
Let p(m) = 7*m - 1. Let r be p(-3). Let t = 89/4 + r. Find j, given that -t*j - 1/4*j**3 - 1/2*j**2 + 0 = 0.
-1, 0
Let a(p) = -6*p + 4*p**2 + 8*p + p**3 + 0*p. Let q be a(-3). Let -8/7*l**q + 4/7*l**2 - 8/7*l**4 + 10/7*l - 2/7*l**5 + 4/7 = 0. Calculate l.
-2, -1, 1
Determine p so that 5*p**2 + 4*p - 2*p**3 - 3*p**5 - p**3 - p**2 - 4*p**4 + 2*p**5 = 0.
-2, -1, 0, 1
Let n(k) be the third derivative of k**7/140 - k**6/120 - k**5/30 + k**4/24 + k**3/12 + 4*k**2. Find q such that n(q) = 0.
-1, -1/3, 1
Let k(c) = 22*c - 8. Let r be k(11). Let m = 1174/5 - r. Factor -2/5*v**2 + m*v - 2/5*v**3 + 0.
-2*v*(v - 1)*(v + 2)/5
Suppose -9 = n + 1. Let w(h) = -2*h + 1. Let c be w(2). Let f(p) = -3*p**2 + 8*p - 5. Let q(v) = 8*v**2 - 24*v + 16. Let k(m) = c*q(m) + n*f(m). Factor k(g).
2*(g - 1)*(3*g - 1)
Let l(g) = -5*g**3 + 35*g**2 - 15*g - 65. Let j(k) = 3*k**3 - 18*k**2 + 7*k + 32. Let b(c) = -5*j(c) - 2*l(c). Factor b(y).
-5*(y - 3)*(y - 2)*(y + 1)
Let j(t) = 7*t**4 - 11*t**3 - 65*t**2 - 69*t - 17. Let m(d) = d**4 + d**3 - d**2 - d + 1. Let q(n) = -j(n) + 5*m(n). Factor q(s).
-2*(s - 11)*(s + 1)**3
Let l(w) be the second derivative of w**6/60 + 3*w**5/40 + w**4/24 - w**3/4 - w**2/2 + 8*w. Factor l(y).
(y - 1)*(y + 1)**2*(y + 2)/2
Factor 12*z**5 + 4*z - 40*z**4 - 3*z**2 - 13*z**2 - 8*z**2 + 20*z**3 + 28*z**3.
4*z*(z - 1)**3*(3*z - 1)
Let x(v) be the second derivative of v**7/126 - 7*v**6/180 + v**5/15 - v**4/36 - v**3/18 + v**2/12 + 3*v. Find l such that x(l) = 0.
-1/2, 1
Suppose 11 = -14*w + 39. Factor -13/3*c + 5/3*c**2 - w.
(c - 3)*(5*c + 2)/3
Let m(l) be the second derivative of 0*l**2 - 1/60*l**6 + 0*l**4 + 1/40*l**5 + 0 + 0*l**3 + 1/336*l**7 + 2*l. Let m(y) = 0. Calculate y.
0, 2
Suppose -3*p + 7*p + 18 = 5*d, -5*d + 16 = -3*p. Let g(v) be the second derivative of 1/12*v**3 + 1/8*v**d - v + 0 + 1/48*v**4. Factor g(h).
(h + 1)**2/4
Solve -36*a**4 + 2*a + 69*a**4 - 34*a**4 + 1 - 2*a**3 = 0 for a.
-1, 1
Suppose 0*m - 2*m = 0. Let d(o) be the first derivative of 4/27*o**3 + m*o - 1/18*o**4 - 1/9*o**2 - 1. Factor d(f).
-2*f*(f - 1)**2/9
Suppose -22 = -4*t - 2*v, 10 = 3*t - 4*v - 12. Suppose -z = z - t. Find k such that -2*k**3 + z*k**2 - 3*k**2 + 2*k = 0.
-1, 0, 1
Factor -6*s**2 + 2*s**4 - s**3 - 2*s**3 + 4*s**4 + 3*s**5.
3*s**2*(s - 1)*(s + 1)*(s + 2)
Suppose 0*y - 20 = -5*y. Solve -h**3 - 2*h**5 + 2*h + 0*h**3 + h**3 + 4*h**2 - 4*h**y = 0.
-1, 0, 1
Let g(h) be the first derivative of 2*h**6/3 - 16*h**5/5 + 4*h**4 - 30. Solve g(q) = 0 for q.
0, 2
Let k be 7 + -1 - (0 + 3). Factor 5*g**5 + g**k - 2*g**5 + 0*g**5 - 2*g**4 - 2*g**5.
g**3*(g - 1)**2
Factor 2*h**3 + 0*h**3 + 16*h + 8 - 3*h**2 - 2*h**2 + 15*h**2.
2*(h + 1)*(h + 2)**2
Let a be ((-48)/(-15))/(9/5). What is k in -2*k**4 + a*k - 44/9*k**2 - 2/9 + 16/3*k**3 = 0?
1/3, 1
What is g in 25*g - 18*g - 49 + g**2 + 21*g + 245 = 0?
-14
Let a(y) be the second derivative of 5*y - 1/9*y**3 + 0*y**2 - 1/18*y**4 + 0. Determine x so that a(x) = 0.
-1, 0
Let y = -31 - -34. Let -8/3*p + 8/3*p**2 - 2/3*p**y + 0 = 0. What is p?
0, 2
Let w(y) be the first derivative of y**3 - 3*y**2/2 - 6. Determine t so that w(t) = 0.
0, 1
Let x(h) be the third derivative of -h**7/21 - h**6/8 + 22*h**2. Find i, given that x(i) = 0.
-3/2, 0
Let c be (-12)/(-2)*(-9)/6. Let s be 24/c*(-3)/18. Find z such that -2/3*z**3 + 14/9*z**2 - s - 10/9*z**4 + 2/3*z = 0.
-1, 2/5, 1
Let t(v) be the second derivative of -v**5/4 - 25*v**4/12 - 5*v**3 - 2*v - 18. Solve t(r) = 0.
-3, -2, 0
Let g(o) be the first derivative of -11*o**4 - 8*o**3/3 + 22*o**2 + 8*o + 27. Factor g(r).
-4*(r - 1)*(r + 1)*(11*r + 2)
Let q = 14/57 + -3/38. Let l(v) be the first derivative of 2 + q*v**2 - 5/12*v**4 + 0*v - 1/9*v**3 - 1/5*v**5. Factor l(d).
-d*(d + 1)**2*(3*d - 1)/3
Let p be -2 + -2 + 2 + -1. Let b be 8/(-12) - 8/p. Factor -3 + b*r + 10*r**2 + 3 + 4*r**3 - 4*r**2.
2*r*(r + 1)*(2*r + 1)
Let a(m) = m**3 + 4*m**2 - 1. Let r be (6/(-4))/((-2)/(-4)). Let j be a(r). Suppose -5*g**2 - 1 - j*g + 0*g - 3 - g**3 = 0. What is g?
-2, -1
Factor -5/2*f + 0 - 5*f**3 - 45/4*f**2.
-5*f*(f + 2)*(4*f + 1)/4
Let s(d) = -3*d. Let z be s(-1). Let q = -35 + 37. Factor -1/2 + q*t**z + 5/2*t - 4*t**2.
(t - 1)*(2*t - 1)**2/2
Let m(c) be the second derivative of 1/10*c**2 - 1/30*c**3 - 5*c - 1/60*c**4 + 0 + 1/100*c**5. Solve m(f) = 0.
-1, 1
Let b(j) be the third derivative of 1/60*j**6 - 1/30*j**5 + 0 + 0*j - 1/6*j**4 + j**2 + 0*j**3. Factor b(v).
2*v*(v - 2)*(v + 1)
Let o be (-1 - 0 - -2)*2/4. Let c(w) be the first derivative of 0*w**5 + 0*w**2 - o*w**4 + 1 + 0*w**3 + 0*w + 1/3*w**6. Find d such that c(d) = 0.
-1, 0, 1
Let g(r) be the first derivative of -1/8*r**2 + 1/6*r**6 + 9/16*r**4 + 1/12*r**3 + 11/20*r**5 + 9 + 0*r. Factor g(p).
p*(p + 1)**3*(4*p - 1)/4
Find y, given that 3*y**2 + 2*y**2 - 4*y**2 - y**4 = 0.
-1, 0, 1
Let w = 1 + 0. Let y = w - -1. Find g, given that 2*g**3 + g**4 + 2*g**y - g**2 - 4*g**3 = 0.
0, 1
Factor 0*p + 1/4*p**2 + 0.
p**2/4
Let 1/3*u - 1/3*u**2 - 1/3*u**3 + 1/3 = 0. Calculate u.
-1, 1
Let w(y) be the second derivative of -y**5/60 + y**4/8 - y**3/3 - 3*y**2/2 - 2*y. Let z(i) be the first derivative of w(i). Suppose z(a) = 0. Calculate a.
1, 2
Let t(u) be the third derivative of -1/48*u**4 - 1/480*u**6 + 0*u**3 - 1/80*u**5 + 0*u + 3*u**2 + 0. What is c in t(c) = 0?
-2, -1, 0
Suppose 2/3*o**2 + 2/3 + 4/3*o = 0. What is o?
-1
Let o(b) = b**2 - 7*b. Let p be o(7). Suppose 0 = -3*h + c + 14, -h - c + p = 2. Factor a**3 + 2*a**3 - 2*a**2 + a - 2*a**h.
a*(a - 1)**2
Let i = 47 + -233/5. Suppose 0*p = -4*p + 8. Factor -2/5 - 4/5*c - i*c**p.
-2*(c + 1)**2/5
Let s be 5/(-75)*(-20)/8. Factor 0*d**2 + 0 + 1/3*d**4 + 0*d + 1/6*d**5 + s*d**3.
d**3*(d + 1)**2/6
Let o(s) be the third derivative of -3/40*s**4 - 1/100*s**5 - 1/350*s**7 + 3/200*s**6 + 1/5*s**3 + 0*s + s**2 + 0. Determine h so that o(h) = 0.
-1, 1, 2
Let f(x) = -x**2 + x. Let t(j) = j**5 + 5*j**4 + 9*j**3 + 10*j**2 - j. Let v(w) = 15*f(w) + 5*t(w). Determine k, given that v(k) = 0.
-2, -1, 0
Let m(c) be the third derivative of -1/180*c**5 + 0*c**3 + c**2 + 0*c + 1/360*c**6 - 1/36*c**4 + 0. Factor m(h).
h*(h - 2)*(h + 1)/3
Let m = -4 + 3. Let w be m/(((-9)/12)/3). Factor w*s - 4 + 2*s**3 + 6*s - 8*s**2 + 0*s**3.
2*(s - 2)*(s - 1)**2
Let y(w) be the second derivative of w**6/5 - 2*w**5/5 - w**4/6 + 2*w**3/3 - w. Factor y(b).
2*b*(b - 1)**2*(3*b + 2)
Factor 3*g + 3*g + 4*g - 2*g + 12 - 4*g**2.
-4*(g - 3)*(g + 1)
Let v(o) be the second derivative of -1/9*o**3 + 0 + 5*o + o**2 + 1/30*o**5 - 1/6*o**4. Suppose v(p) = 0. Calculate p.
-1, 1, 3
Factor -2 - 4/3*x + 2/3*x**2.
2*(x - 3)*(x + 1)/3
Let b = -27083/5 + 5434. Let t = -17 + b. Factor 2/5 + 0*k - t*k**2.
-2*(k - 1)*(k + 1)/5
Let d be (1 - 4)*(-8)/8. Let v(y) be the third derivative of 3*y**2 + 1/20*y**4 - 1/75*y**5 + 0*y - 1/15*y**d + 0. Suppose v(l) = 0. Calculate l.
1/2, 1
Let a(b) be the first derivative of -b**5/15 + b**4/6 - b**3/9 + 11. Factor a(f).
-f**2*(f - 1)**2/3
Let v be (-704)/374 - (3 - (6 + -1)). Factor 4/17*y + 0 + v*y**2.
2*y*(y + 2)/17
Suppose -4*w = w - 20. Factor -b**4 - b**3 + 0*b**w - b + 2*b - b**2 + 4*b**2 - 2.
-(b - 1)**2*(b + 1)*(b + 2)
Let z(c) be the second derivative of -2*c**7/21 - 2*c**6/5 + c**5/5 + 11*c**4/3 + 8*c**3 + 8*c**2 + 4*c. Determine w, given that z(w) = 0.
-2, -1, 2
Let p be (4 + -2)/(-1)*(-6)/18. Find b such that -p*b**2 - 2/3 + 4/3*b = 0.
1
Let r(z) be the third derivative of -5*z**2 + 1/12*z**4 + 0*z + 1/60*z**5 + 1/6*z**3 + 0. Suppose r(n) = 0. What is n?
-1
Factor 3*y**3 - 3*y**2 + y**2 + y**3 - 2*y.
2*y*(y - 1)*(2*y + 1)
Suppose 6*t - 3*t = 0. Suppose -5*k - 17 = x - t*x, 0 = -4*x - 5*k - 8. Factor -1/2*j + 0 - 1/2*j**5 + 0*j**2 + 0*j**4 + j**x.
-j*(j - 1)**2*(j + 1)**2/2
Let l = -19/7 - -45/14. Solve l*o**4 - 1/2*o**3 - 1/2*o**2 + 0 + 1/2*o = 0 for o.
-1, 0, 1
Let h = 10 - 4. Suppose -2*v = h - 8. Determine d, given that -d - 1/4*d**2 - v = 0.
-2
Let u(t) be the third derivative of t**6/240 - t**5/120 - t**4/24 + 7*t**2. Factor u(w).
w*(w - 2)*(w + 1)/2
Let f(o) = -14*o - 4. Let z be f(-3). Let 0 + 36*b**2 + 1 + 26*b - z*b = 0. Calculate b.
1/6
Let i be (68/(-51))/(2*-2). Factor 0*v - 2/3*v**4 + 0 + 2/3*v**2 - 1/3*v**3 + i*v**5.
v**2*(v - 2)*(v - 1)*(v + 1)/3
Let v(c) be the third derivative of -c**7/10080 - c**4/