*(t + 2)**2*(t + 16)/3
Let l(t) be the first derivative of t**6/40 + 3*t**5/40 - t**3/4 - 3*t**2/8 - 30*t + 2. Let p(u) be the first derivative of l(u). Find n, given that p(n) = 0.
-1, 1
Let r(k) be the second derivative of -k**5/35 - 68*k**4/21 - 2312*k**3/21 + 684*k + 1. Find d such that r(d) = 0.
-34, 0
Let j(v) = -v + 2. Let m be j(3). Let a(o) = 8*o**3 + 18*o**2 + 22*o. Let l(z) = z**3 - z. Let u(g) = m*a(g) + 5*l(g). Factor u(c).
-3*c*(c + 3)**2
Let d(a) be the second derivative of -a**5/110 + 2*a**4/11 - 2*a + 62. Let d(t) = 0. What is t?
0, 12
Let p(d) = d**3 - 50*d**2 + 111*d - 41. Let c(x) = -x**3 + 50*x**2 - 109*x + 42. Let s(o) = 7*c(o) + 6*p(o). Factor s(y).
-(y - 48)*(y - 1)**2
Let j be (2/5)/((-2)/(-80)). Determine n so that -16/5 - 20*n**2 - j*n = 0.
-2/5
Suppose -1/4*a**3 - 1848*a + 3872 - 87/2*a**2 = 0. Calculate a.
-88, 2
Suppose -4*g - 4*o = -20, 45*o - 46*o - 25 = -5*g. Let q(w) be the first derivative of -6*w**2 - 27/5*w**5 + g - 3*w + 9*w**4 + 2*w**3. Factor q(i).
-3*(i - 1)**2*(3*i + 1)**2
Suppose 89/5*r + 0 + 1/5*r**3 + 18*r**2 = 0. Calculate r.
-89, -1, 0
Let y be (-40)/(-8) - 440/90. Let h(j) be the first derivative of 2/9*j - 2/27*j**3 - 10 - 1/18*j**4 + y*j**2. Suppose h(f) = 0. What is f?
-1, 1
Let p = 7105 - 3623549/510. Let w(d) be the third derivative of 0 + 0*d + 0*d**4 + 0*d**3 - d**2 - p*d**6 + 1/1785*d**7 + 1/510*d**5. Factor w(j).
2*j**2*(j - 1)**2/17
Let 0 - 6/5*l**3 + 9/5*l**2 - 3/5*l**4 + 0*l = 0. Calculate l.
-3, 0, 1
Let c(p) = p**2 - 34*p + 35. Let d be c(33). Let m(r) be the first derivative of 0*r + 2/27*r**3 + 0*r**2 + 0*r**4 - 2/45*r**5 + d. Factor m(w).
-2*w**2*(w - 1)*(w + 1)/9
Let p = -602 + 606. Let f(t) be the third derivative of 2*t**2 + 0*t - 1/108*t**p - 1/180*t**6 - 1/90*t**5 + 0 - 1/945*t**7 + 0*t**3. Solve f(u) = 0 for u.
-1, 0
Let w be ((-12)/14)/((-8)/112). Factor 3*q**2 - 8*q**2 + w*q - 11*q + 10 + 4*q.
-5*(q - 2)*(q + 1)
Let r(t) = -t**2 - 16*t + 2. Let k be r(-14). Factor -22*o + 4 + 32*o**2 + 8*o**3 + 8*o**3 - k*o**3.
-2*(o - 1)**2*(7*o - 2)
Let l(i) be the first derivative of -23 - 4*i**2 - 81/2*i**4 + 24*i**3 + 0*i. Factor l(t).
-2*t*(9*t - 2)**2
Let z(r) = 3*r**2 - 4*r + 4. Let x be z(1). Let a(o) be the first derivative of o**x + 5 + 9/2*o**2 + 6*o. Factor a(p).
3*(p + 1)*(p + 2)
Let h be 16/7 - (1079/(-1743) - (-2)/6). Find x such that -27/7 - h*x - 3/7*x**2 = 0.
-3
What is v in -8 - 6/5*v**3 - 104/5*v - 14*v**2 = 0?
-10, -1, -2/3
Let k(f) be the third derivative of 0 + 1/80*f**5 + 0*f**3 + 1/448*f**8 + 0*f + 4*f**2 + 0*f**4 - 1/280*f**7 - 1/160*f**6. Find l, given that k(l) = 0.
-1, 0, 1
Let h(l) be the second derivative of 0*l**2 - 2/3*l**3 - 1/4*l**5 - 5*l - 5/24*l**6 + 0 - 1/8*l**4. Let p(o) be the second derivative of h(o). Factor p(s).
-3*(5*s + 1)**2
Let r(p) = -3*p - p - p - 2*p + 2 - p**2. Let s be r(-7). Factor 2*o**5 - 16*o**4 - 2*o**2 + s*o**4 + 11*o**3 - o**3 + 4*o**5.
2*o**2*(o - 1)**2*(3*o - 1)
Let v be -1 + 1 + -2 - (-23 + 21). Let m(k) be the third derivative of 0*k - 5*k**2 - 1/200*k**6 - 1/24*k**4 + v + 1/30*k**3 + 7/300*k**5. Factor m(w).
-(w - 1)**2*(3*w - 1)/5
Let p(r) be the first derivative of r**4 - 32*r**3/3 + 34*r**2 - 40*r - 94. Factor p(c).
4*(c - 5)*(c - 2)*(c - 1)
Let m(r) be the second derivative of r**4/6 - 5*r**3/2 + 5*r**2 + 18*r - 3. Let p be m(7). Solve 2/3*n - 2/3*n**2 - 2/3*n**p + 2/3 = 0 for n.
-1, 1
Let a(x) be the first derivative of -13/4*x**2 + 0*x + 36 - 1/6*x**3. Factor a(d).
-d*(d + 13)/2
Suppose 0 = -34*z + 4*z. Let d(f) be the third derivative of 0*f**6 + z*f**3 + 0*f - 1/60*f**5 + 0*f**4 - 4*f**2 + 1/210*f**7 + 0. Solve d(b) = 0.
-1, 0, 1
Solve 0 - 1/6*c**4 + 0*c + 1/4*c**2 + 1/12*c**3 = 0.
-1, 0, 3/2
Let i(o) = -4*o + 29. Let k be i(7). Suppose 4*x - 3*q - k - 2 = 0, -2*x = q - 9. Determine c so that 0*c - 2/9*c**x - 4/9*c**2 + 0 = 0.
-2, 0
Let q = -1404 - -23882/17. Let m = 626630/443887 + 2/26111. Find p, given that -8/17 + m*p + q*p**2 = 0.
-2, 2/7
Suppose 4*s - 6*i = -i + 13, -s + i + 2 = 0. Let l be (-4 - -3)*s/3 + 3. Factor 6/7*z**3 - 24/7*z**2 + 6/7*z**l - 6/7 - 3/7*z**5 + 3*z.
-3*(z - 1)**4*(z + 2)/7
Factor 0*f**2 + 4/3*f**5 + 0 + 0*f - 4/3*f**4 + 1/3*f**3.
f**3*(2*f - 1)**2/3
Let k(n) be the first derivative of n**6/135 + 4*n**5/45 + 5*n**4/18 - 8*n**3/27 - 16*n**2/9 - 25*n + 3. Let o(x) be the first derivative of k(x). Factor o(a).
2*(a - 1)*(a + 1)*(a + 4)**2/9
Suppose 2*r = k + 5, -k = -4*r + r + 7. Solve 2*q**r - 2*q + 2*q**2 - 6*q**2 = 0.
-1, 0
Let n be (27/12*1)/(99/120). Factor 0 - n*y + 6/11*y**2.
6*y*(y - 5)/11
Find w such that 15 - 25/2*w - 5/2*w**2 = 0.
-6, 1
Let i(x) be the third derivative of 7*x**6/40 + 43*x**5/10 + 69*x**4/2 + 36*x**3 - x**2 - 13*x. Factor i(r).
3*(r + 6)**2*(7*r + 2)
Solve 39/4*f - 19/4 + 1/4*f**3 - 21/4*f**2 = 0.
1, 19
Let r**3 + 34 - 22 + 3*r**2 - 16 = 0. What is r?
-2, 1
Let p(f) = 14*f + 27. Let w be p(16). Let s = 255 - w. Find l, given that -2/9*l**2 - 4/9*l + 2/9*l**s + 0 + 4/9*l**3 = 0.
-2, -1, 0, 1
Solve 8/5*t**3 - 9/5*t + 4/5 + 2/5*t**2 - 6/5*t**4 + 1/5*t**5 = 0.
-1, 1, 4
Let j = 8705 + -8705. Find u such that -1/6*u + 0 + j*u**2 + 1/6*u**3 = 0.
-1, 0, 1
Let t = 1847 + -1845. Factor -1/3 + 1/3*n**3 + 1/3*n**t - 1/3*n.
(n - 1)*(n + 1)**2/3
Factor 0*v + 0 - 3*v**4 + 21/2*v**3 - 9/2*v**2.
-3*v**2*(v - 3)*(2*v - 1)/2
Let d be (-2)/(-1) + (-1 - -1). Suppose 0 = w - d. Factor -9*t**3 + 0*t**4 + 9*t**2 + t**4 - w*t + 2*t**4 - t.
3*t*(t - 1)**3
Let s(a) be the second derivative of 2*a + 0*a**2 + 1/30*a**4 + 1/50*a**5 + 0*a**3 + 0. Factor s(b).
2*b**2*(b + 1)/5
Suppose -2*c = k - 8, -21 = -c - 5*k + 1. Factor 24 + 27/2*b**c - 36*b - 3/2*b**3.
-3*(b - 4)**2*(b - 1)/2
Let r(l) be the third derivative of 55*l**8/1344 + 31*l**7/140 + 131*l**6/480 - 23*l**5/60 - 9*l**4/8 - 2*l**3/3 + 213*l**2. Suppose r(t) = 0. What is t?
-2, -1, -2/11, 4/5
Let t(x) be the second derivative of -x**6/90 - x**5/30 + x**4/4 + x**3 + 479*x. Factor t(h).
-h*(h - 3)*(h + 2)*(h + 3)/3
Let l(o) be the third derivative of 2*o**7/35 - 7*o**6/30 - 2*o**5/5 + 2*o**4 + 16*o**3/3 - 114*o**2. Factor l(g).
4*(g - 2)**2*(g + 1)*(3*g + 2)
Let m be (-254)/(-5) - (-12)/18*-6. Let i = m + -46. Factor -4/5 - 1/5*d**2 - i*d.
-(d + 2)**2/5
Let n(c) be the first derivative of -3*c**4/16 - 65*c**3/12 - 341*c**2/8 + 121*c/4 - 6. Factor n(f).
-(f + 11)**2*(3*f - 1)/4
Factor 0 + 1/8*w**2 + 1/8*w**3 - 3/2*w.
w*(w - 3)*(w + 4)/8
Let j(l) be the second derivative of -1/5*l**5 - 30*l - 2*l**4 + 0 - 6*l**3 - 8*l**2. Let j(r) = 0. What is r?
-4, -1
Let h(t) be the third derivative of -t**6/120 + 7*t**4/6 - 8*t**3 - t**2 - 11*t. Determine s, given that h(s) = 0.
-6, 2, 4
Factor 6 - 3*x**2 + 2*x - 24 + 2 + 10 + 7*x.
-3*(x - 2)*(x - 1)
Let r(g) = 14*g**2 - 56*g + 10. Let w(j) = -j**2 - 2*j - 1. Let b(a) = r(a) + 10*w(a). Factor b(s).
4*s*(s - 19)
Let g(j) be the third derivative of j**7/105 - j**6/30 + j**5/30 + 38*j**2. Factor g(c).
2*c**2*(c - 1)**2
Factor -157 - 275 + 62*b - 48*b**2 + 100*b + 90*b + 3*b**3.
3*(b - 6)**2*(b - 4)
Let w(c) = -5*c**3 - c**2 - c - 1. Let g be w(-1). Let l be 15/(-2)*2/(-3). Factor -4*z**3 - l*z**2 + 51*z**g + 4*z + z**2 + 0*z**3 - 47*z**4.
4*z*(z - 1)**2*(z + 1)
Let l(a) = 3*a**2 - 9*a + 2. Let p be l(3). Factor -p*t - 2*t + 4 + 6*t - 2*t**3 - 2 - 2*t**2.
-2*(t - 1)*(t + 1)**2
Let u(j) be the first derivative of j**4/18 + 4*j**3/9 - 8*j**2/3 - 128*j/9 - 120. Factor u(v).
2*(v - 4)*(v + 2)*(v + 8)/9
Solve 93*s - 648 + 15*s + 18*s**2 + 141*s**3 - 144*s**3 = 0.
-6, 6
Let g be -7*-2*(1 + 0). Let k be (-3)/(-21) + (-2)/g. Factor 3/5*a**3 + 0*a + k*a**2 + 0 + 3/5*a**4.
3*a**3*(a + 1)/5
Let l(o) be the second derivative of -o**6/15 + o**5/2 - 4*o**4/3 + 4*o**3/3 + 49*o. Factor l(u).
-2*u*(u - 2)**2*(u - 1)
Let x(c) be the second derivative of 0 + 1/4*c**3 - 1/6*c**4 - c + 1/4*c**2. Let x(z) = 0. What is z?
-1/4, 1
Let h(b) = -46*b - 3. Let q be h(3). Let r be 1*3 - (-376)/q. Determine p, given that -1/6 - 1/6*p**2 + r*p = 0.
1
Let j(b) = -11*b + 10 + 26*b - 14*b. Let h be j(-7). Suppose -h + f**2 - 3*f**2 + 4 + 3 - 2*f = 0. What is f?
-2, 1
Let d = -10363 + 31091/3. Solve 2*n**3 - d*n**2 + 0 + 0*n + 2/3*n**5 - 2*n**4 = 0.
0, 1
Let t(u) be the second derivative of u**9/3780 + u**8/420 + u**7/210 - 25*u**4/6 - 16