) be the first derivative of g**9/15120 - g**7/2100 + g**5/600 + g**3/3 - 2. Let h(r) be the third derivative of j(r). Determine x so that h(x) = 0.
-1, 0, 1
Let k(l) = -8*l**2 + 6*l. Let i be (-2 + 0)/((-2)/4). Let h(z) = 4 + z**2 + 3 - 2 - i. Let r(n) = -18*h(n) - 2*k(n). Factor r(u).
-2*(u + 3)**2
Suppose 0 = 20*h - 13*h. Find g such that 1/3*g**3 - 4/3*g**2 + h + 4/3*g = 0.
0, 2
Suppose 3*s - 2*s + 8 = 3*f, -s + 1 = 0. Let a(v) be the second derivative of 0*v**4 - v**f + v**2 - v + 2/5*v**5 + 0. Factor a(k).
2*(k + 1)*(2*k - 1)**2
Let n(t) be the third derivative of -1/70*t**7 - 1/112*t**8 + 0*t**4 + 0*t + 1/40*t**6 + 0*t**3 + 1/20*t**5 + 0 + t**2. Factor n(o).
-3*o**2*(o - 1)*(o + 1)**2
Let c(n) be the third derivative of n**8/672 - n**7/210 + n**5/60 - n**4/48 - 3*n**2. What is f in c(f) = 0?
-1, 0, 1
Let z(p) be the second derivative of -p + 1/42*p**7 + 1/12*p**4 + 0 - 1/20*p**5 + 0*p**2 + 0*p**3 - 1/30*p**6. What is a in z(a) = 0?
-1, 0, 1
Determine y, given that -8/3*y**2 - 2*y - 4/9 - 10/9*y**3 = 0.
-1, -2/5
Let z be (3/(-3))/((-1)/3). Let y = 9 + -7. Factor 4*v + 0*v - v**y + z*v**2.
2*v*(v + 2)
Let b(r) be the second derivative of r**6/6 - 3*r**5/2 + 65*r**4/12 - 10*r**3 + 10*r**2 - 24*r. Factor b(t).
5*(t - 2)**2*(t - 1)**2
Let i be (-58)/(-6) + 4/12. Suppose -i = -3*s + 5. Factor -2*h**s + 4*h**3 - 2*h + 0 + 0.
-2*h*(h - 1)**2*(h + 1)**2
Let k(x) be the second derivative of x**4/36 - x**3/18 + 8*x. Determine y so that k(y) = 0.
0, 1
Let s(g) be the third derivative of 0*g - 1/900*g**6 + 0 + 0*g**3 - 1/150*g**5 - 1/90*g**4 - 11*g**2. Solve s(c) = 0 for c.
-2, -1, 0
Let y be (4/10)/((-7)/(-5)). Let n be 25/56 - (-1)/8. Factor -2/7*o - 4/7*o**2 + n + y*o**3.
2*(o - 2)*(o - 1)*(o + 1)/7
Let r(y) = -y**2 - 1. Let v(p) = -5*p**2 + 5. Let z(x) = -6*r(x) + 2*v(x). Factor z(i).
-4*(i - 2)*(i + 2)
Suppose 0 = 5*o + k - 9, 4*o + k = -4*k + 3. Suppose o*v = 2*l, -2 = 4*l - 2*v - 6. Factor 3*c**2 + l*c + 0*c**2 + c**3 + c - c.
c*(c + 1)*(c + 2)
Let i(j) be the first derivative of -2*j**3/27 - 2*j**2/9 - 2*j/9 + 27. Factor i(x).
-2*(x + 1)**2/9
Suppose 0 = 2*c - 8*c. Let f(l) be the third derivative of 1/240*l**5 + 1/96*l**4 + 2*l**2 - 1/480*l**6 + 0*l - 1/24*l**3 + c. Find b such that f(b) = 0.
-1, 1
Let i(w) be the third derivative of -w**6/900 + w**5/50 - w**4/12 - 5*w**3/9 + 13*w**2. Solve i(g) = 0 for g.
-1, 5
Let t(k) be the first derivative of 2*k**3/3 - 16*k**2 + 128*k + 19. Factor t(g).
2*(g - 8)**2
Let f be (4 + 1 - 4) + 8/(-9). Let k(y) be the second derivative of 0*y**4 + 1/90*y**5 + 2/9*y**2 + 0 - y - f*y**3. Determine q so that k(q) = 0.
-2, 1
Let v be ((-4 - -34)/(-6))/((-10)/4). Factor v*d + 10/7*d**2 + 4/7.
2*(d + 1)*(5*d + 2)/7
Let c(m) be the first derivative of -m**5/5 - 3*m**4/4 + 2*m**2 - 4. Factor c(h).
-h*(h - 1)*(h + 2)**2
Let h(s) be the second derivative of s**7/10080 - s**6/2880 - s**4/3 - 3*s. Let w(a) be the third derivative of h(a). Factor w(v).
v*(v - 1)/4
Suppose -3*x = 5*o - 0*x - 7, x = 4*o - 9. Factor q**3 + 2*q**2 - 6*q**3 + o*q**3 - 3*q + 4*q**2.
-3*q*(q - 1)**2
Find p, given that p**2 - p - p**2 + 4*p**3 + 3*p**2 + 0*p**2 = 0.
-1, 0, 1/4
Suppose -4*n + 12 = 0, 0 = 5*r + n + 2*n - 19. Find j, given that -9/5*j**3 - 3/5*j**4 - 9/5*j**r + 0 - 3/5*j = 0.
-1, 0
Suppose -4*j = h, 0 = h - 0*h + 5*j + 1. Determine b, given that -5/2*b**5 + b**2 + 0 + 6*b**h - 9/2*b**3 + 0*b = 0.
0, 2/5, 1
Let c = -170665/9 - -18934. Let d = 29 + c. Factor 0*o + 2/9*o**4 + d*o**2 + 0 - 4/9*o**3.
2*o**2*(o - 1)**2/9
Let g(o) = o**2 - 6*o + 3. Let z be g(2). Let l = 7 + z. What is i in i - 6*i**2 + i**3 + i**3 - l + 5*i = 0?
1
Let o(p) be the first derivative of 0*p**4 - 2/25*p**5 - 2/5*p - 3 + 4/15*p**3 + 0*p**2. Solve o(y) = 0 for y.
-1, 1
Suppose 35*u - 41*u + 18 = 0. Solve -20*f**2 + 2/3*f + 18*f**u + 4/3 = 0.
-2/9, 1/3, 1
Let s be (-3)/18*-3*12. Let d = s + -4. Suppose -6*w**5 + 4*w**5 + d*w**4 + 4*w**5 = 0. Calculate w.
-1, 0
Suppose 3*w + w - 8 = 0. Factor -t + 4*t**w - 2*t**2 + t**2 - 2*t**3.
-t*(t - 1)*(2*t - 1)
Let u = 21 + -15. Let r(o) = -9*o**3 - 14*o**2 - 7*o - 2. Let h(g) = -8*g**3 - 13*g**2 - 7*g - 2. Let d(y) = u*r(y) - 7*h(y). Solve d(q) = 0.
-2, -1, -1/2
Let z = -6 + 4. Let c be z/4*-1*4. Determine u so that 3*u**2 - 3*u**c + u**3 - u**2 - 2*u = 0.
-1, 0, 2
Suppose 7*q**4 + 6*q**3 - 14*q**4 + 5*q**4 - 4*q**2 = 0. Calculate q.
0, 1, 2
Let k(v) be the third derivative of -1/12*v**4 + 0*v**3 + 0 + 0*v - 5*v**2 + 1/12*v**5 - 1/30*v**6 + 1/210*v**7. Factor k(u).
u*(u - 2)*(u - 1)**2
Let n(x) be the second derivative of -x**7/7560 + x**6/1080 - x**5/360 + x**4/2 + 3*x. Let j(o) be the third derivative of n(o). Factor j(i).
-(i - 1)**2/3
Let q(p) be the third derivative of p**5/60 + p**4/12 - 10*p**2. Solve q(x) = 0.
-2, 0
Let u(j) be the third derivative of -1/12*j**4 + 1/15*j**5 + 0*j + 1/30*j**6 - 1/105*j**7 - 1/168*j**8 - 3*j**2 - 1/3*j**3 + 0. Suppose u(f) = 0. What is f?
-1, 1
Let q(l) be the second derivative of l**7/21 + l**6/15 - l**5/5 + 17*l. Solve q(o) = 0 for o.
-2, 0, 1
Let k = 55 + -52. Let n be (-4)/(-6) - 16/(-66). What is v in 0 - n*v**2 - 14/11*v**k + 4/11*v = 0?
-1, 0, 2/7
Let o = 40 + -40. Let 4/7*j - 2/7*j**4 + 2/7*j**2 + o - 4/7*j**3 = 0. Calculate j.
-2, -1, 0, 1
Let s(u) = -u**2. Let w(b) = -16*b**2 + 72*b - 28. Let i(l) = 22*s(l) - 2*w(l). Solve i(r) = 0 for r.
2/5, 14
Let x(o) be the first derivative of -o**5/20 - 3*o**4/16 - o**3/4 - o**2/8 - 2. Factor x(k).
-k*(k + 1)**3/4
Find q, given that 1/6*q**3 + 0*q**2 + 0 - 1/6*q**4 + 0*q = 0.
0, 1
Let m(w) be the second derivative of -5*w**4/12 - 5*w**3/6 - 3*w**2/2 + w. Let t(j) = -14*j**2 - 14*j - 8. Let x(p) = 8*m(p) - 3*t(p). Factor x(r).
2*r*(r + 1)
Let o(c) be the first derivative of 3*c**5/10 + 3*c**4/4 + c**3/2 - 1. Factor o(t).
3*t**2*(t + 1)**2/2
Suppose 4 = 7*c - 6*c. Factor -18*t**2 + 2*t**3 - c*t - 8*t**3 - 10*t - 2*t**4 - 4 - 4*t**3.
-2*(t + 1)**3*(t + 2)
Let y(p) = p - 3. Let n be y(5). Let r = n + -5/3. Factor 0*l**2 + 0 - r*l**5 + 0*l**4 + 2/3*l**3 - 1/3*l.
-l*(l - 1)**2*(l + 1)**2/3
Let o = 2/71 - -55/568. Let u(i) be the first derivative of 1 + o*i**4 - 1/6*i**3 + 0*i + 0*i**2. Factor u(c).
c**2*(c - 1)/2
Let l be -1 + 3/(6/10). What is d in d**3 - d + 1/2*d**l + 0*d**2 - 1/2 = 0?
-1, 1
Solve 0 + 0*m + 2/9*m**5 + 4/9*m**3 + 0*m**2 + 2/3*m**4 = 0 for m.
-2, -1, 0
Let n(k) be the second derivative of -11*k**5/40 + k**4 - 5*k**3/4 + k**2/2 + 8*k. Let n(q) = 0. What is q?
2/11, 1
Let l(x) be the third derivative of -7*x**6/40 - x**5/10 + 7*x**4/8 + x**3 - 2*x**2. Solve l(r) = 0 for r.
-1, -2/7, 1
Let f = 1393/12 + -116. Let g(y) be the third derivative of 0*y + 0 - 1/120*y**5 - 1/24*y**4 + 2*y**2 - f*y**3. Factor g(s).
-(s + 1)**2/2
Let w(s) be the second derivative of 1/6*s**4 + 0*s**3 - 2*s + 1/2*s**2 + 0 - 1/30*s**5. Let h(a) be the first derivative of w(a). Factor h(z).
-2*z*(z - 2)
Suppose 12/7*t**2 - 2/7*t + 0 = 0. What is t?
0, 1/6
Let y = 2/105 + 8/21. Factor 0 - y*k**2 - 2/5*k**3 + 4/5*k.
-2*k*(k - 1)*(k + 2)/5
Let q(l) be the second derivative of l**5/140 - l**3/42 - 3*l. What is x in q(x) = 0?
-1, 0, 1
Let g(i) be the second derivative of 0*i**3 + 3*i + 0*i**2 - 1/16*i**4 + 1/120*i**6 + 0 - 1/40*i**5. Find c such that g(c) = 0.
-1, 0, 3
Factor 2/3 + 5/3*u + 4/3*u**2 + 1/3*u**3.
(u + 1)**2*(u + 2)/3
Factor -1/6*m**2 - 1/6*m + 1/6*m**3 + 1/6.
(m - 1)**2*(m + 1)/6
What is g in 5/4*g**2 + 0 + 1/2*g - 7/4*g**3 = 0?
-2/7, 0, 1
Factor 12*f - 157 + 76 + 0*f**2 + 4*f**2 + 89.
4*(f + 1)*(f + 2)
Solve 7*u**3 - 3*u**3 - 3*u**4 + 0*u**2 - 7*u**3 + 6*u**2 = 0.
-2, 0, 1
Let y = 71 - 139/2. Let c(m) be the first derivative of 3/5*m**5 + y*m**6 - 5/4*m**4 + 1/3*m**3 + 1 + 0*m**2 + 0*m. Let c(h) = 0. Calculate h.
-1, 0, 1/3
Let w(t) be the second derivative of 0 + 1/126*t**7 - 1/45*t**6 + 0*t**5 + 1/18*t**4 + 0*t**2 - 1/18*t**3 - t. Solve w(a) = 0 for a.
-1, 0, 1
Let z = -362 - -27151/75. Let q(x) be the third derivative of z*x**5 + 1/60*x**4 + 0 + 1/300*x**6 + 0*x**3 + 0*x + x**2. Factor q(k).
2*k*(k + 1)**2/5
Let i(s) = 9*s**5 + 9*s**4 - 29*s**3 + 15*s**2 + 4. Let p(n) = 8*n**5 + 8*n**4 - 28*n**3 + 15*n**2 + 3. Let k(o) = -3*i(o) + 4*p(o). Factor k(y).
5*y**2*(y - 1)**2*(y + 3)
Suppose -2*d + 7*m - 9 = 2*m, 0 = d - 2*m + 4. Let w = d -