x**2 + f - 1/6*x + 1/6*x**5 + 0*x**3.
x*(x - 1)*(x + 1)**3/6
Let b = 53 + -38. Suppose -19 + b = -2*x. Find o, given that 5 - 20*o + 25*o - 10*o**x - 5 = 0.
0, 1/2
Let d(h) = -3*h**2 - 409*h - 4585. Let m be d(-124). Let -50/7*c - 14*c**5 - 4/7 - 16*c**2 + 292/7*c**m - 4*c**4 = 0. Calculate c.
-2, -1/7, 1
Let 62*a**2 + 13*a**5 + 145*a**4 - 260 + 395*a**2 + 38*a**2 + 805*a**3 - 83*a**5 - 35*a**5 - 320*a = 0. Calculate a.
-1, 2/3, 26/7
Solve -1/5*m**2 + 203/5*m - 202/5 = 0 for m.
1, 202
Find s, given that 3/8*s**3 - 81/8*s - 9/2*s**2 + 729/4 = 0.
-6, 9
Suppose 0 = 4*y + 4*m - 20, -10 = -3*y + 3*m - m. Suppose y*u + 6*u = 200. Determine r, given that 7 + 2 - 8*r**3 + u + 6*r**4 - 32*r**2 + 3 + 2*r**5 = 0.
-2, 1, 2
Let c be ((-29)/((-261)/6))/9. Let z(a) be the second derivative of c*a**4 + 2/9*a**2 - 5/27*a**3 - 15*a - 1/90*a**5 + 0. Factor z(l).
-2*(l - 2)*(l - 1)**2/9
Suppose 2*j - 5*i = -1 + 4, 13 = 2*j + 5*i. Factor 17*x + 14*x - 25*x - 12*x**2 - j*x**3 + 10*x.
-4*x*(x - 1)*(x + 4)
Let h be ((-13)/((-351)/18))/(1/12). Let i(z) = -z**2 - 1. Let q(p) = p - 5*p + 2*p**2 + 14 + 4*p**2. Let b(w) = h*i(w) + q(w). Factor b(c).
-2*(c - 1)*(c + 3)
Let y be ((-3)/14)/((-21)/28) + 24/504. Let o = 68 - 68. Factor 1/3*a**4 + o - y*a**3 - a - 5/3*a**2.
a*(a - 3)*(a + 1)**2/3
Let f(w) be the second derivative of -11*w + 2 - 168/5*w**5 - 104*w**3 - 353/3*w**4 + 98/15*w**6 - 40*w**2. Suppose f(n) = 0. What is n?
-1, -2/7, 5
Let g(a) be the third derivative of -10*a**2 + 1/840*a**8 + 0*a**3 + 0*a + 1/60*a**4 + 0*a**5 + 0*a**7 - 1/150*a**6 + 0. Factor g(i).
2*i*(i - 1)**2*(i + 1)**2/5
Let t be (1 + -6)*4/(-170). Let x be ((-48)/(-160))/(((-62424)/(-960))/51). Solve t*q**3 - 8/17*q**2 + 10/17*q - x = 0.
1, 2
Let y = 9480 + -312839/33. Let k(z) be the first derivative of 3/11*z**2 + 8/11*z - 22 + y*z**3. Solve k(h) = 0 for h.
-4, -2
Factor 6/5*u**3 - 4*u**2 - 88/5*u - 48/5.
2*(u - 6)*(u + 2)*(3*u + 2)/5
Let a(r) = 31*r + 68. Let p be a(-2). Let h(w) = -3*w**2 + 17*w + 8. Let y be h(p). Factor 24/7*l**y - 2/7*l**3 + 128/7 - 96/7*l.
-2*(l - 4)**3/7
Let j(k) be the first derivative of -18/5*k**2 + 1/5*k**4 - 36/5*k + 4/15*k**3 - 18. Let j(m) = 0. What is m?
-3, -1, 3
Let s(g) be the third derivative of -7*g**5/300 - 67*g**4/30 - 38*g**3/15 - 3*g**2 + 58*g + 3. Find k, given that s(k) = 0.
-38, -2/7
Suppose 4*z - 15 = 5*d - 243, -3*d = 3*z + 144. Let i = 52 + z. Determine t, given that -3*t**4 + i - 5 + 5 + 3*t**3 = 0.
0, 1
Let n(p) be the second derivative of -p**4 - 2426*p**3/3 + 1620*p**2 - 790*p. Let n(a) = 0. What is a?
-405, 2/3
Let l = 117719/279 + -1027/93. Factor -172/9*q - 2/9*q**2 - l.
-2*(q + 43)**2/9
Suppose -z + 12 = -4*r + 25, 4 = -4*z + 4*r. Let d = 906/7 - 129. Factor -d*h**z + 0 - 12/7*h**2 - 9/7*h.
-3*h*(h + 1)*(h + 3)/7
Let k be (-19984)/(-30) - (-60)/90. Let m = -666 + k. Factor -m*g + 4/5 - 3/5*g**2 + 1/5*g**4 + 2/5*g**3.
(g - 1)**2*(g + 2)**2/5
Let c(l) be the second derivative of 0 + 0*l**2 + 1/70*l**5 - 113*l - 1/105*l**6 + 0*l**3 + 0*l**4. Factor c(x).
-2*x**3*(x - 1)/7
Let b(g) = -5*g**2 - 48*g + 22. Let d be b(-10). Factor 54*m**2 - 243*m - m**4 - 119*m**2 - 390*m**3 + 369*m**3 - 70*m**d.
-m*(m + 3)*(m + 9)**2
Let y(w) = w**3 - 85*w**2 + 245*w + 85. Let t be y(82). Let r be ((-15)/(-13) - 1) + (-68)/(-65). Determine j so that 0 - r*j**2 - 3/5*j**t - 3/5*j = 0.
-1, 0
Let s(v) = -v**2 - 115*v - 102. Suppose -2*h = 9 - 1. Let n(x) = -15*x**2 - 1610*x - 1430. Let j(u) = h*n(u) + 55*s(u). Let j(r) = 0. Calculate r.
-22, -1
Let m(w) be the third derivative of 1/1008*w**8 + 2 - 8*w**2 + 7/24*w**4 + 1/70*w**7 + 17/90*w**5 + 0*w + 5/18*w**3 + 13/180*w**6. Determine c so that m(c) = 0.
-5, -1
Let d(a) be the second derivative of a**6/480 - 7*a**5/80 + 49*a**4/32 - 73*a**3/6 - 19*a. Let j(z) be the second derivative of d(z). Factor j(o).
3*(o - 7)**2/4
Let u(c) = c**2 + 33*c - 3. Let v(s) = -6*s**2 - 164*s + 14. Let j(y) = 14*u(y) + 3*v(y). Let b(z) = 2*z**2 + 14*z. Let a(t) = 7*b(t) + 4*j(t). Factor a(w).
-2*w*(w + 11)
Let a = 189836 + -189836. Factor -4/3*q**2 + 4/3*q**3 + a*q - 1/3*q**4 + 0.
-q**2*(q - 2)**2/3
Let x(f) be the third derivative of -3/40*f**6 + 1/20*f**5 + f**2 - 80 + 3/8*f**4 + 0*f - f**3 + 1/70*f**7. Suppose x(l) = 0. Calculate l.
-1, 1, 2
Let i(m) be the second derivative of m**7/168 - 7*m**6/72 + 7*m**5/12 - 5*m**4/3 - 10*m**3/3 - 8*m. Let r(z) be the second derivative of i(z). Factor r(u).
5*(u - 4)*(u - 2)*(u - 1)
Let j(f) = -8*f + 399. Let l be j(49). Let t be l/(-6)*(-272)/119. Factor -4/3*i**2 - t + 4*i.
-4*(i - 2)*(i - 1)/3
Let y(v) = 3*v + 6. Let l be y(-7). Let w(u) = -2*u**3 - 27*u**2 + 46*u + 18. Let q be w(l). Factor -p**2 + 1/3 + 2/3*p**q + 0*p.
(p - 1)**2*(2*p + 1)/3
Let b(v) be the first derivative of -v**5 - 1285*v**4/4 + 5200*v**3/3 - 2610*v**2 + 13957. Factor b(p).
-5*p*(p - 2)**2*(p + 261)
Suppose 4*y + q + 2 = -5, 0 = 3*y + 4*q + 54. Factor 0 - 195/4*n**3 - 15*n - 5/4*n**5 - 185/4*n**y - 75/4*n**4.
-5*n*(n + 1)**3*(n + 12)/4
Determine u so that 20*u**3 + 1589*u**2 - 3121*u**2 + 17*u**3 + 2720*u + 496 - 13*u**3 = 0.
-1/6, 2, 62
Factor -31*d**3 + 566*d - 38*d**3 - 3 + 280*d**2 + 98*d**3 + 287 - 31*d**3.
-2*(d - 142)*(d + 1)**2
Let x(g) be the second derivative of -9*g**6/10 - 138*g**5/5 - 2206*g**4/9 - 1840*g**3/9 - 200*g**2/3 + 752*g. Determine j, given that x(j) = 0.
-10, -2/9
Let b(g) be the first derivative of -2*g**3/15 + 2*g**2 + 48*g/5 - 10780. Factor b(l).
-2*(l - 12)*(l + 2)/5
Suppose 20 = 5*l - p - 2, 4*l - 5 = 5*p. Let u(i) be the third derivative of 0*i**3 + 0*i + 1/24*i**4 - 11*i**2 - 1/60*i**l + 0. Factor u(w).
-w*(w - 1)
Let w(i) = -76995308*i**3 - 6034076*i**2 - 157584*i - 1372. Let x(a) = -a**3 + 43*a**2. Let o(g) = w(g) + 20*x(g). Factor o(t).
-4*(268*t + 7)**3
Let c be (2715/(-3258))/(-2*(-3)/(-30)*15/24). Factor -200/3*z**2 - c*z - 1/6.
-(20*z + 1)**2/6
Let p(c) = -711*c - 7108. Let v be p(-10). Let u(j) be the first derivative of 8/3*j + 1/6*j**4 - 8 + 8/3*j**v + 10/9*j**3. Determine h so that u(h) = 0.
-2, -1
Let v(h) be the third derivative of -h**7/420 - h**6/180 - 23*h**3/3 + 113*h**2. Let z(i) be the first derivative of v(i). Factor z(t).
-2*t**2*(t + 1)
Let k = -362 - -622. Suppose -132*l**3 - 114*l**3 + k*l**3 + 2*l**4 + 16 + 36*l**2 + 40*l = 0. What is l?
-2, -1
Let b(m) be the second derivative of m**5/70 - 3*m**4/7 + 36*m**3/7 - 216*m**2/7 + 3*m + 97. Factor b(k).
2*(k - 6)**3/7
Let g(n) be the third derivative of -n**5/330 + 13*n**4/66 + 9*n**3/11 - 68*n**2 + 3*n. Find a, given that g(a) = 0.
-1, 27
Let v be 0 + -2 + (10 - 5). Find w such that -72 + 60*w**2 - 12*w + 4*w**v - 44*w**2 + 0*w**3 = 0.
-3, 2
Let s(x) be the first derivative of 1/8*x**4 + 0*x + 7/2*x**2 + 7 + 5/2*x**3. Solve s(q) = 0 for q.
-14, -1, 0
Suppose -4*q - 4*n - 28 = 4, 22 = -4*q - 2*n. Let a be 1*(q + 5)*(4 - 2). Factor -20*x + 5*x**a + 0*x**2 + 40*x**2 + 55 - 55 - 25*x**3.
5*x*(x - 2)**2*(x - 1)
Let k(q) be the third derivative of q**8/4032 + q**7/84 + 11*q**6/144 - q**5/30 + 3*q**3 + 11*q**2 - 5. Let w(h) be the third derivative of k(h). Factor w(p).
5*(p + 1)*(p + 11)
Factor -1/6*j**2 + 235/2 + 116/3*j.
-(j - 235)*(j + 3)/6
Let h(a) = -55*a**2 + 114*a