4*n**2 - m*n.
4*(3*n - 1)**2/9
Let q = 859/312 + -9/104. Let c(n) be the second derivative of q*n**2 - 4*n + 4/9*n**3 + 1/36*n**4 + 0. Factor c(s).
(s + 4)**2/3
Let x(p) be the second derivative of p**4/12 + p**3/6 + 2*p**2 + 13*p. Let f(l) = 4. Let o = -4 - -2. Let c(k) = o*x(k) + 3*f(k). Factor c(g).
-2*(g - 1)*(g + 2)
Let b(r) be the first derivative of 8 + 3/2*r**2 - 1/4*r - 8/3*r**3. Factor b(v).
-(4*v - 1)*(8*v - 1)/4
Let h(u) be the second derivative of -u**5/80 + 5*u**4/24 + u**3 + 36*u. Solve h(b) = 0.
-2, 0, 12
Let p(i) be the second derivative of -i**4/6 + 26*i**3/3 - 13*i. Factor p(a).
-2*a*(a - 26)
Find q such that 0*q - 2/3*q**2 + 0 = 0.
0
Let f(t) be the third derivative of t**7/105 + 23*t**6/60 - 5*t**5/2 + 77*t**4/12 - 26*t**3/3 - 227*t**2. Factor f(k).
2*(k - 1)**3*(k + 26)
Suppose -189*z + 180*z + 45 = 0. Let v(f) be the first derivative of -1/6*f**6 + 0*f**3 + 0*f**z - 1/2*f**2 + 0*f + 1/2*f**4 - 8. Solve v(n) = 0.
-1, 0, 1
Let k = 35 - 38. Let w be (-1)/5*(1 + k)*1. Factor 0 - 2*n**2 + w*n.
-2*n*(5*n - 1)/5
Let h(o) be the first derivative of o**6/4 - 3*o**4/4 + 3*o**2/4 - 27. Factor h(s).
3*s*(s - 1)**2*(s + 1)**2/2
Determine z, given that -16/5 - 2/15*z**2 - 22/15*z = 0.
-8, -3
Let i(j) be the second derivative of j**5/5 + 38*j**4 + 2166*j**3 + 23*j - 2. Factor i(k).
4*k*(k + 57)**2
Let y be 2 - (-2148)/(-1440) - (-1)/(-3). Let p(d) be the third derivative of 2/15*d**5 + 0 + 0*d**3 - y*d**6 + 0*d - 4*d**2 + 1/6*d**4. Solve p(q) = 0.
-2/7, 0, 2/3
Let h = 29 + -25. Factor 50*a**5 - 816*a + 606*a**4 - 278*a**5 + 1344*a**h - 147*a**5 + 96 + 2544*a**2 - 3480*a**3.
-3*(a - 2)**2*(5*a - 2)**3
Let t be (-2)/(-15) + (-864)/(-1620). Factor 0*u + 0 + 8/3*u**3 - t*u**2.
2*u**2*(4*u - 1)/3
Suppose -a - 38 = -39. Let q be (-33)/(-45) + a/10*-4. What is l in -l + q*l**2 + 0 = 0?
0, 3
Let k(a) be the first derivative of 2/7*a**3 + 4/7*a - 24 - a**2. Determine c, given that k(c) = 0.
1/3, 2
Let p(s) = s**3 - s**2 - s - 2. Suppose -r + 0 = -2. Let h be p(r). Factor 0 - 3*d + 9 + h - 3*d**2 - 3.
-3*(d - 1)*(d + 2)
Let c(s) be the third derivative of -s**7/945 + s**6/60 - 5*s**5/54 + s**4/4 - 10*s**3/27 + 495*s**2. Determine a, given that c(a) = 0.
1, 2, 5
Suppose 73 = 7*t + 52. Determine m, given that -330/7*m**t - 51*m**2 - 120/7*m - 12/7 = 0.
-1/2, -2/5, -2/11
Let u(p) be the third derivative of -5*p**8/336 - 4*p**7/21 - 3*p**6/4 - 4*p**5/3 - 25*p**4/24 + 235*p**2. Factor u(f).
-5*f*(f + 1)**3*(f + 5)
Suppose -x = 2 - 5. Find l, given that -l - 15*l - 6*l**2 + 24 + 4*l + x*l**3 = 0.
-2, 2
Let x(c) be the third derivative of 34/105*c**7 + 2/3*c**3 - 4/3*c**4 + 22/15*c**5 - 14/15*c**6 + 0 + 0*c - 1/21*c**8 - 12*c**2. Let x(k) = 0. Calculate k.
1/4, 1
Let o(x) be the first derivative of -5/3*x**3 + 10*x**2 + 25 - 20*x. Factor o(z).
-5*(z - 2)**2
Let n(b) be the third derivative of -1/5*b**4 + 0*b + 1/50*b**5 - 1/175*b**7 + 1/25*b**6 + 31*b**2 + 0 + 0*b**3. Factor n(y).
-6*y*(y - 4)*(y - 1)*(y + 1)/5
Let q(u) = -u**4 + u**3 - u. Let s(g) = 5*g**4 - 3*g**3 - g**2 + 3*g. Let a = 20 - 21. Let w(k) = a*s(k) - 4*q(k). Suppose w(z) = 0. What is z?
-1, 0, 1
Let y be (1/3)/(4/36). Factor -12*t**4 + 10*t**y - 8*t**2 - 15*t - 3*t**2 + 5*t**5 + 27*t**4 + t**2 - 5.
5*(t - 1)*(t + 1)**4
Suppose -5*b = -13*l - 7*b + 40, l - 9 = -b. Let 4/7 + 2*p + 10/7*p**l = 0. Calculate p.
-1, -2/5
Let w(s) = -s**3 - 12*s**2 - 11*s + 6. Let c be w(-11). Factor 3*b + 2*b**2 + 2*b + b - 2*b - c.
2*(b - 1)*(b + 3)
Let o be ((-530)/(-1855))/(3/(21/4)). Let 1/2*p - o*p**2 + 0 = 0. What is p?
0, 1
Let i(q) be the second derivative of q**6/75 - q**4/6 + 4*q**2/5 + 109*q - 2. Let i(r) = 0. Calculate r.
-2, -1, 1, 2
Let -12*h**4 + 0*h**3 + 13*h**4 - h - 3*h**2 + 2 - h**3 + 2*h**3 = 0. Calculate h.
-2, -1, 1
Find j such that 600*j**2 + j - 598*j**2 - j**3 - 2 + 0*j**3 = 0.
-1, 1, 2
Let m = -25 - -29. Let a be 2 - (126/(-114) - m/(-38)). Suppose 3/4*o**a - 1/4*o**4 + 0 + 1/4*o - 3/4*o**2 = 0. Calculate o.
0, 1
Let i(g) be the second derivative of g**6/105 - g**5/70 - 5*g**4/14 - 23*g**3/21 - 10*g**2/7 - 3*g - 2. Factor i(x).
2*(x - 5)*(x + 1)**2*(x + 2)/7
Let r(u) be the second derivative of -u**6/45 + 17*u**5/15 - 11*u**4/6 - 621*u. Factor r(x).
-2*x**2*(x - 33)*(x - 1)/3
Determine h so that 0 - 68/7*h**2 - 4/7*h**4 + 40/7*h + 32/7*h**3 = 0.
0, 1, 2, 5
Suppose -6/5*u**4 + 54/5*u**2 + 0 + 18/5*u - 2/5*u**3 = 0. What is u?
-3, -1/3, 0, 3
Suppose 3*o - 4*o + 4 = 0, -p + 4*o + 9 = 0. Determine r so that -38*r**4 - 10*r**5 - 5*r**2 - 10*r**5 - p*r**3 - 2*r**4 = 0.
-1, -1/2, 0
Solve -23/9*w - 16/9*w**2 - 2/3 - 1/3*w**3 = 0 for w.
-3, -2, -1/3
Let n(b) be the second derivative of 2*b**7/7 + 4*b**6/15 - 21*b**5/5 + 4*b**4/3 + 8*b**3 + 152*b. Determine m, given that n(m) = 0.
-3, -2/3, 0, 1, 2
Let o(d) be the first derivative of d**3/4 + 30*d**2 + 1200*d - 262. Let o(w) = 0. Calculate w.
-40
Let x(t) be the first derivative of -2*t**6/21 + 24*t**5/35 - 10*t**4/7 + 22*t**2/7 - 24*t/7 + 246. What is a in x(a) = 0?
-1, 1, 2, 3
Find y, given that -4/5*y**2 + 0*y + 0 + 2/5*y**3 + 2/5*y**4 = 0.
-2, 0, 1
Let a = 47264/26255 - 1/5251. Suppose -a*j**4 - 3/5*j**5 + 6/5*j**2 + 3/5 - 6/5*j**3 + 9/5*j = 0. Calculate j.
-1, 1
Suppose 3*o - 5 = u, -3*u - u + 2*o + 30 = 0. Let j = u + -7. Find r such that 3*r + 2*r**5 - 3*r**5 + j*r**5 - 6*r**3 + 3 + 3*r**4 + r**5 - 6*r**2 = 0.
-1, 1
Let y(q) = -3*q**2 - 4*q + 6. Let f be y(-2). Determine u, given that 0 + 25/2*u**3 + 5*u**4 + 0*u - 25/2*u**5 - 5*u**f = 0.
-1, 0, 2/5, 1
Let b(a) be the second derivative of -5*a**4/12 + 25*a**3 - 1125*a**2/2 + 3*a + 16. Factor b(y).
-5*(y - 15)**2
Suppose 0 = -82*u + 79*u + 63. Let -17*m - u*m + 34*m - 3*m**2 + 7 = 0. What is m?
-7/3, 1
Factor 448*x**3 - 3*x**2 + 5*x - 2*x**2 - 906*x**3 - x + 449*x**3.
-x*(x + 1)*(9*x - 4)
Suppose 2*y - o - 3*o = 16, -5*y + 4 = -o. Let c(k) be the second derivative of -4/75*k**6 + y*k**2 + 1/15*k**3 + 3*k + 0 + 9/50*k**5 - 1/5*k**4. Factor c(x).
-2*x*(x - 1)**2*(4*x - 1)/5
Let y = -203 + 207. Suppose -5*a - 4*w = -3*w, -5*a = -3*w. Determine t, given that 3*t**2 + 0*t**3 + a*t**3 - y*t**3 + t**2 = 0.
0, 1
Let g(q) be the first derivative of -q**4 + 20*q**3/3 - 14*q**2 + 12*q + 76. Factor g(y).
-4*(y - 3)*(y - 1)**2
Suppose 0 = -8*f + 6*f + 234. Factor -18*z - 5*z**4 - f*z - 48*z**3 - 135*z**2 + 3*z**3.
-5*z*(z + 3)**3
Let s(f) = -19*f - 54. Let x be s(-3). Find t such that 2/5*t**x - 12/5*t**2 - 1/5*t**5 - 9/5*t + 0 + 4/5*t**4 = 0.
-1, 0, 3
Let n(f) be the third derivative of f**8/2016 - 2*f**7/315 - 81*f**2 - 2*f. Factor n(r).
r**4*(r - 8)/6
Suppose 3*a**2 + 54563 - 1056*a + 21759 + 40586 - 23980 = 0. Calculate a.
176
Suppose 7*q = -52 + 87. Let m(s) be the third derivative of q*s**2 + 0 - 1/20*s**5 + 0*s + 1/40*s**6 + 1/2*s**3 - 1/8*s**4. What is o in m(o) = 0?
-1, 1
Let l = -2/157 + 165/628. Let f(d) be the second derivative of -3/2*d**2 + 10*d + 0*d**3 + 0 + l*d**4. What is i in f(i) = 0?
-1, 1
Let n(t) = -2*t**4 - 15*t**3 + 49*t**2 + 99*t - 128. Let s(g) = g**4 - g**2 - g. Let y(d) = 5*n(d) + 15*s(d). Find h such that y(h) = 0.
-2, 1, 8
Let n(c) = 6*c**4 - 2*c**3 + 7*c + 4. Let r(m) = 6*m + 17 + 5*m**4 - 2*m**3 + 8 - 22. Let w(v) = -4*n(v) + 5*r(v). Factor w(u).
(u - 1)**3*(u + 1)
Suppose 0 = 4*s - 24 + 8. Let g(l) be the third derivative of 0*l - 1/40*l**6 - 3*l**2 + l**3 + 1/8*l**s - 1/10*l**5 + 0. Factor g(c).
-3*(c - 1)*(c + 1)*(c + 2)
Let j(o) be the third derivative of o**6/200 + o**5/50 + 54*o**2 - 1. Factor j(u).
3*u**2*(u + 2)/5
Let r(n) be the second derivative of 0 - 5/12*n**4 + 8*n + 5/6*n**3 + 0*n**2. Solve r(z) = 0.
0, 1
Determine s so that -414*s**2 - 134 + 120*s**3 - 138 + 4*s**4 - 110*s**2 + 124*s + 198*s + 350*s = 0.
-34, 1, 2
Let k(p) be the third derivative of 0*p + 5/156*p**4 + 0 + 0*p**3 - 2*p**2 - 1/780*p**6 + 2/195*p**5. Suppose k(t) = 0. Calculate t.
-1, 0, 5
Find g such that -32/7 - 18*g + 8/7*g**2 = 0.
-1/4, 16
Solve -23*j - 11*j**3 + 83*j**2 - 4 + 8 - 56*j**2 + j**4 - 2*j + 4 = 0 for j.
1, 8
Let o(j) be the first derivative of -8/5*j**5 - 5 + 0*j + 0*j**4 - 2/3*j**6 + 8/3*j**3 + 2*j**2. Factor o(s).
-4*s*(s - 1)*(s + 1)**3
Let c(m) = m**3 + 9*m**2 + 4*m + 38. Let f be c(-9). Suppose 3*y + 3 + 3 = 4*w, -3*y - f*w + 12 = 0. Let 0 + 10/17*j**y - 4/17*j =