2*(m + 1)**2/2
Factor 2*n**3 + n**3 - 7*n**2 + 3*n**2 + n.
n*(n - 1)*(3*n - 1)
Let x(d) be the first derivative of -d**3/8 + 15*d**2/16 - 52. Find p such that x(p) = 0.
0, 5
Solve 0*j**3 + 0*j + 1/6*j**2 + 0 - 1/6*j**4 = 0 for j.
-1, 0, 1
Let t(s) be the third derivative of -s**8/336 + s**7/210 - 6*s**2. Factor t(g).
-g**4*(g - 1)
Let p(g) = -2*g**3 + 15*g**2 + 10*g - 14. Let w be p(8). Factor -2/3*z**w + 0*z + 0.
-2*z**2/3
Let o(q) be the third derivative of q**8/168 + 3*q**7/70 + 7*q**6/120 - 7*q**5/30 - q**4/2 + 4*q**3/3 - 6*q**2. Solve o(y) = 0.
-2, 1/2, 1
Let s be 3/(2/(-1)*(-1)/2). Let i(u) be the third derivative of 0*u**4 + 0*u + 0*u**3 + 0 - 1/120*u**6 + 0*u**5 + 0*u**7 + 1/336*u**8 + s*u**2. Factor i(z).
z**3*(z - 1)*(z + 1)
Factor 16/7*m**2 - 16/7*m**3 + 4/7*m**4 + 0*m + 0.
4*m**2*(m - 2)**2/7
Let w(r) = r**3 - 4*r**2 - r - 2. Let p(d) = d**3 - d**2 - 1. Let y(m) = -4*p(m) + 2*w(m). Solve y(j) = 0 for j.
-1, 0
Let k = 79 + -76. Let y(d) be the first derivative of -2 + 16*d**2 - 8*d - 14/3*d**k. Factor y(l).
-2*(l - 2)*(7*l - 2)
Let y(u) be the third derivative of u**5/20 + u**4/24 - u**3/6 + u**2. Let o be y(1). Solve -2/5*x**o + 2/5 + 6/5*x**2 - 6/5*x = 0 for x.
1
Suppose 5*b + 1128 = o, 3*b = -2*b - 3*o - 1136. Let f = -670/3 - b. Determine a, given that -f*a - 8/3 - 2/3*a**2 = 0.
-2
Let g(n) be the second derivative of n**4/24 + n**3/12 - 10*n. Solve g(z) = 0 for z.
-1, 0
Let j(l) be the second derivative of -l**4/12 + l**3 - 5*l**2/2 - 2*l. Let z be j(4). Factor 0*g**z - 6*g**3 + 6*g**2 - 8*g**2.
-2*g**2*(3*g + 1)
Let d(m) be the second derivative of 5*m**4/12 - 10*m**3/3 - 11*m + 1. Factor d(o).
5*o*(o - 4)
Let b(i) = 16*i**5 - 20*i**4 + 12*i**2 - 4. Let u be -1*8*6/(-12). Let w(q) = 33*q**5 - 41*q**4 + q**3 + 25*q**2 - 9. Let m(r) = u*w(r) - 9*b(r). Factor m(v).
-4*v**2*(v - 1)**2*(3*v + 2)
Suppose -2*c = f - 83, 0*c + 2*f = 2*c - 68. Let b = -193/5 + c. Factor 0 + 2/5*z**2 + b*z.
2*z*(z + 1)/5
Let l(z) = -z**2 + 30*z + 64. Let y be l(32). Solve 2/7 + 2/7*g**4 - 4/7*g**2 + 0*g + y*g**3 = 0.
-1, 1
Let n(m) be the third derivative of 3*m**8/4480 + m**7/560 - m**6/360 - m**5/60 - m**4/6 - 4*m**2. Let t(d) be the second derivative of n(d). Factor t(q).
(q + 1)*(3*q - 2)*(3*q + 2)/2
Let a(l) be the first derivative of -5*l**4/12 + 25*l**3/9 - 35*l**2/6 + 5*l - 8. Factor a(k).
-5*(k - 3)*(k - 1)**2/3
Let l(j) be the third derivative of -1/40*j**6 + 0*j**3 - 1/96*j**4 + 0*j - 1/84*j**7 + 0 + j**2 - 1/448*j**8 - 1/40*j**5. Factor l(f).
-f*(f + 1)**3*(3*f + 1)/4
Let l(n) = 2*n - 1. Let s be l(3). Let x = 8 - s. Factor 1/3*t**x - 1/3*t + 0*t**2 + 0.
t*(t - 1)*(t + 1)/3
Suppose c = 5*c - 3*r + 29, 0 = -4*c - 4*r - 36. Let w be (0 + -3 - c) + -3. Factor 0*p**4 - 3*p**3 - 16*p**w + 21*p**4 - 4*p - 3*p**3 + 5*p**3.
p*(p - 1)*(3*p + 2)*(7*p + 2)
Let w(x) = -x + 7. Let n be w(5). Factor -2*k**3 + 3*k - 2*k**4 + 0*k - 1 + 5*k**4 - k**5 - 2*k**n.
-(k - 1)**4*(k + 1)
Let i be ((-14)/196)/((-2)/8). Factor -6/7*j**3 + 6/7*j**2 + i*j**4 - 2/7*j + 0.
2*j*(j - 1)**3/7
Let d(z) be the first derivative of 2 + 1/20*z**4 + 1/25*z**5 - 1/15*z**3 + 0*z - 1/10*z**2. Factor d(c).
c*(c - 1)*(c + 1)**2/5
Let t(z) be the second derivative of 5/9*z**3 + 2/9*z**4 + 0 + 2/3*z**2 + 5*z + 1/30*z**5. Factor t(p).
2*(p + 1)**2*(p + 2)/3
Let s(b) = -b - 5. Suppose 5*l + 35 = -5*x, -2*l + x = -0*x + 14. Let m be s(l). What is v in 2*v**m - 3*v**3 - 5*v**3 + v**3 = 0?
0, 2/7
Let s(u) be the third derivative of 0*u - 1/48*u**4 - 1/240*u**5 + 0 - 3*u**2 - 1/24*u**3. Solve s(b) = 0 for b.
-1
Suppose 0 = -2*l - 3*k + 194, 3*l - 160 - 97 = 4*k. Let g = l - 453/5. Factor -4/5 - g*d**2 + 6/5*d.
-2*(d - 2)*(d - 1)/5
Factor -1/2*g**3 - 4 + 2*g + g**2.
-(g - 2)**2*(g + 2)/2
Suppose 4/9 - 8/3*v**3 + 46/9*v**2 - 26/9*v = 0. Calculate v.
1/4, 2/3, 1
Let i = 3/4 + -1/4. Factor 0*f - 1/4*f**2 - i*f**3 - 1/4*f**4 + 0.
-f**2*(f + 1)**2/4
Let s be (5/(-7))/(33/(-77)). Factor 0 - h**2 - 1/3*h**5 - 7/3*h**3 - s*h**4 + 0*h.
-h**2*(h + 1)**2*(h + 3)/3
Suppose 2*u = -4*m + 82, -115 = -5*m - 0*m - 5*u. Let l = 18 - m. Find j, given that l*j**4 + 1/2*j**5 + 0*j**2 + 0 - 1/2*j**3 + 0*j = 0.
-1, 0, 1
Factor -q**5 + 0 + 2*q**4 - 3*q**4 + 0 - 2*q + 3*q**3 + q**2.
-q*(q - 1)**2*(q + 1)*(q + 2)
Let x(j) be the third derivative of -1/105*j**7 - j**2 - 19/420*j**6 + 0 + 0*j - 1/1176*j**8 - 4/21*j**3 - 5/42*j**5 - 4/21*j**4. Suppose x(b) = 0. What is b?
-2, -1
Solve -14/3*t + 2/3*t**5 - 4/3*t**3 - 16/3*t**2 + 4/3*t**4 - 4/3 = 0.
-1, 2
Suppose 0 = -7*j + 8 + 27. Let r(m) be the third derivative of 0*m**j + m**2 + 0*m + 0 + 1/48*m**4 - 1/240*m**6 + 0*m**3. Find w, given that r(w) = 0.
-1, 0, 1
Let w be (-2 + 1)/(-3 - -2). Let c be (w - (4 + 0)) + 4. Factor -2*t**2 + 5/2*t - c + 1/2*t**3.
(t - 2)*(t - 1)**2/2
Let p = -1576/3 + 526. Let d = 155/3 - 51. Determine g so that -p*g**3 + 4/3*g**2 - d*g + 0 = 0.
0, 1
Let n(k) be the first derivative of -k**3/2 + 9*k**2 - 54*k + 2. What is x in n(x) = 0?
6
Let n(a) be the first derivative of 4*a**3/3 - 8*a**2/3 - 16*a/3 + 9. Factor n(x).
4*(x - 2)*(3*x + 2)/3
Factor 0 + 0*f**2 + 0*f**3 + 4/5*f**4 + 0*f - 6/5*f**5.
-2*f**4*(3*f - 2)/5
Factor -6/11*k**2 - 12/11 - 18/11*k.
-6*(k + 1)*(k + 2)/11
Let o(u) be the second derivative of 3/2*u**2 + 0 - 1/4*u**4 + 5*u + 0*u**3. Factor o(r).
-3*(r - 1)*(r + 1)
Suppose 0 = -2*z + 6*z. Factor z*w - 2/3*w**2 + 2/3.
-2*(w - 1)*(w + 1)/3
Let b(p) be the third derivative of p**8/336 + 2*p**7/105 + p**6/20 + p**5/15 + p**4/6 - 5*p**2. Let d(j) be the second derivative of b(j). Factor d(u).
4*(u + 1)**2*(5*u + 2)
Let g(h) be the first derivative of 2*h**3/27 + 8*h**2/9 + 32*h/9 - 9. Factor g(p).
2*(p + 4)**2/9
Let t(v) be the second derivative of v**6/2 + 19*v**5/4 + 95*v**4/12 - 35*v**3/6 - 25*v**2 - 35*v. What is r in t(r) = 0?
-5, -1, 2/3
Let m(i) be the second derivative of -i**6/15 + i**5/5 - 2*i**3/3 + i**2 + 5*i. Factor m(p).
-2*(p - 1)**3*(p + 1)
What is w in -3*w**3 - 3*w**2 - w**4 + 4*w**4 + 0*w**4 + 3*w**5 = 0?
-1, 0, 1
Let v(l) = -l**3 + l**2 - l - 1. Let f(m) = 3*m**3 - 33*m**2 + 12*m + 24. Let k(q) = f(q) + 12*v(q). Suppose k(d) = 0. What is d?
-2, -1, 2/3
Suppose -4*s = -52 - 32. Let h be (1/(-4))/(s/(-24)). Factor 0*u + 2/7*u**3 + 0 - 2/7*u**4 + h*u**2 - 2/7*u**5.
-2*u**2*(u - 1)*(u + 1)**2/7
Suppose 0 = 2*s - 4*s + 10. Suppose 0 = -s*w + 21 - 6. Factor 0 + 0*q - 1/3*q**2 + 1/3*q**4 - 1/3*q**w + 1/3*q**5.
q**2*(q - 1)*(q + 1)**2/3
Let r(s) = 2*s**2 + 7*s - 26. Let x be r(-6). Let n(g) be the first derivative of 0*g**3 + 0*g**2 - 3 - 1/8*g**x + 0*g. Factor n(h).
-h**3/2
Let u be 1*1/(-2)*0. Let l be 20/15*3/5. Factor l*r - 2/5*r**2 + u.
-2*r*(r - 2)/5
Let m(j) be the third derivative of -j**8/84 + 4*j**7/105 - 2*j**5/15 + j**4/6 + 8*j**2. Factor m(b).
-4*b*(b - 1)**3*(b + 1)
Let a be 3 - (-1 + 0)/1. Factor 4*p + 2*p**5 + 4*p**2 + 0 - 6*p + 0 - 4*p**a.
2*p*(p - 1)**3*(p + 1)
Let t(o) = 2*o - 2. Let z be t(3). Suppose 3*r = r + z. Factor -r*j**4 - 2*j**4 + j**4 - 3*j**3.
-3*j**3*(j + 1)
Let x(y) be the first derivative of -3*y**5/25 - 3*y**4/20 + 2*y**3/5 + 14. Suppose x(z) = 0. What is z?
-2, 0, 1
Let o = -2 + 2. Let m be 8 - 4 - 1/1. Factor 0*w**2 + w**3 + o*w**m - w**2.
w**2*(w - 1)
Suppose -8 = 5*m - 18. Let y(j) be the first derivative of -3 + 0*j**m - 1/6*j**3 + 1/2*j. Factor y(c).
-(c - 1)*(c + 1)/2
Let a(o) = o**3 - 9*o**2 + o - 7. Let d be a(9). Factor -162*i**3 - 5*i**2 - 3 + 7 + 14*i**d + 0*i**2 + 28*i.
-(2*i - 1)*(9*i + 2)**2
Let n(l) = -l**2 + 9*l - 12. Let b be n(9). Let q be (b/15)/(2/(-5)). Let -1/4*v**q - 3/4*v - 1/2 = 0. What is v?
-2, -1
Let w(s) = -s**3 - 11*s**2 - 13*s - 30. Let k be w(-10). Let c(n) be the first derivative of -2 - 2*n**2 + k*n - 2/3*n**3. Factor c(i).
-2*i*(i + 2)
Let p = 19 + -14. Let m be ((-2)/p)/((-11)/55). Factor 6/7*l**m - 2/7*l**3 - 8/7 + 0*l.
-2*(l - 2)**2*(l + 1)/7
Let -1/3*r - 2/3*r**2 + 0 + r**3 = 0. What is r?
-1/3, 0, 1
Let g(v) be the first derivative of -v**6/100 + 7*v**5/300 + v**4/30 - 2*v**3 + 8. Let a(t) be the third derivative of g(t). Determine o so that a(o) = 0.
-2/9, 1
Let u(b) be the third derivative of -b**10/6720 + b**9/10080 + b**8/6720 - b**4/12 - b**2. Let p(g) be the second derivative of u(g). Find m such that p(m) = 0.
-1/3, 0, 2/3
Let j(v) be the 