n).
n*(n + 1)**2
Factor 4/7 + 6/7*s**4 + 18/7*s + 22/7*s**3 + 30/7*s**2.
2*(s + 1)**3*(3*s + 2)/7
Let g be 12/40*(-6)/(-18). Let o(y) be the third derivative of 0*y**3 - g*y**5 + 1/6*y**4 + 0*y + 3*y**2 + 0. Let o(d) = 0. Calculate d.
0, 2/3
Suppose -2*i + 2 = -0. Let g be 0*(-3 + 2)*i. Solve -4/5*h**2 + g + 2/5*h + 2/5*h**3 = 0.
0, 1
Let a(d) be the second derivative of d**5/90 + d**4/6 + 8*d**3/9 + 16*d**2/9 + d. Let a(t) = 0. What is t?
-4, -1
Let d(u) be the third derivative of u**7/105 - u**5/10 - u**4/6 + 3*u**2 - 4. Factor d(a).
2*a*(a - 2)*(a + 1)**2
Suppose -3/5*t**2 + 3/5*t + 6/5 = 0. What is t?
-1, 2
Let x(b) = 3*b**2 - 7*b + 4. Let o(c) = -5*c**2 + 11*c - 6. Let n = -16 + 8. Let q(l) = n*x(l) - 5*o(l). Factor q(t).
(t - 1)*(t + 2)
Let a(n) be the first derivative of -2/15*n**3 - 1/30*n**6 + 1/25*n**5 + 1/5*n - 1/10*n**2 + 1/10*n**4 + 3. Factor a(r).
-(r - 1)**3*(r + 1)**2/5
Let q(l) be the second derivative of l**4/18 - l**3/9 - 8*l. Determine r, given that q(r) = 0.
0, 1
Suppose 4*s - 6 - 14 = 0. Solve -99*x**4 - 99*x**2 - 3 + 9*x**2 + 6*x**s + 27*x + 21*x**5 + 138*x**3 = 0 for x.
1/3, 1
Let u be -1 + 1 - (-2 - -1). Factor 4 - 2*j**2 + u - 3.
-2*(j - 1)*(j + 1)
Let i(d) be the second derivative of d**6/40 - 3*d**5/80 - d**4/16 + d**3/8 - 5*d. Find f such that i(f) = 0.
-1, 0, 1
Suppose -2*d = 1 - 5. Solve 7*f**2 + 9*f**d - 15*f + 6 - 7*f**2 = 0 for f.
2/3, 1
Let l(c) be the second derivative of -c**5/10 - c**4/3 - c**3/3 + 48*c. Factor l(x).
-2*x*(x + 1)**2
Let i be (4/(-6))/((-2)/15). Let f be (1 - 6)*(-10)/25. Solve 4*z**i + 6*z**3 - z**f + 3*z**2 - 10*z**4 - 4*z + 2*z = 0 for z.
-1/2, 0, 1
Let a(s) be the third derivative of -s**8/336 + s**7/105 - s**6/120 + 27*s**2. Factor a(r).
-r**3*(r - 1)**2
Let c(i) be the second derivative of i**4/28 - 4*i**3/7 + 24*i**2/7 + 2*i. Factor c(j).
3*(j - 4)**2/7
Solve 8*u**3 + 6*u**3 + 10*u**3 - 21*u**3 + 33*u**2 = 0.
-11, 0
Let -2/3*q**3 + 0*q + 0 - 10/3*q**2 = 0. What is q?
-5, 0
Let g = -3 - -5. Let b = 3 - g. Find t such that -b - t**4 - 5 + 2*t**2 + 5 = 0.
-1, 1
Let k(b) = 21*b**2 + 4 + 9*b - b + 19*b**3 + 2*b. Let z(m) = 39*m**3 + 42*m**2 + 21*m + 9. Let g(c) = -9*k(c) + 4*z(c). Factor g(n).
-3*n*(n + 1)*(5*n + 2)
Let n(r) be the second derivative of -1/2*r**3 + 0 + 0*r**2 + 2*r - 1/2*r**4 - 3/20*r**5. What is l in n(l) = 0?
-1, 0
Suppose 4*r = 11 + 1. Suppose 2/7*p - 2/7*p**r + 0 + 2/7*p**2 - 2/7*p**4 = 0. Calculate p.
-1, 0, 1
Let n be 2/(-45)*1254/56 + 1. Let u(z) be the third derivative of -n*z**5 - z**2 + 0*z**4 + 0 + 0*z + 0*z**3. Factor u(k).
-2*k**2/7
Let v = -37315/36 + 3183/4. Let n = 241 + v. Factor -4/9*i**2 + 2/9*i + 0 + n*i**3.
2*i*(i - 1)**2/9
Let m = 41/1044 - 1/87. Let h = 2/9 + m. Determine r so that 1/4*r - h*r**2 - 1/4*r**3 + 1/4 = 0.
-1, 1
Factor -21/4*y - 3/2*y**4 - 3/2*y**3 + 3/4*y**5 + 6*y**2 + 3/2.
3*(y - 1)**4*(y + 2)/4
Let d(g) be the first derivative of 2*g**5 - g**4 - 10*g**3/3 + 2*g**2 - 14. Determine l, given that d(l) = 0.
-1, 0, 2/5, 1
Let o(r) be the first derivative of -2*r**5/15 - r**4/3 + 2*r**3/3 + 4*r**2/3 - 8*r/3 - 19. Determine t so that o(t) = 0.
-2, 1
Let q(a) = 2*a - 3. Let x be q(7). Let r = x + -5. Factor 4*j + j - j**2 - r*j.
-j*(j + 1)
Let r(j) = j**2 + 1. Let i(z) = 8*z**2 + 8*z - 7. Let g(o) = -4*i(o) + 36*r(o). Solve g(k) = 0 for k.
4
Determine j, given that -1/8*j**2 + 7/8*j + 1 = 0.
-1, 8
Factor 0*s - 2 - 2 - 6*s + 0 - 2*s**2.
-2*(s + 1)*(s + 2)
Let d(p) = 7*p**2 + 9*p + 2. Let z(l) = 13*l**2 + 17*l + 4. Let s(k) = -11*d(k) + 6*z(k). Factor s(h).
(h + 1)*(h + 2)
Let a(g) be the second derivative of -g**4/3 + 5*g. Solve a(c) = 0.
0
Find i, given that 3*i**2 - 117*i + 33*i**4 - 28*i**2 + 111*i - 36*i**3 - 8*i**2 + 42*i**5 = 0.
-1, -1/2, -2/7, 0, 1
Let h(x) be the second derivative of 0 + 1/15*x**3 + 0*x**4 + 2*x + 0*x**2 - 1/50*x**5. Let h(j) = 0. Calculate j.
-1, 0, 1
Let b = -64 + 66. Factor 2/7*j + 0 + 1/7*j**b.
j*(j + 2)/7
Determine i so that -21*i - 9*i**2 + 21*i**2 + 3*i - 2*i**3 = 0.
0, 3
Let m(l) be the second derivative of -l**4/36 + 5*l**3/6 + l + 25. Solve m(f) = 0.
0, 15
Let s(v) be the third derivative of 1/110*v**5 + 0*v - 6*v**2 + 1/66*v**4 + 0 + 0*v**3. Find b such that s(b) = 0.
-2/3, 0
Let x(y) = y**2 - 5*y - 1. Let b = 3 + 2. Let k(c) = 5*c - c - 2*c. Let n(i) = b*k(i) + 2*x(i). Factor n(l).
2*(l - 1)*(l + 1)
Let z(i) be the second derivative of 0 + 1/12*i**4 + 1/8*i**2 - 3*i - 5/24*i**3. Factor z(g).
(g - 1)*(4*g - 1)/4
Let y(c) = -4*c**4 - 104*c**3 - 164*c**2 - 80*c - 16. Let n(f) = f**4 + 21*f**3 + 33*f**2 + 16*f + 3. Let u(d) = 16*n(d) + 3*y(d). Factor u(i).
4*i*(i + 1)**2*(i + 4)
Let o(h) be the second derivative of -3*h - 1/3*h**3 - h**2 + 1/6*h**4 + 0 + 1/10*h**5. Factor o(z).
2*(z - 1)*(z + 1)**2
Let x(s) be the third derivative of s**8/11200 + s**7/700 + 3*s**6/400 + 7*s**4/24 + 3*s**2. Let d(f) be the second derivative of x(f). Factor d(m).
3*m*(m + 3)**2/5
Let v(c) be the third derivative of -5*c**7/14 - 2*c**6/3 + 7*c**5/6 + 10*c**4/3 + 5*c**3/6 - 44*c**2. Determine p so that v(p) = 0.
-1, -1/15, 1
Let u(y) be the first derivative of 1/5*y**5 - 1/3*y**3 + 1/2*y**6 + 0*y + y**2 - 5/4*y**4 + 3. Factor u(v).
v*(v - 1)*(v + 1)**2*(3*v - 2)
Let q(c) be the first derivative of 3/5*c**5 + 0*c + 3/2*c**2 - 5 - c**3 - 3/4*c**4. Let q(g) = 0. Calculate g.
-1, 0, 1
Let t(g) be the third derivative of -g**6/45 + 7*g**5/30 - 29*g**4/36 + 2*g**3/3 + 31*g**2. Let t(d) = 0. What is d?
1/4, 2, 3
Let m(o) be the third derivative of o**8/3360 + o**7/315 + o**6/90 - o**5/12 - 7*o**2. Let f(z) be the third derivative of m(z). Factor f(s).
2*(s + 2)*(3*s + 2)
Suppose -4*r + 16 = 4. Factor -13*i**2 + 2*i**r + 11*i**2 - 1 + 6*i**3 - 5*i.
(i - 1)*(2*i + 1)*(4*i + 1)
Let n(o) be the second derivative of -o**4/6 + o**3 - 2*o**2 - 4*o. Factor n(s).
-2*(s - 2)*(s - 1)
Let f = -190 + 574/3. Factor -f*l + 0 + 4/3*l**3 + 0*l**2.
4*l*(l - 1)*(l + 1)/3
Suppose -3*r - 5*s - 5 = 0, -5*r + 7 = 4*s - 2. Suppose -2*p - r = -9. Factor 1/3*u**p + 0 + 1/3*u.
u*(u + 1)/3
Factor -73*s**2 + 77*s**2 - 36*s**3 - 64*s**5 + 20*s**4 + 76*s**4.
-4*s**2*(s - 1)*(4*s - 1)**2
Suppose 26 = 2*y - 110. Suppose 0*a = 4*a - y. Factor -147*x**4 - a*x**3 + 28*x**2 + 16*x**2 - 8*x + 3*x**3.
-x*(3*x + 2)*(7*x - 2)**2
Let l be 66/(-8) + (-5)/(-20). Let x be (16/30)/(l/(-20)). Factor 0 - 2*u**3 + 0*u + x*u**2.
-2*u**2*(3*u - 2)/3
Let d(n) = -n**3 + 9*n**2 + 9*n + 14. Let s be d(10). Let x(h) be the second derivative of -4/3*h**2 - h - 1/18*h**s - 4/9*h**3 + 0. Factor x(z).
-2*(z + 2)**2/3
Suppose 1/3*x**5 + 0 - 1/3*x + 0*x**3 - 2/3*x**4 + 2/3*x**2 = 0. What is x?
-1, 0, 1
Let z(t) = t**2 - t. Let h(d) = d**2 - 11*d - 8. Let u(k) = h(k) - 3*z(k). Find o such that u(o) = 0.
-2
Let p = -21/52 - -167/156. Factor -2*m - 2*m**2 - 2/3*m**3 - p.
-2*(m + 1)**3/3
Let o(r) be the second derivative of 2*r**6/15 - r**4/3 - 14*r. Solve o(p) = 0.
-1, 0, 1
Determine t, given that -9/2*t**2 + 81/2*t + 1/6*t**3 - 243/2 = 0.
9
Let p(i) be the third derivative of 5*i**2 - i**3 - 5/6*i**4 + 0 - 2/5*i**5 + 0*i - 1/10*i**6 - 1/105*i**7. Solve p(w) = 0.
-3, -1
Let u(y) = 7*y**3 + 7*y**2 - 4*y + 4. Let t(m) = 20*m**3 + 20*m**2 - 11*m + 11. Let x(a) = -4*t(a) + 11*u(a). Determine q so that x(q) = 0.
-1, 0
Suppose 2*u + 1 = u - 3*s, -4*s - 5 = 5*u. Let j = u + 3. Suppose 3*w**2 - 2*w**2 - j*w + 3*w = 0. What is w?
-1, 0
Find f, given that 5/7*f**3 - 2/7 - f**4 - 5/7*f + 9/7*f**2 = 0.
-1, -2/7, 1
Let x = -778 + 15563/20. Let m(a) be the first derivative of 0*a**2 - x*a**4 + 0*a**3 - 3 + 3/25*a**5 + 0*a. Factor m(z).
3*z**3*(z - 1)/5
Let -10/9*o + 4/9 + 2/9*o**3 - 2/9*o**4 + 2/3*o**2 = 0. Calculate o.
-2, 1
Let d(y) = -3*y. Let k be d(-1). Factor k*p**2 + 2 - 2.
3*p**2
Suppose 0 = 5*t - u - 7, -4*u = 2*t - 2*u - 10. Let s(h) be the third derivative of 0*h + 1/48*h**4 + 0 + 1/240*h**5 - 2*h**t + 0*h**3. Factor s(g).
g*(g + 2)/4
Factor -28*w**5 - 2*w**3 + 17*w**5 + 13*w**5.
2*w**3*(w - 1)*(w + 1)
Let x(z) be the second derivative of -z**6/180 + z**4/24 + z**3/18 - 3*z - 7. What is p in x(p) = 0?
-1, 0, 2
Let p(m) be the first derivative of -m**4/2 - 10*m**3/3 - 7*m**2 - 6*m - 8. Factor p(w).
-2*(w + 1)**2*(w + 3)
Let u(t) = -t + 1. Let o(y) = -3*y**2 - 4*y + 5*y**2 + 2*y**2. Let c(a) = o(a) - 4*