*(n + 1)**2
Let g(o) be the first derivative of -o**7/1470 + o**6/1260 + o**5/420 + o**3 + 3. Let x(u) be the third derivative of g(u). Factor x(n).
-2*n*(n - 1)*(2*n + 1)/7
Let v(a) = 7*a**2 + 2*a - 9. Let n(p) = -p + 1. Let j = -5 + 18. Suppose -4*o + 5*i + 65 + j = 0, -16 = -o + 3*i. Let c(q) = o*n(q) + 2*v(q). Factor c(w).
2*(w - 1)*(7*w - 2)
Let c(j) be the second derivative of 3/5*j**6 + 0 + j**2 + 7/3*j**4 + 8/5*j**5 - 4*j + 2*j**3 + 2/21*j**7. Factor c(t).
2*(t + 1)**4*(2*t + 1)
Factor 8/3*p**5 + 2/3*p - 26/3*p**4 + 0 - 14/3*p**2 + 10*p**3.
2*p*(p - 1)**3*(4*p - 1)/3
Let x(i) = -i + 0*i + 2*i + 15. Let c be x(-13). Solve r + 2/5 + 3/5*r**c = 0 for r.
-1, -2/3
Let s(w) be the third derivative of w**8/336 - w**7/210 - w**6/24 - w**5/20 + 2*w**2 - 15*w. Determine c so that s(c) = 0.
-1, 0, 3
Suppose 5*c - 55 = -3*q, 0*q + 2*q = 4*c + 44. Solve -q*d**2 + 9*d**4 - 16*d**2 - 8 - 13*d**4 - 20*d**3 - 28*d = 0.
-2, -1
Factor -4/3 - 2*d - 2/3*d**2.
-2*(d + 1)*(d + 2)/3
Suppose -4*n + 5*p = -n + 19, 5*n = 3*p - 5. Let z(o) be the second derivative of -1/48*o**4 + 0 - n*o + 1/24*o**3 + 0*o**2. Find y, given that z(y) = 0.
0, 1
Let u be (-526)/12*6/(-20). Let w = u + -62/5. Factor 1/4 + w*l + 1/4*l**3 + 3/4*l**2.
(l + 1)**3/4
Let y(j) be the second derivative of -3*j**5/4 - 7*j**4/4 + 4*j**3 + 6*j**2 - 7*j. Determine o, given that y(o) = 0.
-2, -2/5, 1
Let n(t) = t**3 - t**2 + 6. Let d be n(0). Let o be (1 + -1)*(-3)/d. Factor o*s - 2/9*s**2 + 0 - 2/9*s**3.
-2*s**2*(s + 1)/9
Let n(b) = -11*b**3 - 12*b**2 + 13*b. Let l(w) = 5*w**3 + 6*w**2 - 7*w. Let f(m) = 5*l(m) + 2*n(m). Solve f(j) = 0.
-3, 0, 1
Determine z so that -9/2*z - 3/4*z**2 - 15/4 = 0.
-5, -1
Let f be 4/(4/3) - (1 + -3). Let p(t) be the first derivative of 0*t**4 - 3 + 0*t**2 + 0*t - 3/20*t**f + 1/3*t**3 + 1/24*t**6. Let p(l) = 0. What is l?
-1, 0, 2
Let i(q) be the second derivative of q**7/28 - 7*q**6/20 + 9*q**5/8 - 13*q**4/8 + q**3 + 43*q. Factor i(f).
3*f*(f - 4)*(f - 1)**3/2
Let f(i) = -i**2 - 11*i - 14. Let a be f(-9). Let t(c) be the second derivative of 0 - 1/4*c**2 - c + 0*c**3 + 1/24*c**a. Solve t(m) = 0 for m.
-1, 1
Factor -11*q**3 - q**4 + 7*q**3 + 5*q**4.
4*q**3*(q - 1)
Factor 5 + 5/3*p**2 - 20/3*p.
5*(p - 3)*(p - 1)/3
Factor h**2 - 2*h - 8/3 + 1/3*h**3.
(h - 2)*(h + 1)*(h + 4)/3
Determine r, given that -3*r + 3/2*r**2 - 1/4*r**3 + 2 = 0.
2
Let -13/4*t**2 - 1/2*t + 0 = 0. What is t?
-2/13, 0
Let b be (-72)/32*(-4)/18. Suppose 1 - b*k**2 + 1/2*k = 0. Calculate k.
-1, 2
Factor 3*i**3 - 9*i**2 - i**3 + 7*i**2 + 2*i**4 - 2*i.
2*i*(i - 1)*(i + 1)**2
Suppose 3*j - 35 = -2*j. Suppose j*c = 3*c. Factor -2/9*b**2 - 4/9*b + c + 2/9*b**3.
2*b*(b - 2)*(b + 1)/9
Let n(g) = -13*g**3 - 2*g - 1. Let y be n(-1). Let m = y - 11. Factor -14/5*b**m - 6/5*b**2 - 6/5*b**4 + 4/5 + 6/5*b.
-2*(b + 1)**3*(3*b - 2)/5
Let o = -4 - -7. Find r such that -2*r**2 - 2*r + 1 + o*r**2 + 0*r**2 = 0.
1
Let f = -2/3 - -8/9. Determine g so that 4/9 + 2/3*g + f*g**2 = 0.
-2, -1
Factor -4/9*l + 2/9*l**3 + 0 + 2/9*l**2.
2*l*(l - 1)*(l + 2)/9
Let b = -453/2 + 691/3. Let d = b + -5/2. Suppose 8/3*p**2 + 0 - 2/3*p + d*p**4 - 10/3*p**3 = 0. Calculate p.
0, 1/2, 1
Let h(k) be the first derivative of 0*k**2 + 0*k - 1/6*k**6 - 6 - 1/3*k**3 - 3/4*k**4 - 3/5*k**5. Factor h(c).
-c**2*(c + 1)**3
Let j(p) be the third derivative of 5*p**2 + 0*p + 2*p**3 + 9/20*p**5 - 27/140*p**7 + 27/80*p**6 + 0 - 7/4*p**4. Suppose j(w) = 0. What is w?
-1, 2/3
Determine b, given that -49/4 - 1/4*b**2 - 7/2*b = 0.
-7
Let j(n) be the third derivative of 1/300*n**6 + 1/60*n**4 + n**2 + 1/75*n**5 + 0*n + 0 + 0*n**3. What is w in j(w) = 0?
-1, 0
Let s(a) be the first derivative of 2*a + 1/54*a**4 + 2 - 2/27*a**3 + 0*a**2. Let c(m) be the first derivative of s(m). Factor c(l).
2*l*(l - 2)/9
Let p(t) be the third derivative of -t**7/70 + 3*t**6/40 - 3*t**5/20 + t**4/8 - 4*t**2. Suppose p(x) = 0. What is x?
0, 1
Suppose 0 = -4*t + 2*t + 120. Let g be 88/t + (-6)/9. Factor 0 + 0*k**3 + 2/5*k**2 + 0*k - g*k**5 - 6/5*k**4.
-2*k**2*(k + 1)**2*(2*k - 1)/5
Factor -2/3*o**2 + 4/3 + 2/3*o.
-2*(o - 2)*(o + 1)/3
Let h(n) be the first derivative of 2*n**5/55 - 5*n**4/22 + 16*n**3/33 - 4*n**2/11 - 2. Factor h(b).
2*b*(b - 2)**2*(b - 1)/11
Let p = -5 + 5. Let m(k) be the second derivative of 1/4*k**3 + 2*k + 1/2*k**2 + p + 1/24*k**4. Factor m(i).
(i + 1)*(i + 2)/2
Factor 1/5 - 2/5*l**2 + 1/5*l.
-(l - 1)*(2*l + 1)/5
Let f(d) be the third derivative of d**6/36 + d**5/45 - 5*d**4/36 - 2*d**3/9 + 4*d**2. Factor f(n).
2*(n - 1)*(n + 1)*(5*n + 2)/3
Let c(g) be the third derivative of g**9/362880 + g**8/24192 + g**7/4320 + g**6/1440 - g**5/12 + 3*g**2. Let p(f) be the third derivative of c(f). Factor p(m).
(m + 1)**2*(m + 3)/6
Suppose -2*f + 0 + 4 = 0. Let d(i) = i**3 - i**2 - i + 1. Let q be d(f). Determine w, given that -22*w**2 + 5*w**3 + w**2 + 21*w**4 + 7*w**3 - 6*w**q - 6*w = 0.
-1, -2/7, 0, 1
Let c(h) = h**3 + h**2 - h + 1. Let u(p) = 3*p**3 - p**2 - 11*p + 3. Let k(j) = -5*c(j) + u(j). Suppose k(o) = 0. What is o?
-1
Let y(b) be the third derivative of -b**9/9072 + b**7/840 + b**6/540 - b**3/2 + b**2. Let p(f) be the first derivative of y(f). Factor p(j).
-j**2*(j - 2)*(j + 1)**2/3
Let n(g) = 55*g**2 - 55*g + 23. Let j(h) = 2*h + 1. Let o be j(-3). Let w(u) = -82*u**2 + 83*u - 34. Let z(r) = o*w(r) - 7*n(r). Let z(d) = 0. Calculate d.
3/5
Let a = -46 - -79/2. Let w = a - -9. Find b such that 8*b - w*b**2 - 2 - 25/2*b**3 = 0.
-1, 2/5
Factor 5 + 15*t - 2 + 12*t**2 - 7*t**3 + 10*t**3 + 3.
3*(t + 1)**2*(t + 2)
Let j be 166/(-30) + 6 + 1/5. Let 0 + 2/3*g - j*g**2 = 0. Calculate g.
0, 1
Let j(d) be the first derivative of -d**8/672 + d**7/210 + d**6/240 - d**5/60 + d**2/2 - 1. Let h(w) be the second derivative of j(w). Solve h(o) = 0 for o.
-1, 0, 1, 2
Suppose t = -u + 3*u + 28, -2*t - 5*u + 20 = 0. Let s be (-22)/(-24) - 5/t. Factor -1/3*l + 1/3*l**2 - s.
(l - 2)*(l + 1)/3
Let f be 6 - 96 - 0/2. Let w be ((-12)/(-5))/((-84)/f). Factor 4/7 + 2*z**2 - w*z.
2*(z - 1)*(7*z - 2)/7
Let v be (-2)/8 - (-43)/(-4). Let f(u) = 6*u**2 - 17*u. Let y(q) = 3*q**2 - 9*q. Let c(l) = v*y(l) + 6*f(l). Suppose c(h) = 0. What is h?
0, 1
Let v(l) be the second derivative of 0 + 1/15*l**3 - 2*l + 0*l**2 - 1/50*l**5 + 0*l**4. Factor v(d).
-2*d*(d - 1)*(d + 1)/5
Let i(b) = -5*b - 13. Let p be i(4). Let q be 16/396 + (-6)/p. Find l, given that -2/9*l**3 + 0 + 2/9*l + 2/9*l**2 - q*l**4 = 0.
-1, 0, 1
Factor 16 - 6*z**2 - 39*z + 39*z**2 - 10.
3*(z - 1)*(11*z - 2)
What is f in -f**2 + 1 - 8*f**2 + 8*f**2 - f + f**3 = 0?
-1, 1
Factor 5/2*h - 15*h**3 + 0 + 5/2*h**2.
-5*h*(2*h - 1)*(3*h + 1)/2
Let a(g) be the first derivative of g**7/40 + g**6/60 - 7*g**5/40 - g**4/4 - g**3/3 + 4. Let l(x) be the third derivative of a(x). Factor l(n).
3*(n - 1)*(n + 1)*(7*n + 2)
Let f(d) be the first derivative of 1/2*d**4 + 2/5*d**5 - 8 + 0*d - 1/3*d**6 + 0*d**2 - 2/3*d**3. Factor f(t).
-2*t**2*(t - 1)**2*(t + 1)
Let w(o) be the second derivative of -1/42*o**4 + 1/7*o**2 + 0 + 1/21*o**3 - 1/70*o**5 - 3*o. Factor w(j).
-2*(j - 1)*(j + 1)**2/7
Let o be (-6 + 1)*(-4)/10. Let g = 392/3 + -130. Factor -1/3*l - 1/3*l**o + g.
-(l - 1)*(l + 2)/3
Let q(d) be the second derivative of -d**7/1260 - d**6/270 - d**5/180 + d**3/6 - 4*d. Let h(i) be the second derivative of q(i). Solve h(j) = 0.
-1, 0
Factor 6/5*a + 8/5 - 2/5*a**2.
-2*(a - 4)*(a + 1)/5
Let v = -71 - -31. Let q be v/(-42) - (-2)/(-3). Factor 0 + q*n**3 - 2/7*n**2 + 2/7*n**4 - 2/7*n.
2*n*(n - 1)*(n + 1)**2/7
Let z = 12 + -8. Factor -2*c**5 - 4*c**2 + 4*c**2 + 6*c**3 - z*c**2.
-2*c**2*(c - 1)**2*(c + 2)
Let y(p) be the first derivative of p**6/45 + 2*p**5/15 + 3*p**4/10 + 14*p**3/45 + 2*p**2/15 + 11. Factor y(l).
2*l*(l + 1)**3*(l + 2)/15
Let l(f) be the third derivative of -2*f**7/105 - f**6/10 - f**5/15 + f**4/2 + 4*f**3/3 + 17*f**2. Let l(k) = 0. Calculate k.
-2, -1, 1
Let t(g) = g - 5. Let o be t(6). Determine x, given that 2*x**2 - 4*x**3 - 4*x + o + x**4 - 3*x**4 + 8*x - x**4 = 0.
-1, -1/3, 1
Suppose 2*c**2 - 6*c**2 + 2*c**3 + 6*c - 4*c = 0. What is c?
0, 1
Determine p, given that -359 - 286*p**2 + 190*p**3 + 16 - 23*p**4 + 833*p - 372*p**2 + p**5 = 0.
1, 7
Factor -8/11 - 10/11*a**2 + 16/11*a + 2/11*a**3.
2*(a - 2)**2*(a - 1)/11
Let s(i) = i**3 + i. Let r(a