Let x(j) be the third derivative of -j**5/210 + j**4/84 + 2*j**3/7 - 22*j**2. Factor x(q).
-2*(q - 3)*(q + 2)/7
Let c = 4 + -6. Let l = c + 4. Factor -5*g + g - 2*g**l + 3 - 3.
-2*g*(g + 2)
Let y(l) be the first derivative of l**6/15 + 26*l**5/75 + 11*l**4/15 + 4*l**3/5 + 7*l**2/15 + 2*l/15 + 3. Factor y(u).
2*(u + 1)**4*(3*u + 1)/15
Suppose f + 0*x = -4*x, -f = -3*x. Solve 0 + 1/4*c**5 + 0*c**4 - 1/2*c**3 + f*c**2 + 1/4*c = 0.
-1, 0, 1
Let x(w) be the third derivative of -5/24*w**4 - 1/3*w**3 + 0*w - 1/15*w**5 + w**2 + 0 - 1/120*w**6. Factor x(h).
-(h + 1)**2*(h + 2)
Let q(y) be the third derivative of y**5/140 - y**4/14 + 2*y**3/7 + 3*y**2. Suppose q(k) = 0. What is k?
2
Let d(o) be the third derivative of -o**7/1575 + 5*o**2. Factor d(u).
-2*u**4/15
Suppose 3*c + 246 - 261 = 0. Suppose 0 - 6/11*l**c - 12/11*l**3 + 2/11*l + 0*l**2 + 16/11*l**4 = 0. Calculate l.
-1/3, 0, 1
Let v(t) be the third derivative of 1/360*t**5 + 1/48*t**4 + 1/18*t**3 + 0*t + 0 - t**2. Factor v(m).
(m + 1)*(m + 2)/6
Let y(l) be the first derivative of -2*l**2 + 0*l - 4 - 1/4*l**4 + 4/3*l**3. Solve y(x) = 0.
0, 2
Let j(l) = l - 4. Let i be j(6). Determine b, given that -i*b - 2/3*b**2 - 4/3 = 0.
-2, -1
Let h(c) be the first derivative of c**6/1440 - c**5/240 + c**4/96 - 2*c**3/3 + 1. Let v(m) be the third derivative of h(m). Determine f, given that v(f) = 0.
1
Let c(w) be the first derivative of -w**4/10 + 8*w**3/15 + w**2 - 37. Let c(p) = 0. What is p?
-1, 0, 5
Let o(b) = 6*b**5 - 8*b**4 + b**3 + 3*b**2 - 2*b. Let f(y) = 18*y**5 - 24*y**4 + 4*y**3 + 8*y**2 - 6*y. Let s(j) = -5*f(j) + 16*o(j). Find m such that s(m) = 0.
-1, 0, 1/3, 1
Let t(d) be the third derivative of d**6/40 - d**5/10 - 3*d**4/8 - 8*d**2. Solve t(s) = 0.
-1, 0, 3
Suppose -2*y = -5*u + 12, -4*y + 2 = 2*u - 2*y. Solve 1/3*f + 1/3*f**u + 0 = 0 for f.
-1, 0
Factor 2/7*q**3 + 2/7*q**4 - 4/7 - 6/7*q**2 - 10/7*q.
2*(q - 2)*(q + 1)**3/7
Let n(z) be the third derivative of -z**9/378 + z**7/140 + z**6/180 + z**3/2 + 2*z**2. Let t(b) be the first derivative of n(b). Factor t(u).
-2*u**2*(u - 1)*(2*u + 1)**2
Factor 2*i + 2*i**5 + 5*i**3 + 0*i**3 - 9*i**3.
2*i*(i - 1)**2*(i + 1)**2
Let d be 2 - 1*(-6 - 1). Let l be 2/d + 50/18. Let m(t) = -2*t**3 + 4*t**2 + t. Let g(y) = 3*y**3 - 5*y**2 - 2*y. Let h(i) = l*g(i) + 4*m(i). Factor h(w).
w*(w - 1)*(w + 2)
Let w be (-4)/(-6) + 16/3. Suppose 2*y**5 + 2*y**4 - 8*y - 4*y**2 + w*y + 2*y**4 = 0. Calculate y.
-1, 0, 1
Let q(p) = -p**3 - 5*p**2 - 7*p - 10. Let b be q(-4). Determine v so that -1/2*v**2 - 2 + b*v = 0.
2
Let k(q) be the first derivative of q**4/18 + 8*q**3/27 - 5*q**2/9 - 25. Find t, given that k(t) = 0.
-5, 0, 1
Let g(j) be the first derivative of 2*j**5/25 + j**4/10 - 2*j**3/15 - j**2/5 - 8. Solve g(y) = 0 for y.
-1, 0, 1
Let t(y) = y**3 - y**2 - 1. Let k(b) = -18*b**3 + 9*b**2 + 15. Let n(z) = k(z) + 15*t(z). Find l such that n(l) = 0.
-2, 0
Let g be -2 - -20*(-5)/(-45). Factor g*w**5 - 2/3*w**4 + 0 - 2/9*w**2 + 2/3*w**3 + 0*w.
2*w**2*(w - 1)**3/9
Let a be (12/14)/(3/(-126)*-8). Let 5/2*q**2 + a*q + 1 - 7/2*q**4 - 9/2*q**3 = 0. What is q?
-1, -2/7, 1
Let z(d) = -d**3 - 8*d**2 + d + 8. Let k be -10 - (-3)/(6/4). Let o be z(k). Suppose -2/3*h**5 + 0*h**2 + o*h**4 + 0 + 4/3*h**3 - 2/3*h = 0. What is h?
-1, 0, 1
Let f(r) be the second derivative of r**6/480 - r**4/32 + r**3/12 + r**2 - 4*r. Let k(u) be the first derivative of f(u). Factor k(p).
(p - 1)**2*(p + 2)/4
Let u(g) = g**5 - g**4 - 1. Let m(r) = 2*r - 2. Let o be m(-2). Let s(d) = 9*d**5 - 3*d**4 - 6*d**3 - 6. Let c(z) = o*u(z) + s(z). Find f such that c(f) = 0.
-2, 0, 1
Let b be 12 + 8*(-1)/2. Let a(z) be the first derivative of -b*z - 2/3*z**3 + 4*z**2 + 1. Factor a(m).
-2*(m - 2)**2
Let i(g) = -21*g**2 - 42*g - 36. Let a(l) = -3*l**2 - 6*l - 5. Let r(j) = -15*a(j) + 2*i(j). Factor r(w).
3*(w + 1)**2
Suppose -9*b**4 + 12*b**2 - b**5 + 2*b**5 - 4*b**5 = 0. Calculate b.
-2, 0, 1
Let z(p) be the second derivative of p**4/48 - p**3/24 - 7*p. Solve z(r) = 0 for r.
0, 1
Let t(b) be the first derivative of 1/25*b**5 - 5 + 0*b**2 - 2/15*b**3 + 1/5*b + 0*b**4. Suppose t(u) = 0. What is u?
-1, 1
Let z = 7 - 5. Factor -i**z - 4*i**2 + 2*i**2.
-3*i**2
Suppose -5*n = o - 13, 2*n + 2 = -0*n - 4*o. Solve n*y + 13*y - 26*y - 2*y**2 - 8 = 0 for y.
-4, -1
Let o = -18 + 1. Let j = o - -17. Factor j + 0*l + 1/5*l**2.
l**2/5
Let j = 57 - 57. Determine w, given that -2/5*w**2 + j + 4/5*w - 2/5*w**3 = 0.
-2, 0, 1
Let g(d) be the third derivative of 0*d + 0 + 0*d**3 + 1/315*d**7 + 1/360*d**6 + 1/1008*d**8 + 0*d**4 + 5*d**2 + 0*d**5. Solve g(x) = 0.
-1, 0
Let f be 1 + 2/1 + -3. Suppose f = 4*v - v. Factor t + v*t + t - 4*t - t**2.
-t*(t + 2)
Let s be (-558)/(-270) + (-4)/10. What is j in s*j + j**2 + 2/3 - 1/3*j**4 - 1/3*j**3 = 0?
-1, 2
Let h(j) = 10*j**2 - 55*j + 85. Let w(o) = -5*o**2 + 27*o - 42. Let z(u) = 3*h(u) + 5*w(u). Solve z(i) = 0 for i.
3
Let b(u) = 6*u**3 - 3*u**2. Let r(q) = 13*q**3 - 5*q**2 - q. Suppose 4*d = -3*c + 7*c - 28, 0 = 4*c - 3*d - 28. Let h(y) = c*b(y) - 3*r(y). Factor h(n).
3*n*(n - 1)**2
Let l(u) = -3*u**2 - 13*u + 1. Let i(k) = 2*k**2 + 12*k - 2. Let j(n) = 5*i(n) + 4*l(n). Solve j(v) = 0.
1, 3
Let p = 18955708/7 - 2703360. Let g = p - 4588. Factor 60/7*n**2 + 2*n**3 + 16/7 + g*n.
2*(n + 2)**2*(7*n + 2)/7
What is r in 0 - 15*r**5 - 50*r**4 + 100/3*r**2 - 20/3*r - 65/3*r**3 = 0?
-2, 0, 1/3
Factor -6*a**4 - 1 + 4*a**4 + 16*a**2 - 31.
-2*(a - 2)**2*(a + 2)**2
Let n(x) = 6*x**3 + 21*x**2 - 9*x + 9. Let j(u) = 3*u**3 + 10*u**2 - 4*u + 4. Let r(w) = 9*j(w) - 4*n(w). Suppose r(d) = 0. Calculate d.
-2, 0
Let o(i) be the first derivative of -5*i**3/3 - 25*i**2/2 - 20*i + 9. Factor o(r).
-5*(r + 1)*(r + 4)
Let b(s) be the third derivative of -s**7/70 - 3*s**6/40 + s**4/2 + 3*s**2. Factor b(a).
-3*a*(a - 1)*(a + 2)**2
Suppose 4*h - 7*h**2 + 10*h**2 + 8*h + 12 = 0. Calculate h.
-2
Let m(q) be the third derivative of -2*q**7/105 + q**6/15 + q**5/5 - 2*q**4/3 - 8*q**3/3 - 10*q**2. Factor m(n).
-4*(n - 2)**2*(n + 1)**2
Let y(m) be the second derivative of -m**7/21 + m**6/15 - 7*m. Factor y(g).
-2*g**4*(g - 1)
Let d(m) be the second derivative of m**6/105 + m**5/14 + m**4/6 + m**3/7 + 2*m - 8. Suppose d(r) = 0. Calculate r.
-3, -1, 0
Find q, given that -5/2*q**2 - 1/8*q**4 - 2*q - q**3 + 0 = 0.
-4, -2, 0
Let y = -6 + 5. Let j be ((-14)/(-49))/(y/(-7)). Factor -4/3*a - 1/3*a**j - 4/3.
-(a + 2)**2/3
Let s(r) be the second derivative of r**8/560 + r**7/175 + r**6/200 + 3*r**2/2 + 3*r. Let o(k) be the first derivative of s(k). Factor o(i).
3*i**3*(i + 1)**2/5
Let c(o) be the second derivative of -o**7/7560 + o**6/2160 + o**5/180 + o**4/2 + o. Let n(g) be the third derivative of c(g). Factor n(r).
-(r - 2)*(r + 1)/3
Let p(h) be the first derivative of -h**4/14 + 4*h**3/21 - h**2/7 - 10. Solve p(w) = 0.
0, 1
Let k(j) be the third derivative of -j**6/1260 - j**5/420 + j**3/2 + j**2. Let i(a) be the first derivative of k(a). Factor i(u).
-2*u*(u + 1)/7
Let 2 + 3*i**2 + 12*i + 6 + 1 = 0. Calculate i.
-3, -1
Let q(w) = 6*w**2 - 84*w + 294. Let i(y) = 2*y**2 - 28*y + 98. Let j(g) = 11*i(g) - 4*q(g). Let j(z) = 0. Calculate z.
7
Let h = 3 - 6. Let l(a) = -4*a**4 + a**3 - a**2 - a. Suppose 0*c = 5*c - 25. Let q(o) = -2*o**4 + o**3 - o**2 - o. Let p(s) = c*q(s) + h*l(s). Solve p(n) = 0.
-1, 0, 1
Let v(z) = 11*z**2 + 18*z + 35. Let y(s) = 4*s**2 + 6*s + 12. Let p(c) = -3*v(c) + 8*y(c). What is n in p(n) = 0?
-3
Let q = -5 - 0. Let v(u) = u**2 + u. Let j(y) = -4*y**2 - 3*y + 1. Let p(f) = q*v(f) - j(f). Factor p(a).
-(a + 1)**2
Let d(y) = -y + 13. Let s be d(7). Suppose 2*n - s = -n. Factor 1/3*k**n + 1/3 + 2/3*k.
(k + 1)**2/3
Factor 2*p**4 + 103*p**2 - 48*p**3 + 78*p**3 + 90*p**2 + 98*p - 67*p**2.
2*p*(p + 1)*(p + 7)**2
Let d(i) be the first derivative of -2*i**3/3 - 2*i**2 - 2*i - 3. Determine k so that d(k) = 0.
-1
Let x = 31 + -30. Suppose 2*b + 4*p = 2, 3*b - 7 = -p + x. Determine a so that 2/7*a**b + 0 - 2/7*a + 0*a**2 = 0.
-1, 0, 1
Suppose u + 2*r + r = 2, 5*u - 4*r - 10 = 0. Let a(z) be the third derivative of 5/96*z**4 + 1/160*z**6 + z**u + 7/240*z**5 + 1/24*z**3 + 0 + 0*z. Factor a(k).
(k + 1)**2*(3*k + 1)/4
Let w(x) be the second derivative of -x**4/78 - 2*x**3/39 + 7*x. Suppose w(i) = 0. Calculate i.
-2, 0
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