k + 1/4*n + 1/4*n**3 + 1/2*n**2.
n*(n + 1)**2/4
Let f = 9 + -7. Factor 4*y**f + y + 2*y + y.
4*y*(y + 1)
Suppose -2*o + 0*o = 6*o. Let u(b) be the third derivative of 0*b**3 + o - b**2 + 0*b**4 - 1/240*b**6 - 1/120*b**5 + 0*b. Let u(p) = 0. What is p?
-1, 0
Let v(q) = -20 + 14 + 13*q + 23*q - 15*q**2. Let p(l) = 1. Let i(h) = -6*p(h) + v(h). Determine z, given that i(z) = 0.
2/5, 2
Let s(i) = i + 3. Let l be s(0). Suppose 5*j - x - 22 = 57, 0 = j - l*x - 13. Factor j*p**2 + 9*p**4 + 0*p**4 + 9*p**3 + 4*p + 12*p**3.
p*(p + 1)*(3*p + 2)**2
Suppose -3*g - 246 = 2*g - 3*r, g = -5*r - 38. Let j be -4 - -2 - g/21. Factor 0 - j*n**2 + 0*n + 2/7*n**3.
2*n**2*(n - 1)/7
Let c(a) be the second derivative of -a**6/120 - a**5/40 + a**4/12 + a**3/3 + 3*a. Solve c(x) = 0.
-2, 0, 2
Let n(o) be the second derivative of o**5/12 - 5*o**4/36 + 8*o. Determine z so that n(z) = 0.
0, 1
Let u = 187/2 + -93. Let f(d) be the second derivative of 2/3*d**3 + 5/3*d**4 + u*d**6 + 0*d**2 + 0 + 31/20*d**5 - d. Factor f(n).
n*(n + 1)*(3*n + 2)*(5*n + 2)
Suppose -18*i + 8*i**2 - 5*i**2 - 12 - 9 = 0. What is i?
-1, 7
Suppose 5*f = -5*s, 0 = 3*s + 3*f - 2*f - 6. Find n, given that 14*n - n**s - 14*n - 2*n**4 - n**5 = 0.
-1, 0
Let f be 2/(2 + 4 + 0). Let z(o) be the second derivative of 0 + 1/3*o**4 - 1/15*o**6 - 1/21*o**7 + 1/5*o**5 - f*o**3 - 3*o - o**2. Solve z(l) = 0.
-1, 1
Let q be (-459)/170*5/(-3). Factor 0 + 15/2*l**3 - q*l**4 + 3*l**2 + 0*l.
-3*l**2*(l - 2)*(3*l + 1)/2
Let j(i) be the second derivative of i**8/6720 + i**7/1680 + i**6/1440 + i**3/6 + i. Let t(o) be the second derivative of j(o). Factor t(f).
f**2*(f + 1)**2/4
Let d(k) be the first derivative of k**3 + 3*k**2 + 3*k - 16. Factor d(l).
3*(l + 1)**2
Suppose a = 2*v, -7*a + 2*a = 2*v - 24. Let c = -2 - -2. Determine i, given that i - 1/2*i**v + c = 0.
0, 2
Let j be ((-72)/(-108))/((-4)/(-18)). Factor 0*f**2 - 2/3*f**j + 2/3*f - 1/3*f**4 + 1/3.
-(f - 1)*(f + 1)**3/3
Let m(k) be the third derivative of -k**6/30 - k**5/3 - 4*k**4/3 - 8*k**3/3 - k**2 - 3. Factor m(d).
-4*(d + 1)*(d + 2)**2
Let n = 2 + 1. Factor t + 0*t + t - 4*t**n + 2*t**3 + t**4 - 1.
(t - 1)**3*(t + 1)
Let y be 14/48 - (-3)/(-12). Let m(a) be the second derivative of 0 + y*a**6 + 0*a**2 + 0*a**3 - 2*a + 7/80*a**5 + 1/24*a**4. Factor m(q).
q**2*(q + 1)*(5*q + 2)/4
Let v be (-22)/(-2) + (3 - 6). Let w(b) = -b**2 + 10*b - 12. Let h be w(v). Factor p**3 + 4*p**2 - p**3 - 2*p + h*p**4 - 8*p**4 + 2*p**5.
2*p*(p - 1)**3*(p + 1)
Let f be (-16)/(-3) - 2/6. Suppose 3*g = f*g - 4. Factor -1/2*m + 1/2*m**4 - 3/2*m**3 + 3/2*m**g + 0.
m*(m - 1)**3/2
Let n be (2 + -1 + 0)/(-1). Let z = 3 - n. Factor 2*y**4 + 0*y**z + 4*y**3 + 14 - 14.
2*y**3*(y + 2)
Let i = -16 - -18. Let b be i/3*9/12. Factor -3*y**3 + 0*y + 9/2*y**4 + b*y**2 + 0.
y**2*(3*y - 1)**2/2
Let a(m) = -m**2 + m. Let t(d) = -7*d**2 + 5*d - 1. Let o(h) = 5*a(h) - t(h). Let u be o(-1). Factor 0*y + 2/5 + 0*y**u - 4/5*y**2 + 2/5*y**4.
2*(y - 1)**2*(y + 1)**2/5
Let o(n) = -n + 4. Suppose -4*u + 7*s - 4*s = -17, 9 = -3*s. Let t be o(u). Factor 1/3*d - 1/3*d**t + 0 - 1/3*d**3 + 1/3*d**4.
d*(d - 1)**2*(d + 1)/3
Let k(h) = -7*h**5 - 3*h**4 + 9*h**3 + 11*h**2 - 3*h + 3. Let m(d) = 8*d**5 + 4*d**4 - 8*d**3 - 12*d**2 + 4*d - 4. Let u(o) = -4*k(o) - 3*m(o). Factor u(q).
4*q**2*(q - 2)*(q + 1)**2
Let a = 16/7 - 226/105. Let g(l) be the first derivative of 2/9*l**3 - 2 + 1/3*l**4 + 0*l + 0*l**2 + a*l**5. Suppose g(r) = 0. Calculate r.
-1, 0
Let a = -8 - -10. Suppose -3*z - a*z = 3*l - 10, -z = -5*l - 2. Find w such that -5*w**4 - 7*w**3 + l*w**4 + 0*w**4 - 2*w**2 = 0.
-1, -2/5, 0
Let i = -70 - -285/4. Let q(u) be the first derivative of 0*u - 1/6*u**2 - 2/9*u**3 + i*u**4 + 32/15*u**5 + 8/9*u**6 + 1. Solve q(k) = 0 for k.
-1, -1/4, 0, 1/4
Let k(c) = c**3 + 3*c**2 - 6*c - 4. Let l be k(-4). Let a(x) be the second derivative of x**3 + 0 + 1/6*x**l + 2*x**2 + 2*x. Factor a(s).
2*(s + 1)*(s + 2)
Let v(b) = b. Let t be v(-1). Let a(c) = 8*c**5 + 5*c**4 - c**3 + 8*c. Let u(p) = p**5 + p**4 + p**3 + p. Let q(f) = t*a(f) + 5*u(f). Solve q(h) = 0.
-1, 0, 1
Factor -60/7*g + 24/7 + 54/7*g**2 - 3*g**3 + 3/7*g**4.
3*(g - 2)**3*(g - 1)/7
Let r(i) be the second derivative of i**7/252 - i**6/180 - i**5/60 - 5*i. Factor r(h).
h**3*(h - 2)*(h + 1)/6
Let o = -155 - -157. Solve 0*h + 0*h**3 + 2/3 - 4/3*h**o + 2/3*h**4 = 0.
-1, 1
Find y such that -35*y**2 - 18 + 38 - 5*y**3 - 20 - 30*y = 0.
-6, -1, 0
Find w such that 32/7*w - 64/7 - 4/7*w**2 = 0.
4
Find j, given that 0 + 4*j**2 - 8/3*j - 4/3*j**3 = 0.
0, 1, 2
Let p(r) be the third derivative of r**9/362880 - r**7/10080 + r**6/2160 + r**5/20 + r**2. Let b(z) be the third derivative of p(z). Factor b(s).
(s - 1)**2*(s + 2)/6
Suppose 2*d + 4*d = -2*d. Solve 0*g**2 + 0*g - 4/11*g**4 + 2/11*g**5 + d + 2/11*g**3 = 0 for g.
0, 1
Let x = -12 - -10. Let a be 6 - x/4*-8. Factor 0*p**3 - 1/6*p**4 + 0*p + 1/6*p**a + 0.
-p**2*(p - 1)*(p + 1)/6
Let f be (-9 + -1)*(-28)/70. Let r(m) be the third derivative of -1/90*m**5 + 0*m**3 + 0*m + 0 - 2*m**2 + 1/36*m**f. Factor r(k).
-2*k*(k - 1)/3
Let j be (-1)/((4/(-12))/((-10)/(-15))). Factor -1/6*x + 1/6*x**4 + 1/6*x**3 + 1/3 - 1/2*x**j.
(x - 1)**2*(x + 1)*(x + 2)/6
Let g = -238 + 722/3. Let h be (-2)/(-6) + 7/3. Find w such that -g - 2/3*w**2 - h*w = 0.
-2
Factor -1/2*f**2 + 0 + 1/2*f.
-f*(f - 1)/2
Let k = -6/13 - -44/39. Factor -2/3 + 2/3*r + k*r**2 - 2/3*r**3.
-2*(r - 1)**2*(r + 1)/3
Factor -8/7*j**2 + 0 - 2/7*j.
-2*j*(4*j + 1)/7
Determine m so that -4/7*m + 8/7 - 4/7*m**2 = 0.
-2, 1
Let m(t) = t**3 - 2*t**2 - 2. Let d(l) = -l**2 - 1. Let c(h) = 3*d(h) - m(h). Let z be c(-2). Factor r**z + 12*r**2 + 2 + 2*r**3 + 9*r + r**3.
(r + 2)*(2*r + 1)**2
Let s = -107 - -109. Find n such that 2/3*n**s + 2/3 - 4/3*n = 0.
1
Factor -2*l + 83*l**2 - 38*l**2 - 41*l**2 - 2.
2*(l - 1)*(2*l + 1)
Let y(f) be the second derivative of 0 - 2*f**2 - 1/3*f**4 + 4/3*f**3 + 5*f. Let y(b) = 0. Calculate b.
1
Suppose 2*s + s = -5*s. Find h such that 0*h + s + 1/2*h**2 = 0.
0
Factor -2*k + 3*k - 2*k**2 + 3*k**2 + 0*k.
k*(k + 1)
Let m(v) be the first derivative of 2/5*v**2 + 1 + 2/15*v**3 + 2/5*v. Find i such that m(i) = 0.
-1
Let g = 147883/735 - 1006/5. Let b(o) be the third derivative of 0 + 1/420*o**6 + 0*o**3 + 1/210*o**5 - 1/84*o**4 + 0*o + 2*o**2 - g*o**7. Factor b(w).
-2*w*(w - 1)**2*(w + 1)/7
Let c(s) = -4*s**3 + 9*s**2 + 21*s - 17. Let j(a) = -a**3 + 2*a**2 + 5*a - 4. Let q(v) = -2*c(v) + 9*j(v). Let q(d) = 0. What is d?
-2, 1
Let l be ((-2)/(-1))/((-4)/26). Let s be 2/l - (-123)/39. Suppose -2 - 4*d**3 + 2*d**2 + 7*d - d**3 - 2*d**s = 0. What is d?
-1, 2/7, 1
Suppose 0 = x - 0*x + x. Let k(c) be the first derivative of -2/15*c**3 + 2/5*c + x*c**2 - 2. Solve k(o) = 0 for o.
-1, 1
Let l(b) be the second derivative of -2*b**7/105 + 2*b**6/75 + 3*b**5/25 - b**4/3 + 4*b**3/15 + 5*b. Solve l(w) = 0 for w.
-2, 0, 1
Let s(c) = -3*c**2 - 12*c + 15. Let h(q) = -2*q**2 - 12*q + 14. Let x(m) = -6*h(m) + 5*s(m). Suppose x(z) = 0. What is z?
1, 3
Let o(i) be the first derivative of 2*i**3/33 + 2*i**2/11 + 2*i/11 - 10. Determine y so that o(y) = 0.
-1
Let l(o) be the third derivative of o**6/150 + o**5/25 + o**4/15 + 8*o**2. Factor l(n).
4*n*(n + 1)*(n + 2)/5
Let k = 1102823/20 + -55153. Let m = k + 49/4. Find j, given that 4/5*j + m*j**2 + 0 = 0.
-2, 0
Let x(z) = -z**4 - 7*z**3 + z**2 + z + 3. Let n(y) = 8*y**3 - 4. Let g(b) = -3*n(b) - 4*x(b). Let g(h) = 0. Calculate h.
-1, 0, 1
Let d(k) = 2*k**4 - k**3 + 5*k**2 - 6. Let t(f) = -4*f**4 + 2*f**3 - 9*f**2 + 11. Let a(x) = 11*d(x) + 6*t(x). Suppose a(l) = 0. What is l?
-1/2, 0, 1
Suppose -69 = 13*y - 95. Factor 1/2 - 9/2*p**y - 3/4*p - 2*p**3.
-(p + 2)*(2*p + 1)*(4*p - 1)/4
Let q(s) be the first derivative of -s**4/54 - s**3/27 + 3*s + 2. Let z(i) be the first derivative of q(i). Factor z(g).
-2*g*(g + 1)/9
Let n(o) = 6*o - 4. Let d be n(1). Let g(w) be the first derivative of 1/2*w**4 + 0*w + w**2 + 4/3*w**3 - d. Find p such that g(p) = 0.
-1, 0
Let c(s) = -5*s**3 - 41*s**2 - 124*s - 80. Let o(v) = -5*v**3 - 42*v**2 - 123*v - 80. Let t(l) = -3*c(l) + 4*o(l). Factor t(a).
-5*(a + 1)*(a + 4)**2
Let r be -1 - (-1 + (-4)/24). Let l(i) be the second derivative of 0*i**2 - r*i**3 + 0 - 1/12*i**4 - i. Factor l(k).
-k*(k + 1)
Let u(a) be the