3 = 0.
-1, 0, 1
Let f be (-68)/336 - (-4)/14. Let o(z) be the third derivative of 2*z**2 + 0*z + f*z**3 - 1/32*z**4 + 1/480*z**6 + 0 + 0*z**5. Factor o(y).
(y - 1)**2*(y + 2)/4
Let w(h) be the second derivative of -h**7/3780 + h**6/540 - h**5/180 - h**4/12 - 4*h. Let u(x) be the third derivative of w(x). What is r in u(r) = 0?
1
Let c(p) be the third derivative of 0*p + 1/60*p**4 - 1/300*p**6 - 1/150*p**5 + 1/15*p**3 + 0 + 4*p**2. Solve c(i) = 0 for i.
-1, 1
Let f(s) be the first derivative of -s**4/12 - s**3/6 + s**2 - 2*s + 8. Let k(d) be the first derivative of f(d). Find p such that k(p) = 0.
-2, 1
Factor 8/3*u**2 + 4/3 + 2/3*u**3 + 10/3*u.
2*(u + 1)**2*(u + 2)/3
Let j(t) be the first derivative of t**5/110 - t**4/66 - 6*t + 6. Let q(x) be the first derivative of j(x). Factor q(l).
2*l**2*(l - 1)/11
Suppose 4*g + k + 110 = 6*k, -2*g = 3*k + 44. Let n = g + 27. Factor -3/7*a**3 - 3/7*a + 6/7*a**n + 0.
-3*a*(a - 1)**2/7
Let u = 39 - 39. Let b(h) be the first derivative of 0*h**4 + 0*h - 1/9*h**3 - 2 + u*h**2 + 1/15*h**5. Factor b(t).
t**2*(t - 1)*(t + 1)/3
Let i(k) be the third derivative of 0 - 1/10*k**5 + 3/40*k**6 + 0*k**3 + 0*k + 3*k**2 + 0*k**4. Solve i(m) = 0.
0, 2/3
Let w(i) = i**2 + 2*i + 3. Let j be w(-3). Let z(d) be the third derivative of -1/40*d**j - 2*d**2 - 1/60*d**5 + 0*d + 1/8*d**4 + 1/6*d**3 + 0. Factor z(n).
-(n - 1)*(n + 1)*(3*n + 1)
Suppose -2*j - 4*o + 6 = -8, -2*j + o = -9. Suppose -4*x + 3*n + 12 = 0, -2*x + 6 = j*n - n. Determine r, given that 1/5*r**4 + 1/5*r**x + 0*r**2 + 0 + 0*r = 0.
-1, 0
Let x be (-4)/(-7) - 12/(-126). Find o such that 14/3*o + x*o**3 + 2 + 10/3*o**2 = 0.
-3, -1
Let k = -28 + -5. Let g = k + 33. Factor p**4 + g - 1/4*p**3 - p**2 + 1/4*p.
p*(p - 1)*(p + 1)*(4*p - 1)/4
Let n(p) be the first derivative of 5*p**4/16 + 3*p**3/2 - p**2 + 11. Factor n(d).
d*(d + 4)*(5*d - 2)/4
Suppose 0*y = -5*d - 5*y + 30, 2*d - 4*y = -6. Suppose 0 = 6*m - 7*m + d. Determine x so that 0 + 8/5*x**2 - 98/5*x**4 - 98/5*x**m + 8/5*x = 0.
-1, -2/7, 0, 2/7
Let s(q) = q**2 + 2*q. Let d be s(-3). Find x, given that 2*x**2 + 2*x**3 - 4*x - d*x**3 + 3*x = 0.
0, 1
Let q = 31 + -31. Let p(i) be the third derivative of 0*i - 1/30*i**5 + 0 - 3*i**2 + 1/105*i**7 + q*i**3 + 1/12*i**4 - 1/60*i**6. Solve p(a) = 0 for a.
-1, 0, 1
Find t, given that -3 - 27*t**2 + 30*t**2 + 0 = 0.
-1, 1
Let d(u) be the third derivative of -3*u**2 - 1/120*u**4 + 1/15*u**3 + 1/600*u**6 + 0*u - 1/150*u**5 + 0. Determine a, given that d(a) = 0.
-1, 1, 2
Let 2/11*j**2 - 2/11 + 0*j = 0. What is j?
-1, 1
Let y = -3/535 + 217/535. Factor -y*r**5 + 4/5*r**3 - 2/5*r + 0*r**4 + 0*r**2 + 0.
-2*r*(r - 1)**2*(r + 1)**2/5
Suppose l - 6 = -4. Let r(i) be the first derivative of -2 + i**l - 2/3*i**3 + 0*i. Factor r(z).
-2*z*(z - 1)
Let y(g) = -2*g - 9. Let m be y(-5). Let p be (m/2*0)/1. Factor 0 + 1/2*x + p*x**3 + x**2 - 1/2*x**5 - x**4.
-x*(x - 1)*(x + 1)**3/2
Let g = -17/9 + 155/63. Determine w, given that g*w**3 - 8/7*w + 2/7*w**4 - 6/7*w**2 + 8/7 = 0.
-2, 1
Let g(n) = 4*n**2 + 8*n - 2. Let o(r) = -r**2 - r + 1. Let i(v) = -g(v) - 6*o(v). Suppose i(b) = 0. Calculate b.
-1, 2
Let q(m) = -5*m**3 - 45*m**2 - 139*m - 135. Let j(o) = -10*o**3 - 90*o**2 - 279*o - 270. Let w(u) = 4*j(u) - 9*q(u). Factor w(b).
5*(b + 3)**3
Let z(r) = -r + 3. Let b be z(5). Let q(j) = j**4 - 2*j**3 - j**2 - 2*j - 2. Let g(h) = -h**3 - h - 1. Let s(f) = b*g(f) + q(f). Solve s(t) = 0 for t.
-1, 0, 1
Let a(q) = -3*q**2 - 3*q - 3*q**3 - 2*q - 4*q**4 + 11*q**4. Let h(m) = 15*m**4 - 7*m**3 - 7*m**2 - 11*m. Let l(u) = -13*a(u) + 6*h(u). Factor l(z).
-z*(z + 1)**3
Let s(u) be the third derivative of -u**5/60 + u**4/12 - u**3/6 + u**2. Find y, given that s(y) = 0.
1
Let g(w) = -w**3. Let k(u) = 0*u**3 + 6*u**3 + 4*u**3 + 6*u**2 - 5*u**2. Let v(d) = 22*g(d) + 2*k(d). Determine q so that v(q) = 0.
0, 1
Let q(y) = -y**3 + 14*y**2 + y - 12. Let d be q(14). Solve 0*c**3 - d*c**2 + 4*c + 2*c**3 - 4*c**2 = 0 for c.
0, 1, 2
Let b(g) be the second derivative of -8/3*g**3 + 3/5*g**5 + 11/3*g**6 - 14/3*g**4 - g + 0 + 0*g**2 - 25/21*g**7. Determine t, given that b(t) = 0.
-2/5, 0, 1, 2
Let w(m) = m**3 + 5*m**2 - 2*m - 4. Let f be w(-5). What is p in -f*p**2 + 3*p**3 + 0*p**2 - p**5 + 4*p**2 + 0*p**5 = 0?
-2, 0, 1
Factor -5*v**3 + 2*v + 0*v**3 + 12 + 7*v**3 - 24*v**2 + 8*v**3.
2*(v - 2)*(v - 1)*(5*v + 3)
Suppose 2*y = -4*b + 34, -3*b = y + 2*y - 33. Suppose -a - 4 = -b. Factor 0 + 10/7*n**a + 6/7*n**3 - 4/7*n.
2*n*(n + 2)*(3*n - 1)/7
Let d(k) be the third derivative of 1/120*k**6 + 0*k**5 + 0*k**3 + 0*k + 0*k**4 + 6*k**2 + 0. Solve d(c) = 0 for c.
0
Let z(n) = n**2 + 4*n + 6. Let l(c) = 2*c**2 + 9*c + 12. Let x(i) = -3*l(i) + 5*z(i). Solve x(y) = 0.
-6, -1
Suppose 4*w - 2*s + s = 9, 5*s = -2*w + 21. Suppose -w*m = -0*m - 9. Factor -15*p - 16*p**2 - 6 + 4*p**2 + 2*p**3 - 5*p**m.
-3*(p + 1)**2*(p + 2)
Factor 1/7*z**2 + 0 - 1/7*z.
z*(z - 1)/7
Let w(b) be the first derivative of -4*b**3/9 - b**2 + 4*b/3 - 1. Determine x, given that w(x) = 0.
-2, 1/2
Let y(h) be the second derivative of -h**5/80 - h**4/24 - h**3/24 + 2*h. What is v in y(v) = 0?
-1, 0
Let a = -53 + 213/4. Suppose 1/4*n**2 + 0 + a*n = 0. Calculate n.
-1, 0
Let y be 10/(-70) + 50/14. Let t = 26/7 - y. Factor t + 0*v - 2/7*v**2.
-2*(v - 1)*(v + 1)/7
Suppose i + 3*i = 0. Let w(t) be the second derivative of -1/21*t**3 + 1/70*t**5 - 1/42*t**4 + i + 1/7*t**2 + 2*t. Factor w(x).
2*(x - 1)**2*(x + 1)/7
Let g(u) be the second derivative of u**6/840 - u**5/140 + u**4/84 + 3*u**2 - 11*u. Let b(m) be the first derivative of g(m). Determine j, given that b(j) = 0.
0, 1, 2
Suppose 8 = 3*p + 2. Let y(t) be the first derivative of 1/2*t**4 + 0*t**p - 1/9*t**3 + 0*t + 2 - 3/5*t**5. Factor y(h).
-h**2*(3*h - 1)**2/3
Let p = 4167/7 - 593. Let 2/7*i**5 + p*i**2 - 2*i - 4/7*i**3 - 4/7*i**4 + 4/7 = 0. What is i?
-2, 1
Let o(c) be the first derivative of -25*c**9/12096 - 3*c**8/448 - c**7/140 - c**6/360 - c**3/3 - 1. Let f(q) be the third derivative of o(q). Factor f(g).
-g**2*(g + 1)*(5*g + 2)**2/4
Factor 61*h**2 - 40 - 15*h**3 - 10*h**2 - 48*h + 52.
-3*(h - 2)*(h - 1)*(5*h - 2)
Suppose -3*t + 4 = -2*t. Let x = 19 - 19. Factor t*m**2 - 2 + x + 2*m**2 - 2*m**3 - 6.
-2*(m - 2)**2*(m + 1)
Let y(i) be the first derivative of -i**3/4 - 9*i**2/4 - 6*i - 6. Factor y(d).
-3*(d + 2)*(d + 4)/4
Suppose 2*w**2 + 8*w - 123 + 117 - 4*w**2 = 0. What is w?
1, 3
Let k(y) be the second derivative of -y**4/20 + y**3 - 15*y**2/2 + y. Factor k(g).
-3*(g - 5)**2/5
Suppose 10 = w - 3*w, 5*s - 10 = -3*w. Factor -8/9*z**2 + 4/3*z**3 + 2/9*z**s + 0 - 8/9*z**4 + 2/9*z.
2*z*(z - 1)**4/9
Find p such that -1/2*p**2 + 0 - 3/2*p = 0.
-3, 0
Let r(o) be the third derivative of -o**5/360 + o**4/72 - 9*o**2. Let r(x) = 0. Calculate x.
0, 2
Let g = -25 + 101/4. Factor 1/4*j**4 - g*j - 3/4*j**3 + 0 + 3/4*j**2.
j*(j - 1)**3/4
Let t be (-3)/(((-40)/156)/((-32)/(-36))). Let r(h) be the first derivative of -t*h**2 - 63/10*h**4 - 68/5*h**3 + 1 - 16/5*h. Suppose r(u) = 0. What is u?
-2/3, -2/7
Let m(l) be the first derivative of l**5/10 - l**4/8 - 2*l**3/3 + l**2 + 34. Factor m(q).
q*(q - 2)*(q - 1)*(q + 2)/2
Suppose 12 = -f + 19. Let w be (-16)/f*2/(-8). Factor -w + 2/7*d + 2/7*d**2.
2*(d - 1)*(d + 2)/7
Let k(r) be the third derivative of r**6/540 + r**5/270 - 4*r**2. Solve k(g) = 0.
-1, 0
Let x(p) be the first derivative of -2*p**5/15 + p**4/12 + 2*p**3/9 - p**2/6 + 2. Solve x(f) = 0 for f.
-1, 0, 1/2, 1
Let g(x) be the second derivative of 0*x**3 - 1/8*x**2 + 0 + 4*x + 1/48*x**4. Find a, given that g(a) = 0.
-1, 1
Let b be (-2)/2 + 4 + 2. Suppose -b*t = 0, n - 5 = 2*t - 2. Factor n*p + 2*p + 2 + 6*p**2 - 4*p**2.
(p + 2)*(2*p + 1)
Let m(c) be the third derivative of -c**7/630 - c**6/720 + c**5/120 + c**4/144 - c**3/36 + 2*c**2. Find d, given that m(d) = 0.
-1, 1/2, 1
Let j(b) be the third derivative of 9*b**7/70 - 27*b**6/40 + 21*b**5/20 - 19*b**4/24 + b**3/3 - 14*b**2. Factor j(m).
(m - 2)*(3*m - 1)**3
Let j(r) be the third derivative of -r**6/60 - r**5/15 - 13*r**2. What is v in j(v) = 0?
-2, 0
Let y(t) = 2*t**3 + 4*t**2 - 6*t - 4. Let f(s) = 2*s**3 + 4*s**2 - 7*s - 4. Let j(q) = 4*f(q) - 5*y(q). Let j(p) = 0. What is p?
-2, -1, 1
Let i(t) be the second derivative of -2*t**6/15 - t**5/3 - t**4/6 + t**2 + 7*t.