 g**4/16 + 20*g**2. Factor j(v).
v*(v - 3)*(v + 1)*(5*v + 2)/4
Let o(i) be the first derivative of -2*i**6/21 - 18*i**5/35 - i**4 - 6*i**3/7 - 2*i**2/7 - 1. Let o(d) = 0. What is d?
-2, -1, -1/2, 0
Let v(y) be the first derivative of y**3/18 + y**2/3 + y/2 - 9. Find a such that v(a) = 0.
-3, -1
Let i = 48 - 50. Let l = 0 - i. Factor 2/7*g**l + 2/7*g - 4/7.
2*(g - 1)*(g + 2)/7
Let y(o) = -o - 1. Let l be y(-3). What is k in 4*k**4 + 5*k**2 - k**2 - 10*k**3 - l*k**5 + 4*k**4 = 0?
0, 1, 2
Factor 2/3*b**2 - 32/3 + 0*b.
2*(b - 4)*(b + 4)/3
Let v = 37 + 6. Factor 41*h**2 - 4*h - v*h**2 - 2 + 0.
-2*(h + 1)**2
Let d = 123 + -614/5. Determine w, given that d*w**2 + 2/5*w + 0 = 0.
-2, 0
Suppose -12 = -4*r, 2*h - r = 7*h - 28. Suppose -h*v + v = 0. Factor 1/4*i + v + 1/4*i**4 - 1/4*i**3 - 1/4*i**2.
i*(i - 1)**2*(i + 1)/4
Let f(b) = 3*b - 27. Let m be f(15). Let t be m/105 + 8/20. Factor -2/7*i**2 - t + 6/7*i.
-2*(i - 2)*(i - 1)/7
Suppose -q = 4*f - 16, -2*f - 2*q = -3 - 5. Factor 2*l**5 + 3 + 6*l**f - 4*l**2 - 5 + 0 + 0*l**3 + 4*l**3 - 6*l.
2*(l - 1)*(l + 1)**4
Let k = -130 + 132. Solve 2/5*w**3 + 2/5*w**k - 2/5 - 2/5*w = 0.
-1, 1
Let v = 1/8 - -3/8. Let 0 - v*d**4 + 0*d**3 + 0*d**2 + 0*d = 0. What is d?
0
Let b(z) be the third derivative of -z**7/70 + z**6/120 + 3*z**5/5 + 3*z**4/2 - 8*z**3/3 - 12*z**2. What is d in b(d) = 0?
-2, 1/3, 4
Let s = 2 - 0. Suppose l**2 - l**s + 0*l - l + l**3 = 0. What is l?
-1, 0, 1
Let c be (-1 + -1)/(-13 + 7). Let i(u) be the third derivative of 0*u + 1/30*u**5 + 0 - c*u**4 + 4/3*u**3 + u**2. Factor i(t).
2*(t - 2)**2
Let g be (5 - 4)*(-2 + 2). Let k(l) be the first derivative of 1 + 1/2*l**4 + 1/3*l**2 + 2/3*l**3 + 2/15*l**5 + g*l. Factor k(j).
2*j*(j + 1)**3/3
Suppose 4*k + 2*m = -10, -2*k + 2*m - 6*m - 20 = 0. Suppose 2*x - 3*d = -2*d + 9, -4*d - 10 = 5*x. Factor -1/3*i - 4/3*i**4 - 2*i**x + k - 3*i**3.
-i*(i + 1)**2*(4*i + 1)/3
Let d be -10*(4/(-10) + 0). Find f, given that -4 - 3*f**d + f**2 - f**3 + 3*f**3 + 4 = 0.
-1/3, 0, 1
Factor 36/5*q**2 + 1/5 + 12/5*q.
(6*q + 1)**2/5
Let t be 1/(7/(28/8)). Let i(j) be the first derivative of -1/2*j**2 + 1/6*j**3 + t*j - 1. Find a such that i(a) = 0.
1
Let o(t) = -t**4 - t**3 + t**2. Let k(n) = 6*n**4 - 3*n**3 - 24*n**2 - 6*n. Suppose i - 27 = 4*i. Let b(q) = i*o(q) - k(q). Factor b(g).
3*g*(g + 1)**2*(g + 2)
Let d(p) = p**3 + 8*p**2 + 8*p + 5. Let l be d(-7). Let v = 0 - l. Factor 0 + 2*n + 0 - 2*n**3 - v + 2*n**2.
-2*(n - 1)**2*(n + 1)
Let i(u) = -17*u**4 - 17*u**3 + 17*u**2 - u. Let d(m) = 4*m**4 + 4*m**3 - 4*m**2. Let t(f) = -9*d(f) - 2*i(f). Factor t(z).
-2*z*(z - 1)*(z + 1)**2
Let l(j) = j**4 - j**2 + j. Let f(m) = m**3 - 5*m**2 - 5*m + 5*m**4 + 8*m + 0*m. Let u(v) = -f(v) + 4*l(v). Factor u(p).
-p*(p - 1)*(p + 1)**2
Determine h so that 63/2*h**4 - 24*h + 21/2*h**3 + 27/2*h**5 - 6 - 51/2*h**2 = 0.
-1, -2/3, 1
Let a be (-4)/14 - 448/(-1225). Let m(r) be the first derivative of -a*r**5 + 2 + 0*r - 1/10*r**4 + 0*r**2 + 0*r**3. Determine t, given that m(t) = 0.
-1, 0
Let s(g) = -4*g**2 - g**2 - 9*g**3 - 2*g**3 + 2 + 11*g. Let d(b) = 56*b**3 + 26*b**2 - 56*b - 10. Let h = -2 + 18. Let u(p) = h*s(p) + 3*d(p). Factor u(i).
-2*(i - 1)*(i + 1)*(4*i + 1)
Let o(k) be the third derivative of 0*k**3 + 0*k + 1/36*k**5 - 1/36*k**4 - 3*k**2 - 1/180*k**6 + 0. Solve o(b) = 0 for b.
0, 1/2, 2
Let j(m) = -2*m**2 - 68*m - 64. Let g be j(-33). What is w in -2/9*w**g + 0 - 2/9*w = 0?
-1, 0
Let d(s) be the first derivative of s**4/2 + 4*s**3/3 + s**2 - 10. Find c, given that d(c) = 0.
-1, 0
What is h in h**2 - 1/2*h + 1/2*h**5 - h**4 + 0*h**3 + 0 = 0?
-1, 0, 1
Let o(y) = -21*y + 1. Let w be o(1). Let a be (-5)/14*w/25. What is k in a*k**2 - 6/7*k**3 + 4/7*k**4 + 0 + 0*k = 0?
0, 1/2, 1
Suppose -3*o - 138 = -3*a, 0 = a - 3*a - 4*o + 68. Let h be ((-2)/(-6))/(a/36). Find z such that 4/7*z**4 - 2/7*z + h*z**3 - 4/7*z**2 + 0 = 0.
-1, -1/2, 0, 1
Factor -16*p + 12*p**2 + 9*p**3 + 8*p**3 - 19*p**3.
-2*p*(p - 4)*(p - 2)
Let k(f) be the third derivative of -f**8/112 - 3*f**7/70 - f**6/20 + 8*f**2. Factor k(z).
-3*z**3*(z + 1)*(z + 2)
Let x(q) be the second derivative of -q**7/840 + q**6/240 + q**4/12 - 2*q. Let f(m) be the third derivative of x(m). Factor f(c).
-3*c*(c - 1)
Let w be (-8)/(-6) + (-1)/3. Factor l + 0*l + w - l**2 - l**3 + 0*l.
-(l - 1)*(l + 1)**2
Suppose 0 = u - 4*o - 37, 2*o = u + 24 - 69. Find v such that -14*v**3 + 27*v**4 + 158*v**3 + 192*v + u - 5 + 264*v**2 = 0.
-2, -2/3
Suppose 2*g - 10 = 2*n - 0*n, g = 2*n + 9. Let p(j) = j**2 + 4*j + 4. Let k be p(n). Determine o so that 2/5*o**2 + 0*o - 4/5*o**3 + 0 + 2/5*o**k = 0.
0, 1
Let b(k) be the first derivative of k**4/2 - 10*k**3/9 + 2*k**2/3 + 6. Find h, given that b(h) = 0.
0, 2/3, 1
Let h be (-2)/(-12)*12/10. Let s(u) be the second derivative of u + 1/5*u**4 + h*u**2 - 4/15*u**3 - 2/25*u**5 + 1/75*u**6 + 0. Determine k so that s(k) = 0.
1
Let x(s) be the third derivative of -s**5/90 + s**4/18 - s**3/9 - 8*s**2. Factor x(o).
-2*(o - 1)**2/3
Let o(v) be the first derivative of -3*v**4/4 + 3*v**3 - 9*v**2/2 + 3*v + 19. Factor o(g).
-3*(g - 1)**3
Let x = -83/10 - -25/3. Let k(v) be the third derivative of -1/3*v**4 + 0 - 4/3*v**3 - x*v**5 + 4*v**2 + 0*v. Suppose k(f) = 0. Calculate f.
-2
Let j(n) be the third derivative of n**8/336 + n**7/105 + n**6/120 - 7*n**2. Find p, given that j(p) = 0.
-1, 0
Let o(s) be the first derivative of -5 + 0*s**2 + 9/8*s**4 + 4/3*s**6 + 1/6*s**3 + 0*s + 12/5*s**5. Factor o(n).
n**2*(n + 1)*(4*n + 1)**2/2
Solve -16 - 16*t - 4*t**4 - 60*t**2 + 0 + 8*t**3 + 72*t**2 = 0 for t.
-1, 2
Let a(d) be the third derivative of d**7/420 - d**5/20 + d**4/6 - d**3/4 - 8*d**2. Suppose a(t) = 0. Calculate t.
-3, 1
Let h(c) = 2*c. Let n be h(-2). Let t be (-2)/8 + (-1)/n. Factor m**3 - 2*m**4 - 3*m**3 + 2*m**2 + t*m**4 + 2*m.
-2*m*(m - 1)*(m + 1)**2
Let s = 1/46 + 17/276. Let i(u) be the first derivative of 0*u - 1/9*u**3 + s*u**4 + 1 + 0*u**2. Determine g so that i(g) = 0.
0, 1
Let r(p) = -p**3 - 3*p**2 - 4*p - 2. Let w be r(-2). Determine c, given that 7*c**3 - 25*c**3 + 14*c**2 + w*c - 4*c - 2*c**2 = 0.
0, 1/3
Let k(c) be the third derivative of -7/90*c**5 + 0*c + 2/45*c**6 + 0 - 3*c**2 + 0*c**3 - 1/105*c**7 + 1/18*c**4. Factor k(o).
-2*o*(o - 1)**2*(3*o - 2)/3
Suppose -2*g + 9 - 1 = 0. Suppose 2 - 12*s**4 - 4*s**2 - 2 - g*s**2 + 28*s**3 = 0. What is s?
0, 1/3, 2
Let r be (11/22)/(2/8). Let a(c) be the second derivative of 1/24*c**4 - 1/24*c**3 - 1/80*c**5 + 0*c**r + c + 0. Solve a(b) = 0 for b.
0, 1
Let d = 12 + -18. Let q be (-2)/((d - 0) + 0). Solve -1/3*j**2 + q + 0*j = 0 for j.
-1, 1
Factor 0 + 0*w**3 + 0*w + 2/9*w**5 + 0*w**2 + 2/3*w**4.
2*w**4*(w + 3)/9
Let 7 + 27/2*p + 6*p**2 - 1/2*p**3 = 0. Calculate p.
-1, 14
Let z be 10/3 - 1/3. Determine y so that -z*y**2 - y - 2*y**4 + 1 - 3*y**3 - 1 + y**4 = 0.
-1, 0
Solve -9/7*c**3 - 3/7*c**5 + 0 + 3/7*c**2 + 0*c + 9/7*c**4 = 0.
0, 1
Let y be ((-1)/(-2)*-2)/9. Let a = y - -11/18. What is q in -2*q - a*q**2 - 2 = 0?
-2
Let z(x) be the first derivative of -6 + 0*x**2 + 0*x + 1/6*x**3 + 1/8*x**4. Factor z(s).
s**2*(s + 1)/2
Let g be (4/(-6))/((-10)/(-30)). Let u(y) = -4*y**2 + 6. Let t(d) = -d**3 - 8*d**2 + d + 13. Let s(b) = g*t(b) + 5*u(b). Factor s(v).
2*(v - 2)*(v - 1)*(v + 1)
Let o = 278 + -824/3. Factor 4/3*c**3 + 0 + 0*c**2 - o*c**4 + 0*c.
-2*c**3*(5*c - 2)/3
Let g be (2 + -3)*-1 - 1. Factor -5*w + 2*w**3 + w**4 + w + g*w**3 + 2*w - 1.
(w - 1)*(w + 1)**3
Let x(q) be the second derivative of -2*q**7/49 + 17*q**6/105 + q**5/10 - 13*q**4/42 + q**3/7 + q + 7. Let x(r) = 0. What is r?
-1, 0, 1/3, 1/2, 3
Suppose g = -g + 10. Factor g*k**2 + 1 - 2*k + k - 7*k**2.
-(k + 1)*(2*k - 1)
Let p(k) be the first derivative of 8/3*k**2 + 0*k**4 - 2 + 2/15*k**5 - 2*k - 4/3*k**3. Determine o, given that p(o) = 0.
-3, 1
Let k(c) = 10*c**2 + 56*c - 35. Let s(g) = -5*g**2 - 28*g + 18. Let i(d) = 6*k(d) + 11*s(d). Let i(f) = 0. What is f?
-6, 2/5
Suppose -3 = -2*q - q. Let x be q + (3 - (-1)/(-1)). Factor -2*m**3 - m**x + m**3 - 2*m**5 - 4*m**4.
-2*m**3*(m + 1)**2
Suppose 3*u = -5*m - 3, -2*u + 2*m + 14 = -0. Factor 2/7*j**2 + 0*j + 0 + 2/7*j**u + 4/7*j**3.
2*j**2*(j + 1)**2/7
Let a(s) be the first derivative of 0*s**2 - 3/2*s**4 + 0*s - 3 - 2/3*s**3. Factor a(f).
-2*f**2*(3*f + 1)
Let p(h