 n**2 - n**3 - 1.
-(n - 1)**2*(n + 1)
What is i in -2 - 500*i**4 + 34 + 35*i - 383*i**3 - 317*i**3 - 120*i**2 + 77*i = 0?
-1, -2/5, 2/5
Let z(a) = 5*a**4 + 5*a**3 - 5*a**2 - 9*a. Let r(n) = -n. Let u(g) = -4*r(g) + z(g). What is w in u(w) = 0?
-1, 0, 1
Suppose 3*g = -1 + 7. Factor d - g*d + 4*d + 0*d**3 - 3 + 3*d**2 - 3*d**3.
-3*(d - 1)**2*(d + 1)
Let y be (-82)/26 - (-20)/130. Let l be -2*y/42*2. Factor 2/7*f**4 + 2/7*f**5 - l*f**2 + 0*f - 2/7*f**3 + 0.
2*f**2*(f - 1)*(f + 1)**2/7
Factor -139*h + 3*h**4 - 3*h**5 + h**3 + 137*h + 4*h**5 - 3*h**2.
h*(h - 1)*(h + 1)**2*(h + 2)
Let g(f) be the third derivative of 2*f**7/105 - f**6/6 - 2*f**5/5 + 21*f**2. Determine n so that g(n) = 0.
-1, 0, 6
Suppose 0*r - 8/13*r**4 + 0 - 2/13*r**3 + 0*r**2 = 0. Calculate r.
-1/4, 0
Let l = -16/171 + 6/19. Factor -l*u**2 + 0 - 2/9*u.
-2*u*(u + 1)/9
Let j(b) = -3*b**2 + b. Let k(h) = -7*h**2 + 3*h. Let t be (-2)/(-5) + (-69)/(-15). Let o(n) = t*j(n) - 2*k(n). Suppose o(s) = 0. Calculate s.
-1, 0
Let m(f) be the second derivative of -f**4/84 + 2*f**3/7 - 18*f**2/7 + 2*f - 19. Determine d so that m(d) = 0.
6
Let q be 3/(-1 - 10/(-4)). What is m in 3*m**q + 0 + 1 - 1 = 0?
0
Let a(r) be the third derivative of r**7/630 + 7*r**6/360 - 4*r**2 + 11. Suppose a(g) = 0. Calculate g.
-7, 0
Let v(z) = -2*z**2 + 8*z - 6. Let o(p) = 5*p**2 - 24*p + 17. Let l(c) = -6*o(c) - 17*v(c). Factor l(g).
4*g*(g + 2)
Let o(m) be the second derivative of -m**5/40 - m**4/8 - m**3/6 + 7*m. Factor o(g).
-g*(g + 1)*(g + 2)/2
What is f in 0 - 1/4*f**4 + 0*f - 1/2*f**2 - 3/4*f**3 = 0?
-2, -1, 0
Let j = 49 + -33. Let n be j/(-24)*(-3)/9. Let 0*f**3 + n*f**5 - 2/9*f - 4/9*f**2 + 4/9*f**4 + 0 = 0. What is f?
-1, 0, 1
Suppose -7 = -3*l - 1. Find j such that 19*j**l + 2 - 2 + 3*j - 16*j**2 = 0.
-1, 0
Let n = 515 - 2572/5. Suppose 1/5*t**4 + 2/5*t**2 + 0*t + n*t**3 + 0 = 0. What is t?
-2, -1, 0
Let s(n) be the second derivative of -n**4/12 - n**3/6 + n**2 + 2*n. Factor s(t).
-(t - 1)*(t + 2)
Let b = -10 - -14. Suppose 0*l + 2*l + 20 = 5*m, 3*l = -b*m - 7. Factor 1/2 - 1/2*r**m - 1/2*r**3 + 1/2*r.
-(r - 1)*(r + 1)**2/2
Let r be (6/5)/(12/(-30)). Let n be 1/4 - (r - -3). Factor 0*w + 1/4*w**4 - n*w**2 - 1/4*w**3 + 1/4*w**5 + 0.
w**2*(w - 1)*(w + 1)**2/4
Let m(g) be the third derivative of 1/180*g**5 + 0 + 1/1008*g**8 + 4*g**2 + 0*g - 1/630*g**7 - 1/360*g**6 + 0*g**3 + 0*g**4. Factor m(s).
s**2*(s - 1)**2*(s + 1)/3
Let w(g) be the first derivative of -3 + 1/9*g**3 - 2/3*g - 1/6*g**2. Factor w(t).
(t - 2)*(t + 1)/3
Let i = -226/3 - -76. Let t = 3/7 - 2/21. Factor t*m + i - 1/3*m**2.
-(m - 2)*(m + 1)/3
Let q be 160/75 + (-8)/10. Factor 2/3 + 4/3*t**2 - 2*t**4 - q*t**3 + 2*t - 2/3*t**5.
-2*(t - 1)*(t + 1)**4/3
Let f be (-8)/2*((-213)/(-27) + -8). Factor 2/9 + f*u - 4/9*u**3 - 2/9*u**4 + 0*u**2.
-2*(u - 1)*(u + 1)**3/9
Let m(r) = -4 + 18*r**2 - 8*r**2 + 5 - 9*r**2. Let l = 1 - 2. Let x(t) = -1. Let s(w) = l*x(w) - m(w). Factor s(y).
-y**2
Let n(j) be the third derivative of j**7/420 - j**6/144 + j**5/360 + j**4/144 + j**2 - 10*j. Determine w so that n(w) = 0.
-1/3, 0, 1
Let d(s) = -20*s**4 - 28*s**3 + 39*s**2 + 23*s - 7. Let n(p) = -10*p**4 - 14*p**3 + 19*p**2 + 11*p - 3. Let f(h) = 3*d(h) - 7*n(h). Factor f(a).
2*a*(a - 1)*(a + 2)*(5*a + 2)
Suppose -4*q - 4*r + 4 = -12, 0 = 3*q - 4*r - 12. Suppose q + 5 = 3*h. Determine s, given that -2/3 - 4/3*s + 4/3*s**h + 0*s**2 + 2/3*s**4 = 0.
-1, 1
Let h(o) = o**3 - 4*o**2 + o + 1. Let l be h(4). Factor -r**2 - r**5 - 4*r**4 - l*r**3 + 2*r**3 + r**4.
-r**2*(r + 1)**3
Let b(d) be the second derivative of d**7/280 - d**6/40 + 3*d**5/40 - d**4/8 + d**3/6 + 4*d. Let o(c) be the second derivative of b(c). Factor o(j).
3*(j - 1)**3
Let p = 11 - 7. Solve -l**2 - 5*l**4 + 2*l**p + 4*l**2 = 0 for l.
-1, 0, 1
Suppose -3 = -p - 1. Factor -2/3*n**3 + 2/3 - 2*n + 2*n**p.
-2*(n - 1)**3/3
Let w(s) be the third derivative of s**9/1890 + 3*s**8/1400 + s**7/350 + s**6/900 + s**3/3 - s**2. Let k(m) be the first derivative of w(m). Factor k(f).
2*f**2*(f + 1)**2*(4*f + 1)/5
Factor -8*m**5 - 15*m + 2*m**4 + 11*m + 3*m**3 - 4*m**2 + 7*m**5.
-m*(m - 2)**2*(m + 1)**2
Suppose -4/7*h**3 + 0 + 2/7*h + 0*h**4 + 2/7*h**5 + 0*h**2 = 0. What is h?
-1, 0, 1
Let p(f) = -f**3 + 4*f**2 - 4*f + 2. Let s be p(2). Let n(k) be the first derivative of 1/8*k**4 + 1/4*k**2 + 0*k + s + 1/3*k**3. Factor n(v).
v*(v + 1)**2/2
Factor 4*m + 3*m**2 + m + 4*m + 6.
3*(m + 1)*(m + 2)
Let r(a) be the second derivative of -a**5/36 - a**4/36 + 2*a**2 + 7*a. Let z(b) be the first derivative of r(b). Solve z(m) = 0.
-2/5, 0
Let d = 85 - 85. Let w = -3 + 6. What is q in -1/2*q**w + 1/2*q**2 + 0 + d*q = 0?
0, 1
Factor -1427*y + 0*y**4 + 1419*y - 3*y**4 + 5*y**4 + 6*y**3.
2*y*(y - 1)*(y + 2)**2
Suppose -9*j + 11*j - 6 = 0. Factor -6*i**2 + 38*i**3 - 3 + j - 35*i**3.
3*i**2*(i - 2)
Factor 15/2 - 9*d + 3/2*d**2.
3*(d - 5)*(d - 1)/2
Let b(d) be the second derivative of -7*d**6/120 + 3*d**5/20 + d**4/12 + 19*d. Find q such that b(q) = 0.
-2/7, 0, 2
Let d = -82 + 329/4. Let a(z) be the first derivative of -d*z + 2 - 1/12*z**3 + 1/4*z**2. Factor a(o).
-(o - 1)**2/4
Let p = -30932 + 215336/7. Let d = p - -170. Factor 0 + 2/7*c + d*c**3 + 4/7*c**2.
2*c*(c + 1)**2/7
Factor 1/3 + 2/3*h - 7/3*h**2 + 4/3*h**3.
(h - 1)**2*(4*h + 1)/3
Let a(o) be the third derivative of o**8/1344 + o**7/420 - o**6/160 - o**5/60 + o**4/24 + 8*o**2. Factor a(j).
j*(j - 1)**2*(j + 2)**2/4
Suppose 0 = 7*r - 3*r. Let p(g) be the third derivative of -1/180*g**6 + 1/45*g**5 + r*g + 0*g**3 + 0 - 1/36*g**4 - 2*g**2. Factor p(l).
-2*l*(l - 1)**2/3
Solve 7/5*x**3 + 4/5*x - 16/5*x**2 + 0 = 0.
0, 2/7, 2
Let m be 54/81 + (-1)/(-12). Let m*d**4 + 0*d**2 + 1/2*d**5 + 0 + 0*d + 1/4*d**3 = 0. Calculate d.
-1, -1/2, 0
Let p(r) = -r**4 + r - 1. Let j(l) = -l**2. Let u be j(1). Let b(z) = 3*z**4 + z**3 + 5*z**2 - 7*z + 4. Let s(w) = u*b(w) - 6*p(w). What is i in s(i) = 0?
-1, -2/3, 1
Let o be (-6)/(-21) + 250/105. Let u(f) be the first derivative of -3 + 0*f - 2/5*f**5 - o*f**3 + 0*f**2 - 2*f**4. Let u(v) = 0. Calculate v.
-2, 0
Let f(i) be the third derivative of i**10/50400 - i**8/6720 - i**5/30 - i**2. Let h(z) be the third derivative of f(z). Factor h(w).
3*w**2*(w - 1)*(w + 1)
Let t(u) = 2*u**2 - 9*u + 15. Let l(m) = -m**2 + m + 1. Let c(k) = -l(k) - t(k). Determine n so that c(n) = 0.
4
Let d(p) be the first derivative of -4*p**3/9 + 4*p/3 - 6. Let d(l) = 0. What is l?
-1, 1
Let c(h) = -5*h**3 - 15*h**2 - 21*h - 11. Let m(d) = 5*d**3 + 15*d**2 + 20*d + 10. Let i(w) = 5*c(w) + 6*m(w). Determine u so that i(u) = 0.
-1
Solve 3/7*q**2 + 1/7 - 1/7*q**3 - 3/7*q = 0.
1
Let w(l) be the first derivative of 0*l**4 + 0*l + 1/18*l**6 + 0*l**2 + 1/15*l**5 + 5 + 0*l**3. Find d such that w(d) = 0.
-1, 0
Let l = 13 + -10. Factor -15 - 8*b - 11*b**4 - 2*b**5 + 13 - 23*b**2 - 23*b**l - 3*b.
-(b + 1)**3*(b + 2)*(2*b + 1)
Let h(n) be the third derivative of -n**5/480 + n**4/192 + n**3/24 - 19*n**2. Factor h(g).
-(g - 2)*(g + 1)/8
Suppose 0*i**2 + 2/13*i**3 - 6/13*i - 4/13 = 0. What is i?
-1, 2
Let q(n) be the first derivative of -2*n**5/35 - n**4/14 + 6. Factor q(m).
-2*m**3*(m + 1)/7
Let r = 261 + -1303/5. Factor 0*k - 2/5*k**2 + 0 - r*k**3.
-2*k**2*(k + 1)/5
Let i(h) = -h**5 + 4*h**4 - 6*h**3 + 4*h**2 + 2*h + 3. Let m(b) = b + 1. Let g(z) = 2*i(z) - 6*m(z). Factor g(s).
-2*s*(s - 1)**4
Let f(d) be the first derivative of 3 + 4/3*d**2 - 8/3*d - 2/9*d**3. Solve f(l) = 0 for l.
2
Suppose 8 - 1 = v. Let l be (v/14)/((-5)/(-4)). Factor 32/5*f**2 + 12/5*f**4 + 4/5 + l*f**5 + 18/5*f + 28/5*f**3.
2*(f + 1)**4*(f + 2)/5
Suppose 12 = 4*b - 0. Let x(k) be the third derivative of 2*k**2 + 0 + 1/180*k**6 + 0*k**b + 1/90*k**5 + 0*k + 0*k**4. Suppose x(a) = 0. Calculate a.
-1, 0
Factor 0 + 6/5*h**2 + 3/5*h**3 + 3/5*h.
3*h*(h + 1)**2/5
Factor 0 + 1/4*t**3 - 3/2*t - 5/4*t**2.
t*(t - 6)*(t + 1)/4
Suppose -5*x + 10 = 3*q - 4, 4*x - 3*q = 22. Let o(p) be the second derivative of 3*p + 1/3*p**3 + 2*p**2 - 1/6*p**x + 0. Determine f, given that o(f) = 0.
-1, 2
Let y be (0 - 1)/(14/(-4)). Let -8/7*q + y + 8/7*q**2 = 0. Calculate q.
1/2
Let n(b) = -b**5 - b**4 + b**3 - b**2 - b. Let p(d) = 12*d**5 + 21*d**4 - 15*d**3 - 15*d**2 + 12*d + 12. Let m(w) = -9*n(w) - p(w). Find y such that m(y) = 0.
-4, -1, 1
Let b(