)/(-7) + 8/28. Let t(i) = -5*i - 1 + 4*i + v*i - i**2. Let u(g) = -3*g**2 + 8*g - 1. Let m(j) = -t(j) - u(j). Find p, given that m(p) = 0.
1/4, 2
Let s(d) be the third derivative of d**5/360 - d**4/36 + d**3/9 - d**2. Factor s(w).
(w - 2)**2/6
Suppose -2*u + 22 - 4 = 0. Determine n so that 9 + n**2 - n - u = 0.
0, 1
Let v = 84 - 57. Let k = v + -22. Determine r, given that -3/2*r**3 + 0*r - 1/2*r**k - 3/2*r**4 + 0 - 1/2*r**2 = 0.
-1, 0
Let t be (-52)/(-28) - 1/(-7). Let k(m) be the second derivative of 0 - t*m + 1/80*m**5 - 1/24*m**3 - 1/48*m**4 + 1/8*m**2. Factor k(r).
(r - 1)**2*(r + 1)/4
Let m be (-2)/(-14) + (-141)/7. Let v = m - -20. Factor -6*g**4 + v + 27/2*g**3 + 3/2*g - 9*g**2.
-3*g*(g - 1)**2*(4*g - 1)/2
Let c(n) be the first derivative of n**7/56 - 7*n**6/160 + n**5/40 + 3*n**2/2 + 2. Let p(b) be the second derivative of c(b). Let p(k) = 0. Calculate k.
0, 2/5, 1
Let b(r) be the second derivative of -r**4/12 + r**3 + r**2 + 2*r. Let a be b(6). Let a*p**2 + 4*p + 2 - 3*p + 3*p = 0. What is p?
-1
Suppose 2*v - 10 = -6. Determine d so that 0*d**v + 1/2*d**3 - 1/4 + 1/4*d**4 - 1/2*d = 0.
-1, 1
Let d be 6/18 - 4/(-6). Let y(x) be the first derivative of d + 1/4*x**2 + 0*x**3 - 1/8*x**4 + 0*x. Let y(c) = 0. Calculate c.
-1, 0, 1
Let n(w) = -2*w**2 + w. Let o(u) = 4*u**2 - 3*u. Let k(l) = -7*n(l) - 3*o(l). Factor k(z).
2*z*(z + 1)
Let q(t) be the second derivative of 1/36*t**4 + 0 + 0*t**3 + 0*t**2 - 2*t. Find y, given that q(y) = 0.
0
Find v such that 1/2*v**2 + 0 - v = 0.
0, 2
Solve -6*l**3 - 46*l**2 + 2*l**3 + 54*l**2 = 0 for l.
0, 2
Let b(d) be the first derivative of 2*d**4/3 - 26*d**3/9 + d**2 + 22. Factor b(c).
2*c*(c - 3)*(4*c - 1)/3
Let v(t) be the first derivative of -t**3/3 - 2*t**2 + 14*t - 5. Let l be v(-6). Factor 1/2*m - 1/2*m**l + 0.
-m*(m - 1)/2
Let l(a) be the first derivative of a**6/12 - a**5/10 - a**4/8 + a**3/6 - 9. Determine v, given that l(v) = 0.
-1, 0, 1
Suppose 0*n + 5*n - 10 = -5*p, -4*n - 6 = -3*p. Let c(y) be the third derivative of 0*y**4 - 1/600*y**6 + 0*y + 0*y**3 + 1/300*y**5 + y**p + 0. Factor c(k).
-k**2*(k - 1)/5
Let p(s) = -15*s**3 + 9*s**2 - 15*s + 13. Let d(m) = 10*m**2 - 7*m**3 - m - 6*m**2 - 6*m + 6. Let n(c) = -13*d(c) + 6*p(c). Factor n(b).
b*(b + 1)**2
Let j be (-24)/(-9)*3/4. Suppose -3*w + 1 - 3*w**j + 1 + 4 + 0*w = 0. Calculate w.
-2, 1
Let h(u) be the second derivative of 2*u**7/21 + 8*u**6/15 + 3*u**5/5 - 4*u**4/3 - 8*u**3/3 + 15*u. Factor h(b).
4*b*(b - 1)*(b + 1)*(b + 2)**2
Factor 10*i - i**2 - 2*i**2 - 16*i.
-3*i*(i + 2)
Let q be 5/(-30) + -2*(-2)/24. Let s(x) = x**2 + 2*x + 2. Let c be s(-2). Suppose q + 3/7*z**c + 0*z = 0. Calculate z.
0
Suppose -3*x - 19 = -55. Factor 0 - x*d**2 - 25/2*d**4 + 2*d + 45/2*d**3.
-d*(d - 1)*(5*d - 2)**2/2
Let d(s) be the first derivative of s**5/5 + 2*s**4/3 - 14*s**3/3 + 8*s**2 - 2*s + 2. Let j(c) be the first derivative of d(c). Factor j(m).
4*(m - 1)**2*(m + 4)
Let i(x) be the second derivative of -x**6/540 + x**5/270 + x**4/54 - x**2/2 + 7*x. Let y(j) be the first derivative of i(j). Let y(n) = 0. Calculate n.
-1, 0, 2
Let n(u) be the third derivative of 0*u**3 - 1/1050*u**7 + 0*u + 1/300*u**5 + 0 - 1/600*u**6 + 1/120*u**4 + 5*u**2. Factor n(o).
-o*(o - 1)*(o + 1)**2/5
Suppose -a - 2*g = -10 - 6, -a = 5*g - 22. Suppose -s - 13 = -2*l, -3*s = -2*l + a + 11. Solve -3*y**4 + 2*y**l + 2*y**2 - y**2 = 0.
-1, 0, 1
Factor -8/9*k**2 + 4/9 + 0*k + 4/9*k**4 + 0*k**3.
4*(k - 1)**2*(k + 1)**2/9
What is n in -34 - 1560*n**2 - 22 - 245*n**4 - 31 - 640*n - 1120*n**3 + 7 = 0?
-2, -2/7
Let n(p) be the second derivative of -p**5/50 + p**3/15 + 6*p. Factor n(f).
-2*f*(f - 1)*(f + 1)/5
Let l be (-5)/(-3)*322/10. Let n = l + -53. Factor -4/3*g - 2/3 - n*g**2.
-2*(g + 1)**2/3
Let z be (7 - 7)*(-1)/3. Factor -3 + 6*i**2 - 5 + 4*i**3 - 8*i + z*i**4 - 2*i**4.
-2*(i - 2)**2*(i + 1)**2
Let a(s) be the third derivative of s**7/70 - 7*s**6/40 + 9*s**5/10 - 5*s**4/2 + 4*s**3 - 6*s**2. Factor a(f).
3*(f - 2)**3*(f - 1)
Let i(j) = 11*j**5 - 6*j**4 - 12*j**3 + 12*j**2 + 6*j - 11. Let w(v) = -5*v**5 + 3*v**4 + 6*v**3 - 6*v**2 - 3*v + 5. Let m(l) = -2*i(l) - 5*w(l). Factor m(g).
3*(g - 1)**3*(g + 1)**2
Let a(t) be the first derivative of 2 + 1/2*t - 1/12*t**3 - 1/8*t**2. Find d, given that a(d) = 0.
-2, 1
Let i be (-22)/(-99) - 148/585. Let p = i + 73/260. Factor -1/4*y**3 - 1/4*y**2 + 0 + 1/4*y**5 + p*y**4 + 0*y.
y**2*(y - 1)*(y + 1)**2/4
Let w = 0 + 4. Factor -w - 6*u**2 + 8 - 6*u - 4*u**2.
-2*(u + 1)*(5*u - 2)
Let w be (-15)/(-25) + 34/10. Factor 3*y**3 - y - 9*y + w - 5*y**3 + 8*y**2.
-2*(y - 2)*(y - 1)**2
Let l(z) be the third derivative of z**6/80 - 3*z**5/40 + z**4/8 + 6*z**2. Factor l(v).
3*v*(v - 2)*(v - 1)/2
Let l(k) be the first derivative of -k**5/100 + k**4/40 + k**3/5 + 3*k**2/2 + 4. Let w(x) be the second derivative of l(x). Find q, given that w(q) = 0.
-1, 2
Let w be (-16)/(-80) + 1/(-5). Let r(y) be the second derivative of 1/9*y**7 + w - 2*y - 1/18*y**4 - 2/9*y**3 + 0*y**2 + 1/2*y**5 - 19/45*y**6. Factor r(c).
2*c*(c - 1)**3*(7*c + 2)/3
Let i(j) = j**4 - j**3 - j**2 + j - 1. Let c(s) be the third derivative of -s**6/60 - s**5/60 + s**4/24 - s**3/6 - 7*s**2. Let d(y) = c(y) - i(y). Factor d(n).
-n**3*(n + 1)
Find w such that 2*w**4 + 6*w - 9*w**2 + w**4 - 3*w**3 - 3*w + 3 + 3 = 0.
-1, 1, 2
Determine p so that 8/5 + 4/5*p**2 + 12/5*p = 0.
-2, -1
Factor 6 + 0 + 982*t**2 + 0 + 11*t + t**3 - 976*t**2.
(t + 1)*(t + 2)*(t + 3)
Let s(x) be the second derivative of 3*x**5/50 - x**4/5 - x**3 + 18*x**2/5 - 33*x. Factor s(d).
6*(d - 3)*(d - 1)*(d + 2)/5
Suppose 5*q = 11 + 4. Let l(f) be the second derivative of -f**2 + 0 + 0*f**4 - 7/6*f**q - f + 9/20*f**5. Factor l(i).
(i - 1)*(3*i + 1)*(3*i + 2)
Factor 0 + 1/4*m**2 + 1/8*m**3 - 1/8*m**4 + 0*m.
-m**2*(m - 2)*(m + 1)/8
Let x(n) be the first derivative of -3/2*n**2 + 1/120*n**6 - 2 + 0*n**3 + 0*n**5 + 0*n + 0*n**4. Let g(z) be the second derivative of x(z). Solve g(f) = 0.
0
Let j(n) be the second derivative of -n**7/168 - n**6/120 + n**5/40 + n**4/24 - n**3/24 - n**2/8 + 6*n. Factor j(y).
-(y - 1)**2*(y + 1)**3/4
Suppose l - 7 + 3 = 0. Suppose 0 = l*s - 13 + 1. Suppose 0 - 2/3*h**5 + 0*h + 2/3*h**4 + 0*h**2 + 0*h**s = 0. What is h?
0, 1
Factor 549*t**2 - 189*t**2 - 549*t - 10*t**4 + 640 - 251*t - 70*t**3 + 15*t**4.
5*(t - 4)**3*(t - 2)
Let q = 4 - -1. Factor -1/2*a + 0*a**3 - a**2 + 1/2*a**q + a**4 + 0.
a*(a - 1)*(a + 1)**3/2
Let d(f) = f**3 - 6*f**2 - 6*f - 5. Let w be d(7). Suppose 3*z**3 - 1 + 8 + 4 - 9*z**w + 1 = 0. Calculate z.
-1, 2
Suppose -6*o - 25 = -3*t - 2*o, 21 = 3*t - 3*o. Determine f so that -t*f**2 + 5*f**3 + 0*f + 0*f - 2*f**3 = 0.
0, 1
Let j(v) be the first derivative of -5*v**4 - 2 + 8*v - 14*v**2 + 4/5*v**5 + 12*v**3. Solve j(x) = 0.
1, 2
Let b(j) be the third derivative of 2*j**7/735 + 3*j**6/280 + j**5/70 + j**4/168 + 2*j**2. Factor b(u).
u*(u + 1)**2*(4*u + 1)/7
Let j(r) be the first derivative of -r**4/18 - 8*r**3/3 - 48*r**2 - 384*r + 10. Let j(q) = 0. What is q?
-12
Let n(c) be the third derivative of -c**5/30 + 5*c**4/6 - 25*c**3/3 + 8*c**2. Find j such that n(j) = 0.
5
Factor 9/2*q**3 - 8*q**2 + 1 + 5/2*q.
(q - 1)**2*(9*q + 2)/2
Let u(h) be the third derivative of 1/60*h**4 + 0*h + 3*h**2 - 2/15*h**3 + 0 + 1/150*h**5. Factor u(p).
2*(p - 1)*(p + 2)/5
Let a(z) = 14*z**2 - 8*z + 2. Let m(q) = -9*q**2 + 5*q - 1. Suppose 0*d - 15 = 3*d. Let r(n) = d*a(n) - 8*m(n). Solve r(p) = 0 for p.
-1, 1
What is s in 3 - s**2 - 3 - 3 + 3*s + 1 = 0?
1, 2
Suppose 6*k - 11*k = 0. Solve 1/2*d**4 - d**2 + k + 0*d - 1/2*d**3 = 0.
-1, 0, 2
What is w in -2*w**3 - 1/3*w**5 + 4/3*w**2 + 0 + 4/3*w**4 - 1/3*w = 0?
0, 1
Let r(v) be the second derivative of -v**7/70 - v**6/20 - v**5/20 - 2*v**2 - 2*v. Let d(w) be the first derivative of r(w). Factor d(k).
-3*k**2*(k + 1)**2
Suppose -6*v + 2*p = -3*v - 16, -2*v = p - 6. Factor -v*h**2 + h**4 - h**5 + 0*h**2 + 2*h**4.
-h**2*(h - 2)**2*(h + 1)
Let y(a) be the second derivative of 1/360*a**6 + 0*a**4 - 4*a + 0*a**2 + 1/120*a**5 + 0 + 2/3*a**3. Let p(w) be the second derivative of y(w). Factor p(s).
s*(s + 1)
Factor -37 + 25*o + 5*o**2 - 40 - 6 + 13.
5*(o - 2)*(o + 7)
Let l(c) = -c**2 + 2*c + 1. Let q be l(1). Find h, given that 2/7*h**q + 12/7*h + 18/7 = 0.
-3
Let t = -132 + 198. Fa