*6 - 1/5*d**5 + 0*d. Factor q(i).
i**2*(i - 1)**3/3
Let z(a) be the third derivative of a**5/300 - a**4/120 - 10*a**2. Determine u so that z(u) = 0.
0, 1
Let b = 2/7 + 1/21. Let s(y) be the first derivative of -y + y**2 - 2 - b*y**3. Find a such that s(a) = 0.
1
Let x(h) be the first derivative of -h**4/18 + 2*h**3/9 - h**2/3 + 2*h + 4. Let y(g) be the first derivative of x(g). Factor y(m).
-2*(m - 1)**2/3
Let d(q) = 2*q**2 - 4*q. Let c(t) = 2*t**2 - 5*t. Let p(b) = 2*c(b) - 3*d(b). Factor p(j).
-2*j*(j - 1)
Let h = -192/5 + 39. Factor -3/5*v**2 - h*v + 3/5 + 3/5*v**3.
3*(v - 1)**2*(v + 1)/5
What is i in 3/2*i + 1/2 + 1/2*i**3 + 3/2*i**2 = 0?
-1
Suppose 4*g = 6*g - 8. Let k(u) = u**2 - u + 5. Let c be k(0). Suppose 10*j**3 + 8*j**2 - j + c*j - 5*j**3 + j**g = 0. What is j?
-2, -1, 0
Let a(t) be the second derivative of 2/5*t**2 - 8*t + 1/5*t**4 - 2/5*t**3 - 1/25*t**5 + 0. Factor a(z).
-4*(z - 1)**3/5
Suppose -g + 5*x + 17 - 6 = 0, -4*g - x = -23. Factor 4*f - g - 3*f**2 - 13*f + 0*f**2.
-3*(f + 1)*(f + 2)
Let f be ((-5)/10 - -1)*(-3 - -4). Factor 0 + g - 3/2*g**3 + 1/2*g**5 - 1/2*g**2 + f*g**4.
g*(g - 1)**2*(g + 1)*(g + 2)/2
Let g(n) = 11*n**3 + 13*n**2 + 12*n. Let o(r) = -7*r**2 - 75*r**3 + 27*r**2 + 18*r + 91*r**3. Let j(d) = 7*g(d) - 5*o(d). Factor j(h).
-3*h*(h + 1)*(h + 2)
Let -2*r**3 - 13*r**2 + 7*r**2 + 10*r**2 - 2*r**4 = 0. What is r?
-2, 0, 1
Factor 0 + 0*p + 3/2*p**2 + 9/2*p**4 - 3/2*p**5 - 9/2*p**3.
-3*p**2*(p - 1)**3/2
Let f be (-3225)/1809 - 4/(-2). Let u = f - -1/201. Factor -2/9*q**5 + u*q**3 + 0*q + 2/9*q**4 - 2/9*q**2 + 0.
-2*q**2*(q - 1)**2*(q + 1)/9
Let r(j) be the first derivative of j**7/210 + j**6/75 + j**5/100 + 4*j + 1. Let p(o) be the first derivative of r(o). Factor p(s).
s**3*(s + 1)**2/5
Let d(s) be the second derivative of s**7/84 - s**6/10 + s**5/40 + s**4 + 4*s**3/3 + 65*s. Factor d(h).
h*(h - 4)**2*(h + 1)**2/2
Let z be (-3)/(-9)*-2*(-36)/16. Suppose z*m + 0 + 3/4*m**2 = 0. What is m?
-2, 0
Factor t**3 + t**3 + 3*t**4 + 6*t + 4*t**2 - 8*t**3 - 7*t**2.
3*t*(t - 2)*(t - 1)*(t + 1)
Let w(f) be the second derivative of f**6/75 + f**5/25 + f**4/30 + 11*f. Let w(r) = 0. What is r?
-1, 0
Let o(m) = -6*m**3 - 10*m**2 + 2*m + 6. Let q(l) = 11*l**3 + 19*l**2 - 4*l - 12. Let s(g) = -7*o(g) - 4*q(g). Let s(r) = 0. Calculate r.
-3, -1, 1
Suppose 0 = -g - 0 - 1. Let n be g/(-5) + 8/20. Factor -1/5 + n*i + 4/5*i**2.
(i + 1)*(4*i - 1)/5
Let s(l) be the third derivative of 0*l**4 + 0*l - 1/240*l**6 - 2*l**2 + 0*l**3 + 0 + 1/420*l**7 + 0*l**5. Find m, given that s(m) = 0.
0, 1
Let x(o) be the third derivative of -o**5/180 + o**4/72 + o**3/9 - 22*o**2. Solve x(w) = 0 for w.
-1, 2
Let b(n) be the second derivative of n**6/90 - n**5/15 + n**4/6 - 2*n**3/9 + n**2/6 - 4*n. Factor b(k).
(k - 1)**4/3
Determine c so that -1/5*c**3 + 3/5*c**2 - 2/5*c + 0 = 0.
0, 1, 2
Let c(s) = -4*s**5 - 4*s**4 + 5*s**3 + 23*s**2 - 61*s + 32. Let a(w) = -w**5 - 2*w**3 - w**2 + w. Let l(t) = -3*a(t) + c(t). Solve l(n) = 0.
-4, 1, 2
Let r(b) = b**2 + 12*b + 1. Let p be r(-12). Let c be p*((-12)/(-3) - 4). Factor -1/5*q**2 + 1/5*q**4 - 2/5*q + c + 2/5*q**3.
q*(q - 1)*(q + 1)*(q + 2)/5
Let n(j) be the third derivative of 0 + 4/75*j**5 + 1/30*j**3 + 3*j**2 - 1/15*j**4 + 0*j. Find w, given that n(w) = 0.
1/4
Let o = 72 - 66. Let m(t) be the first derivative of -1/2*t**4 - 1 - 4/5*t**5 - 1/3*t**o + 0*t**2 + 0*t + 0*t**3. Determine i, given that m(i) = 0.
-1, 0
Factor 0 + 2/3*l**3 + 2/9*l**4 + 0*l**2 - 8/9*l.
2*l*(l - 1)*(l + 2)**2/9
Let n be (6 - 8)/(2 + -6). Factor 0 - 1/2*p**2 + p - p**3 + n*p**4.
p*(p - 2)*(p - 1)*(p + 1)/2
Let j(s) be the third derivative of s**6/360 + s**5/60 + s**3/3 + 2*s**2. Let i(f) be the first derivative of j(f). Factor i(p).
p*(p + 2)
Let g(z) be the first derivative of -2 + 3*z**2 - 2/3*z**3 - 4*z. Determine m, given that g(m) = 0.
1, 2
Let n = -10 - -32/3. Let w be 0/(0 - (-2 + 3)). Let 2/3*v**3 + 0*v**2 - n*v + w = 0. What is v?
-1, 0, 1
Let o(t) be the third derivative of 22*t**6/45 + 47*t**5/45 + t**4/18 - 4*t**3/9 - 22*t**2. Determine n, given that o(n) = 0.
-1, -1/4, 2/11
Let t(g) be the second derivative of -g**8/48 + 2*g**7/35 + g**6/30 - 3*g**2 - 7*g. Let x(z) be the first derivative of t(z). Find m such that x(m) = 0.
-2/7, 0, 2
Suppose 3*v + 2 = -5*d, 2*v = d - 3*d. Let h(m) = -2*m + 4. Let p be h(v). Find j such that -1/4*j**5 + 1/4*j**2 - p*j - 1/4*j**4 + 5/4*j**3 + 1 = 0.
-2, 1
Let r(l) be the first derivative of l**5/70 + l**4/21 + l**3/21 + 3*l - 1. Let a(f) be the first derivative of r(f). Factor a(n).
2*n*(n + 1)**2/7
Let a(v) = -v**4 - v**3. Let z(p) = 27*p**4 + 3*p**3 - 12*p**2 + 12*p. Let k(s) = -18*a(s) - z(s). Let k(b) = 0. What is b?
-1, 0, 2/3, 2
Let t(s) be the third derivative of s**8/20160 - s**6/720 - s**5/60 + s**2. Let c(b) be the third derivative of t(b). Factor c(u).
(u - 1)*(u + 1)
Let i(u) be the third derivative of u**9/1008 - u**7/140 + u**5/40 - u**3/2 - 3*u**2. Let y(p) be the first derivative of i(p). Solve y(f) = 0.
-1, 0, 1
Let 0*m - 4/5*m**3 + 2/5*m**4 + 0 - 6/5*m**2 = 0. What is m?
-1, 0, 3
Let i be (3 - 3)*(24 + -23). Factor 0*u + i + 0*u**2 - 2/9*u**3 + 0*u**4 + 2/9*u**5.
2*u**3*(u - 1)*(u + 1)/9
Let u = 2 + -2. Suppose l + s - 1 = u, 0*l - 3*s + 9 = 5*l. Factor 6*g**2 + g - l + 7*g + 5.
2*(g + 1)*(3*g + 1)
Let a(p) be the second derivative of 1/3*p**3 + 1/6*p**4 - 2*p**2 - p + 0. Let a(g) = 0. What is g?
-2, 1
Let 21/4*y**3 + 9/4*y**4 + 3/8*y**5 + 27/8*y + 3/4 + 6*y**2 = 0. Calculate y.
-2, -1
Factor 64/9*a**3 + 32/9 + 32/3*a + 112/9*a**2 + 2*a**4 + 2/9*a**5.
2*(a + 1)*(a + 2)**4/9
Let r(v) = 12*v**2 + 8*v. Let s(o) = 12*o**2 + 9*o. Let x(m) = 6*r(m) - 5*s(m). Determine k so that x(k) = 0.
-1/4, 0
Let a(y) be the third derivative of y**6/2160 - y**5/180 + y**4/36 + 5*y**3/6 + 2*y**2. Let c(z) be the first derivative of a(z). Suppose c(d) = 0. Calculate d.
2
Let t be (-2)/9 - 76/(-18). Let q be (-6)/8*(1090/(-105) - -10). Factor -2/7*n**t - q + 4/7*n**2 + 0*n**3 + 0*n.
-2*(n - 1)**2*(n + 1)**2/7
Suppose 5*b = -3*n + 16, 5*n = 2*b - 7*b + 20. Let y be n/(-2) - 8/(-2). Solve 0*v**y + 4/5*v**2 + 2/5*v + 0 - 4/5*v**4 - 2/5*v**5 = 0 for v.
-1, 0, 1
Let j(t) be the first derivative of 2 - 1/12*t**4 + 1/3*t**3 + 1/60*t**6 - 1/2*t**2 + 0*t - 1/30*t**5. Let b(s) be the second derivative of j(s). Factor b(l).
2*(l - 1)**2*(l + 1)
Let t(y) = -y**2 + y + 1. Let x(k) = k**4 + k**3 + k**2 - k - 1. Let g(m) = 2*t(m) + 2*x(m). Factor g(p).
2*p**3*(p + 1)
Let x(a) = -2*a + 2. Let r be x(-1). Let m(w) be the first derivative of -1/6*w**r + 1/3*w**2 - 2 - 2/3*w + 2/9*w**3. Solve m(j) = 0 for j.
-1, 1
Let t(u) = -u**2 + 10*u + 8. Let z be t(11). Let s be z/(-9)*0 - -2. Factor -6/5*o**s - 6/5*o - 2/5*o**3 - 2/5.
-2*(o + 1)**3/5
Let d(n) be the second derivative of n**5/110 - n**4/22 + 2*n**3/33 + 38*n. Suppose d(k) = 0. What is k?
0, 1, 2
Suppose u + 18 = 2*u. Let l be (-4)/(0 + 1 - 3). Factor 6*r - 18*r + u + l*r**2 + 0*r.
2*(r - 3)**2
Determine z, given that 0 - 46/13*z**2 + 4/13*z = 0.
0, 2/23
Factor 0 - z**4 + 0*z - z**3 - 1/4*z**5 + 0*z**2.
-z**3*(z + 2)**2/4
Let m(q) be the third derivative of q**6/480 + q**5/240 - q**4/48 + 4*q**2. Suppose m(i) = 0. Calculate i.
-2, 0, 1
Determine k so that 20*k**4 + 0*k - 4*k**5 + 28*k**2 - 36*k**3 - 5*k - 3*k = 0.
0, 1, 2
Let x(t) be the second derivative of 1/6*t**2 + 1/6*t**3 - 2*t - 1/9*t**4 + 0. Let x(g) = 0. What is g?
-1/4, 1
Determine x, given that 6*x**2 + 5*x**4 - 13*x**2 - x**5 - 7*x**3 + 8*x + 6*x**2 - 4 = 0.
-1, 1, 2
Let n be 2/(-9) - 266/(-63). Let x be (10 - 10)/(n/(-2)). Factor r**2 - 7/2*r**4 + 5/2*r**3 + 0 + x*r.
-r**2*(r - 1)*(7*r + 2)/2
Let k(x) be the second derivative of -x + 0 + 1/3*x**2 - 1/60*x**5 + 1/18*x**3 - 1/18*x**4. Solve k(s) = 0.
-2, -1, 1
Let c(h) = h - 8. Let t be c(8). Let z = -9/14 - -73/70. Factor 2/5*s**5 + 0*s**2 + t*s + 0 + 4/5*s**4 + z*s**3.
2*s**3*(s + 1)**2/5
Let u(o) = -o**2 + 41*o - 328. Let j be u(30). Factor 8/7 - 16/7*n - 2/7*n**3 + 10/7*n**j.
-2*(n - 2)**2*(n - 1)/7
Factor -10*f**3 + 7*f**3 + 0*f**3.
-3*f**3
Let t = 32 - 29. Factor 0*w**t + 0 + 2/7*w**5 - 2/7*w + 4/7*w**2 - 4/7*w**4.
2*w*(w - 1)**3*(w + 1)/7
Factor 27/5*y**4 - 6/5*y - 12*y**3 + 39/5*y**2 + 0.
3*y*(y - 1)**2*(9*y - 2)/5
Factor 0*z + 2/13*z**5 - 4/