(t + 1)*(2*t + 1)/3
Let l = 3 - -7. Suppose -5*a + l + 20 = 0. Find d such that a + d + d**2 - 5 + d = 0.
-1
Suppose -4 - 36 = -10*s. Let -1/5*d**s - 2/5*d**3 + 0*d**2 + 1/5 + 2/5*d = 0. What is d?
-1, 1
Suppose b = -5*z - 3 + 2, 3*b - 8 = -4*z. Suppose b*u = 10 + 2. Let 12/7*f**2 - 2/7*f**u + 16/7 - 24/7*f = 0. What is f?
2
Let x(n) be the first derivative of -n**5/5 - 3*n**4/4 - 2*n**3/3 - 3. Solve x(l) = 0.
-2, -1, 0
Let x = 9 - 6. Factor -3*u**2 - 3*u**3 + 9*u**2 + 0*u**x.
-3*u**2*(u - 2)
Let t(c) be the first derivative of -7*c**2/2 + c + 2. Let q be t(-1). Factor -q*k - 4*k**2 - 14 + 2*k**2 + 6.
-2*(k + 2)**2
Let a be 60/16 + (2 - 22/8). Factor 0*b + 0 + 0*b**2 + 2/11*b**a.
2*b**3/11
Let i(s) be the first derivative of -s**5/210 + s**4/28 - 2*s**3/21 - 3*s**2/2 + 3. Let x(f) be the second derivative of i(f). Solve x(o) = 0 for o.
1, 2
Factor -4*p**3 - p**3 + 7*p**3 - 4*p**3 - 26*p + 12 + 16*p**2.
-2*(p - 6)*(p - 1)**2
Let o(h) = -h**2 - h - 1. Let l(f) = -8*f + 2. Let w(s) = -l(s) - 2*o(s). Factor w(r).
2*r*(r + 5)
Factor -4/9*s + 0 - 2/9*s**4 - 8/9*s**3 - 10/9*s**2.
-2*s*(s + 1)**2*(s + 2)/9
Let n(a) be the first derivative of 3/2*a**2 - 1/2*a**6 - 1 + 2*a**3 + 0*a**4 + 0*a - 6/5*a**5. Factor n(m).
-3*m*(m - 1)*(m + 1)**3
Suppose 5*v = 44*v - 78. What is y in -1/3*y**4 + 0 + 1/3*y**3 + 0*y**v + 0*y = 0?
0, 1
Let q(f) be the third derivative of -f**7/2205 - f**6/252 - f**5/70 - f**4/36 - 2*f**3/63 - 11*f**2. What is n in q(n) = 0?
-2, -1
Let d(m) = m**3 - 16*m**2 + 2*m + 4. Let f(j) = -j**3 + 8*j**2 - j - 2. Let q(v) = 4*d(v) + 9*f(v). Factor q(t).
-(t - 1)**2*(5*t + 2)
Let j be (10/(-75))/((-4)/5). Let h(g) be the third derivative of 0*g**3 + 3*g**2 + 0 - j*g**4 + 0*g - 1/30*g**5. Suppose h(q) = 0. What is q?
-2, 0
Let m be 8/(-20) - 73/(-5). Let p = m + -14. Factor 0 - p*q**2 + 0*q.
-q**2/5
Factor -1 + 3*v + 25*v - 8 - 15 - 28*v**3 + 4*v**4 + 20*v**2.
4*(v - 6)*(v - 1)**2*(v + 1)
Let 6*n + 0 - 21/2*n**2 + 3*n**4 - 3/4*n**5 + 9/4*n**3 = 0. What is n?
-2, 0, 1, 4
Let i be ((-3)/2)/(6/(-64)). Let u be (-10)/4*i/(-60). Suppose u*l**2 + 0 - 2/3*l = 0. Calculate l.
0, 1
Let v(c) = -c**2 - 6*c + 1. Let z be v(-5). Let t = 8 - z. Find i such that t*i**2 + 2/3*i**3 + 2/3 + 2*i = 0.
-1
Let x = -18 + 55/3. Let o = 31/3 + -10. Factor o*b**4 + 0 - 1/3*b**3 - x*b**2 + 1/3*b**5 + 0*b.
b**2*(b - 1)*(b + 1)**2/3
Let a(n) be the third derivative of n**6/60 + n**5/10 - n**4/12 - n**3 - 14*n**2. Factor a(r).
2*(r - 1)*(r + 1)*(r + 3)
Suppose -20*w = 2*w - 1408. Factor -44*u**2 - 104*u**3 + w*u**5 - 64*u**4 - 31/4*u - 1/2.
(u - 2)*(4*u + 1)**4/4
Let d(h) be the first derivative of -1 + 1/5*h**5 - 3/4*h**4 + h**3 + 0*h - 1/2*h**2. Solve d(t) = 0 for t.
0, 1
Let k(f) = -f**3 - 2*f**2 - 6*f + 2. Let c be k(4). Let x = c + 828/7. Let -6/7*n**2 - 6/7*n - 2/7 - x*n**3 = 0. Calculate n.
-1
Let f = 55/24 + -13/8. Solve 1/3*p**3 - 2/3 + f*p**2 - 1/3*p = 0.
-2, -1, 1
Let j(n) be the first derivative of 0*n**2 - 1/40*n**5 - 2*n - 1/12*n**3 - 1 + 1/12*n**4. Let y(v) be the first derivative of j(v). Find o such that y(o) = 0.
0, 1
Let x(q) be the second derivative of q**5/4 - 5*q**4/12 - 5*q**3/6 + 5*q**2/2 - 20*q. Solve x(u) = 0.
-1, 1
Let n = -17 - -27. Suppose -v + 4*w + 0*w = 20, 2*w = -v + n. Let v + 1/2*u + 5/4*u**2 = 0. Calculate u.
-2/5, 0
Factor -1/3*j**2 - 1/3*j + 0.
-j*(j + 1)/3
Let b(z) = 8*z**4 + 2*z**3 - 4*z**2. Let j(t) = 7*t**4 + t**3 - 3*t**2. Let d(y) = 5*b(y) - 6*j(y). Let d(o) = 0. Calculate o.
0, 1
Suppose -3 + 17 = 2*n. Suppose -2 - 3*t + n*t + 2*t**2 + 4 + 0 = 0. What is t?
-1
Let v(i) be the first derivative of i**4/32 - 47. Determine h, given that v(h) = 0.
0
Determine h so that -13*h**4 + 11 - 11*h**4 - 4*h - 3 - 76*h**3 - 4*h**4 - 60*h**2 = 0.
-1, 2/7
Let i = 71713/9 - 7953. Let k(f) be the first derivative of 19*f**4 + 12*f**5 + 19/3*f**2 + 1 + 4/3*f + i*f**3 + 3*f**6. Solve k(m) = 0 for m.
-1, -2/3, -1/3
Let c be (-36)/(-8) - 2/(-4). Let d be 0/((-4)/(2 - 4)). What is p in 0*p - 24/7*p**c + 18/7*p**3 + 4/7*p**2 + d + 2/7*p**4 = 0?
-2/3, -1/4, 0, 1
Let f(l) be the second derivative of -1/48*l**4 + l + 1/24*l**3 + 1/4*l**2 + 0. Factor f(p).
-(p - 2)*(p + 1)/4
Let u(h) = -8*h - 13. Let c be u(-2). Find j such that 3/2*j**3 - 9/2*j + c*j**2 + 0 = 0.
-3, 0, 1
Suppose 0 = 2*h - 8 + 16. Let v = -2 - h. Determine u, given that 4/7 + 10/7*u**4 + 6/7*u**3 - v*u**2 - 6/7*u = 0.
-1, 2/5, 1
Let m(x) = -6*x**2 - 8*x + 2. Let b(k) = -19*k**2 - 24*k + 7. Let a(p) = 2*b(p) - 7*m(p). Factor a(l).
4*l*(l + 2)
Let x(n) = n**2 - 20*n + 49. Let k(z) = -z. Let o(p) = 6*k(p) - x(p). Factor o(f).
-(f - 7)**2
Find y, given that -4*y + 6*y**5 + 6*y**3 + 14*y**4 + 0*y**5 + 2438*y**2 - 2444*y**2 = 0.
-1, 0, 2/3
Let w(x) be the third derivative of x**6/420 + x**5/70 + x**4/42 - 3*x**2. Factor w(h).
2*h*(h + 1)*(h + 2)/7
Let c = 8 + 18. Let x be (-25)/(-14) + c/(-91). Factor -3/2*h**2 - 1/2*h**3 - 1/2 - x*h.
-(h + 1)**3/2
Let p(m) be the third derivative of -m**7/6 - 2*m**6/3 + m**5/4 + 10*m**4/3 + 10*m**3/3 + 24*m**2. Solve p(c) = 0 for c.
-2, -1, -2/7, 1
Factor -2/13*r**5 + 2/13*r**3 + 0*r + 2/13*r**2 + 0 - 2/13*r**4.
-2*r**2*(r - 1)*(r + 1)**2/13
Suppose -5*a + 12 = -a. Let x(f) be the second derivative of 0 + f**a + 1/6*f**4 + 4*f + 2*f**2. Factor x(m).
2*(m + 1)*(m + 2)
Let v be (4/27*-3)/(-3). Let l(k) be the first derivative of 4/45*k**5 + 1/27*k**6 - v*k**3 + 0*k**4 + 0*k - 1/9*k**2 - 1. Factor l(y).
2*y*(y - 1)*(y + 1)**3/9
Factor 3*w + 2*w**2 - 4*w**2 + 4*w**2 + w**2.
3*w*(w + 1)
Let a(h) be the third derivative of h**5/210 - 5*h**4/84 + 42*h**2. Factor a(o).
2*o*(o - 5)/7
Factor -4*x - 3*x**2 + 4*x - 2*x + x**4.
x*(x - 2)*(x + 1)**2
Solve -201/5*d**3 - 513/5*d**2 - 324/5 - 39/5*d**4 - 648/5*d - 3/5*d**5 = 0 for d.
-3, -2
Let m(j) = -j**3 + 2*j**2 + 2*j - 2. Let i be m(2). Factor k**3 - 2*k**i - 3*k**3 - 3*k**4 - 3*k**3.
-k**2*(k + 1)*(3*k + 2)
Let t(d) be the second derivative of -1/3*d**2 + 1/4*d**4 - 7/18*d**3 + 8*d + 0. Factor t(w).
(w - 1)*(9*w + 2)/3
Let k(j) = j**2 + 10*j + 4. Let o be k(-10). Suppose 3*a = 4*a. Suppose -30/11*c**3 - 2/11*c + 16/11*c**2 + 32/11*c**5 - 16/11*c**o + a = 0. What is c?
-1, 0, 1/4, 1
Let c(n) be the second derivative of -n**5/90 - n**4/18 + n**3/3 + 3*n**2/2 - 4*n. Let g(m) be the first derivative of c(m). Factor g(o).
-2*(o - 1)*(o + 3)/3
Factor -26/5*m**2 - 8/5 - 12/5*m**3 - 24/5*m - 2/5*m**4.
-2*(m + 1)**2*(m + 2)**2/5
Let a(s) = 7*s**2 + s - 1. Let u be a(1). Let d(p) = -p**2 + 6*p + 9. Let o be d(u). Find h such that -2*h**o - 48*h + 4*h**2 + 2 + 44*h = 0.
1
Let d(z) be the third derivative of z**9/9072 - z**8/1680 + z**7/840 - z**6/1080 - z**3 - 4*z**2. Let m(p) be the first derivative of d(p). Factor m(h).
h**2*(h - 1)**3/3
Let h(s) be the first derivative of s**4/16 + 3*s**3/4 + s**2 - 10. Find r, given that h(r) = 0.
-8, -1, 0
Let a be 5 + 2/4*4. Let h = a - 2. Determine s so that -h*s**4 + 7*s**3 + 2*s - 9*s**2 - s + 5*s**3 + s = 0.
0, 2/5, 1
Let u = 188/927 - -2/103. Factor -2/9 - 2/9*p**3 + u*p**2 + 2/9*p.
-2*(p - 1)**2*(p + 1)/9
Let i(k) be the third derivative of k**7/70 + k**6/5 + 13*k**5/20 + 3*k**4/4 + 19*k**2. Determine l, given that i(l) = 0.
-6, -1, 0
Let d(b) be the second derivative of 0 - b + 1/30*b**4 + 1/15*b**3 + 0*b**2. Determine w so that d(w) = 0.
-1, 0
Let k(m) = 5*m**4 - 3*m**3 + 5*m**2 + 3*m + 8. Let s(i) = i**4 - i**3 + i**2 + i + 1. Let f(g) = -k(g) + 6*s(g). Let f(v) = 0. What is v?
-1, 1, 2
Suppose -2*y + 13 - 3 = -2*v, -v = y - 1. Factor 2*i**2 - 4/5*i - 6/5*i**y + 0.
-2*i*(i - 1)*(3*i - 2)/5
Let k(b) = b**2 - 7*b + 8. Let j be k(6). Let y be 100/45*9/15. Find g such that -2/3*g**3 + 2/3*g - y*g**j + 4/3 = 0.
-2, -1, 1
Let i(k) = 3*k**2 + k. Let b be i(-2). Let x(t) = b*t**2 + 10*t**2 - 32*t**3 + 6 + 2*t**2 - 2*t. Let f(v) = v**2 + 1. Let l(s) = 6*f(s) - x(s). Factor l(h).
2*h*(4*h - 1)**2
Let z(y) = y**2 - 7*y + 6. Let n(k) = k**2 - 6*k + 5. Let t(m) = -3*n(m) + 2*z(m). Factor t(o).
-(o - 3)*(o - 1)
Let c(k) be the first derivative of k**4/10 + 2*k**3/5 - k**2/5 - 6*k/5 - 58. Factor c(g).
2*(g - 1)*(g + 1)*(g + 3)/5
Let g(m) be the third derivative of m**5/75 - m**4/60 - 13*m**2. Factor g(j).
2*j*(2*j - 1)/5
Let w(g) = -5*g + 31. Let n be w(7). Let j be 36/28 + n + 3. Factor j*q**4 +