*(n + 1)**2
Let p(y) = -7*y**2 + 3*y + 10. Let v(z) = -8*z**2 + 3*z + 11. Let c(g) = 7*p(g) - 6*v(g). Determine m, given that c(m) = 0.
-1, 4
Suppose -1/7*q**2 - 39/7*q - 38/7 = 0. Calculate q.
-38, -1
Let v(l) = l - 3. Let g be v(6). Suppose 4*o = g*o. Find d, given that 2/5*d**4 - 1/5*d + 1/5*d**5 + o + 0*d**3 - 2/5*d**2 = 0.
-1, 0, 1
Let c(t) = t**4 + 3*t**3 + 5*t**2 - 45*t + 52. Let g(u) = 3*u**4 + 5*u**3 + 11*u**2 - 90*u + 103. Let k(d) = -5*c(d) + 2*g(d). Factor k(w).
(w - 3)**2*(w - 2)*(w + 3)
Let c(u) be the first derivative of u**8/5040 - u**7/2520 - 22*u**3/3 - 21. Let t(x) be the third derivative of c(x). Determine o, given that t(o) = 0.
0, 1
Let x be ((-10)/(-105))/((-2)/(-66)) + 86/(-602). Determine j, given that -116/3*j - 8/3 - 448/3*j**2 - 196/3*j**x = 0.
-2, -1/7
Let y(v) be the third derivative of 25*v**2 + 2/35*v**7 - 1/15*v**6 + 2*v**3 + 1/84*v**8 + 1/6*v**4 + 0*v + 0 - 2/5*v**5. Find n such that y(n) = 0.
-3, -1, 1
Suppose k = 2*m - 4*m, -k = 3*m + 1. Factor -h**k - 7/2*h - 2 + 1/2*h**3.
(h - 4)*(h + 1)**2/2
Let z(f) = 4*f - 22. Let s be z(6). Suppose -23*w**2 + 18*w**s + 8*w - 45 + 22*w = 0. Calculate w.
3
Let -11/3*v**3 - 1/3*v**4 + 12*v + 0 - 8*v**2 = 0. Calculate v.
-6, 0, 1
Let t(s) be the third derivative of -s**8/420 + s**6/90 + 19*s**3/6 - 12*s**2. Let j(o) be the first derivative of t(o). Factor j(l).
-4*l**2*(l - 1)*(l + 1)
Let d(x) be the first derivative of -x**4/2 + 8*x**3 - 35*x**2 + 48*x - 129. Factor d(j).
-2*(j - 8)*(j - 3)*(j - 1)
Determine j, given that -24/17*j + 22/17*j**2 - 2/17*j**3 + 2/17*j**5 + 8/17 - 6/17*j**4 = 0.
-2, 1, 2
Let z(f) = -2*f**2 - 83*f - 264. Let n be z(-38). Let b(s) be the second derivative of 10*s + 0*s**4 - 5*s**n + 1/4*s**5 + 0 - 5/2*s**3. Factor b(l).
5*(l - 2)*(l + 1)**2
Suppose 4*q + 8 = 6*q. Let -a**2 - 137*a**4 - a**2 + q*a**2 + 135*a**4 = 0. Calculate a.
-1, 0, 1
Let p(i) be the third derivative of i**5/120 - i**4/48 - i**3/6 - 40*i**2. Solve p(o) = 0.
-1, 2
Factor 8 - 5*a**2 + 10*a**3 + 47*a**4 - 52*a**4 - 8.
-5*a**2*(a - 1)**2
What is u in 0*u**2 + 36 + 24*u - 4/9*u**4 - 8/3*u**3 = 0?
-3, 3
Let h = -970 - -970. Factor -4/9*i**2 + h - 2/3*i**3 + 10/9*i**4 + 0*i.
2*i**2*(i - 1)*(5*i + 2)/9
Let r(h) be the second derivative of 0*h**3 + 0 + 4/5*h**2 - 1/30*h**4 - 11*h. Solve r(a) = 0.
-2, 2
Suppose 0 = -j + 3. What is r in -j*r**4 + 3*r**2 - 228*r + 228*r = 0?
-1, 0, 1
Let f(t) = -4*t + 31. Let y be f(7). What is s in 0*s**2 + y*s**2 + 2*s**2 + 5*s**3 - 10*s**2 = 0?
0, 1
Let q(w) be the third derivative of -w**5/120 - 5*w**4/12 - 19*w**3/12 - w**2 + 2. Determine r, given that q(r) = 0.
-19, -1
Let g(t) = 3*t + 24. Let y be g(-4). Suppose -4*v + 5*j - y = 0, -3*j + 1 + 13 = v. Suppose 5/3*z + 1/3 + v*z**2 = 0. Calculate z.
-1/2, -1/3
Let f(k) be the second derivative of -3*k**5/140 - 31*k**4/28 - 235*k**3/14 - 225*k**2/2 + 37*k - 1. Factor f(t).
-3*(t + 5)**2*(t + 21)/7
Suppose 3*k - a = 10 + 6, 5*a - 20 = -5*k. Determine r so that 509*r**2 + k*r - 529*r**2 + 20*r + 5*r**3 - 10 = 0.
1, 2
Let y(p) = 2*p - 6. Suppose 0 = -5*f + 20. Let v be y(f). Factor v*b**2 - 5*b**2 + b**2.
-2*b**2
Let 9*h**2 - 64*h - 12*h**3 + 18*h**2 + 21*h**2 + h**4 + 0*h**4 = 0. Calculate h.
0, 4
Let d(i) be the first derivative of 3*i**6/25 + 24*i**5/125 - i**4/10 - 8*i**3/25 - 4*i**2/25 + 705. Solve d(b) = 0 for b.
-1, -2/3, 0, 1
Let v(c) = c**2 - 21*c + 2. Let w be v(21). Let g(q) = -2*q - 1. Let y be g(-4). Factor 11*b**w + 5*b**3 + 5*b**3 - y*b**2.
2*b**2*(5*b + 2)
Let u(j) = 1 - 2*j**4 + 8*j**4 - 5*j**4. Let x(y) = -2*y**4 - 3*y**3 - 3*y**2 - y - 1. Let s(n) = 5*u(n) + 5*x(n). Factor s(m).
-5*m*(m + 1)**3
Suppose 0 = -2*o, -o + 6*o = 5*c. Suppose c = 5*g - m - 79, m - 41 = -2*g - g. Find j such that -3*j**4 - 9*j**4 + g*j**3 + 3*j**5 - 6*j**2 + 0*j**2 = 0.
0, 1, 2
Let b(k) = -14*k**3 + 254*k**2 - 5290*k + 37042. Let l(r) = 5*r**3 - r**2 - r + 1. Let d(f) = b(f) + 2*l(f). Factor d(y).
-4*(y - 21)**3
Let c(l) be the third derivative of -5*l**8/336 + l**7/21 - l**5/6 + 5*l**4/24 + l**2 + 100*l. Let c(h) = 0. Calculate h.
-1, 0, 1
Let d be (-10 - (-912)/90)*(-1)/(-4). Let s(h) be the first derivative of -1/12*h**4 + 1/6*h + 1/6*h**2 - d*h**5 + 0*h**3 + 1. Factor s(k).
-(k - 1)*(k + 1)**3/6
Let z(c) = -178*c - 356. Let v be z(-2). Factor -3/2*l**4 + 3*l**2 + 0*l + v + 3/2*l**3.
-3*l**2*(l - 2)*(l + 1)/2
Let o = 1221 + -1221. Factor o*b - 1/7*b**3 - 2/7*b**2 + 2/7*b**4 + 1/7*b**5 + 0.
b**2*(b - 1)*(b + 1)*(b + 2)/7
Let f(b) = b + 26. Let q be f(-24). Factor 37 - z**3 + z**q - 2*z**4 + z**4 - 37 + z**5.
z**2*(z - 1)**2*(z + 1)
Let p(o) = -25*o + 50*o - 30*o - 2 - 4*o**2 + 3*o**2. Let c(s) = s**2 + s + 1. Let v(d) = -10*c(d) - 5*p(d). Factor v(u).
-5*u*(u - 3)
Let m(k) be the first derivative of k**8/336 + k**7/84 - k**6/72 - k**5/12 - 25*k**3/3 - 35. Let v(y) be the third derivative of m(y). Factor v(x).
5*x*(x - 1)*(x + 1)*(x + 2)
Let g(r) = r**3 - 26*r - 3 - 6 + 10*r + 14*r**2 - 4. Let x be g(-15). Suppose -2/3*l**5 - 2/3*l**3 - 2*l**2 + 0 + 4/3*l + x*l**4 = 0. What is l?
-1, 0, 1, 2
Let v be (-2)/((-3 + 8)*-2). Factor 0*c**2 + v*c**4 - 2/5*c - 1/5 + 2/5*c**3.
(c - 1)*(c + 1)**3/5
Let o(h) = 9*h**2 + 10*h - 4. Let j(u) = -10*u**2 - 10*u + 5. Let w be (-11)/3 - 7/21. Let i(t) = w*j(t) - 5*o(t). Factor i(c).
-5*c*(c + 2)
Let o(m) = -m**4 - m**2 + m. Let n = 104 + -108. Let p(y) = 8*y**4 - 4*y**2 - 4*y + 4. Let a(w) = n*o(w) - p(w). Factor a(q).
-4*(q - 1)**2*(q + 1)**2
Let t = 1887 + -1885. Determine z so that 12 + 1/3*z**t - 4*z = 0.
6
Let q(r) be the first derivative of r**3/21 - 62*r**2/7 + 3844*r/7 - 136. Factor q(c).
(c - 62)**2/7
Let m(f) be the second derivative of f**4/16 + 63*f**3/8 + 93*f**2/4 - 29*f - 2. Let m(z) = 0. Calculate z.
-62, -1
Let y(n) be the third derivative of 0*n**3 - 1/42*n**7 + 0*n**4 - 1/8*n**6 + 0 - 16*n**2 + 0*n**5 + 0*n. Solve y(d) = 0 for d.
-3, 0
Suppose -2*m - 16 = -2*u - 6, 5*u = 2*m + 16. What is l in -14*l**2 + 16*l**u + 0 - 3*l**2 + 1 = 0?
-1, 1
Let n = -2783 + 8351/3. Factor 0 - 1/3*a**3 - a**2 - n*a.
-a*(a + 1)*(a + 2)/3
Let j(g) = 2*g**2 - 5*g + 40. Let n be j(6). Let b = n - 491/6. What is i in 0 + 0*i - b*i**3 - 1/6*i**2 + 1/6*i**5 + 1/6*i**4 = 0?
-1, 0, 1
Let u(q) be the second derivative of -q**4/4 + 13*q**3 - 507*q**2/2 + 69*q. Factor u(h).
-3*(h - 13)**2
Let w(z) be the third derivative of 0*z**4 + 0 - 1/80*z**5 + 0*z**7 + 0*z**3 + 3/320*z**6 + 0*z - 1/896*z**8 + 22*z**2. What is d in w(d) = 0?
-2, 0, 1
Let n(i) be the third derivative of 0 - 4/15*i**6 + 29/90*i**5 + 31/315*i**7 + 0*i - 19*i**2 + 0*i**3 - 1/84*i**8 - 1/6*i**4. Solve n(y) = 0.
0, 1/2, 2/3, 1, 3
Let t(x) be the second derivative of 5*x**6/6 + 7*x**5/4 - 2*x**4 - 6*x**3 - 28*x + 1. Determine i, given that t(i) = 0.
-6/5, 0, 1
Let a(u) be the second derivative of -u**8/2240 + u**7/840 + u**6/48 + 3*u**5/40 - 2*u**4/3 + 24*u. Let n(c) be the third derivative of a(c). Factor n(g).
-3*(g - 3)*(g + 1)**2
Let x be (-90)/(-300) - (3/(-5))/3. Let k(r) be the first derivative of -1/3*r**3 - 2 + x*r**4 - 2*r**2 + 3*r. Factor k(f).
(f - 1)**2*(2*f + 3)
Let s(z) = 2170*z**2 - 1260*z + 215. Let q be 35*(-2 + (-6)/(-2)). Let d(k) = 241*k**2 - 140*k + 24. Let r(b) = q*d(b) - 4*s(b). Factor r(u).
-5*(7*u - 2)**2
Let n be (-480)/(-22) + (-10)/(-55). Factor -2*x**2 + n - 3*x**3 - 4*x**2 + 19*x + 2 - 7*x.
-3*(x - 2)*(x + 2)**2
Let d(r) be the second derivative of r**7/210 + r**6/90 - r**5/90 - r**4/18 - r**3/18 - 13*r**2/2 + 7*r. Let l(g) be the first derivative of d(g). Factor l(u).
(u - 1)*(u + 1)**2*(3*u + 1)/3
Let z(v) = -2*v + 4. Let t be z(-8). Suppose 384 - 80*i**3 - 384 - 35*i**4 - t*i**2 = 0. Calculate i.
-2, -2/7, 0
Factor -2*z**2 - 81*z**4 - 72*z**4 + 155*z**4.
2*z**2*(z - 1)*(z + 1)
Let f(v) be the second derivative of v**7/42 - 19*v**6/30 - v**5 - 3*v + 188. Factor f(i).
i**3*(i - 20)*(i + 1)
Let a(d) be the second derivative of 8*d + 0 + 0*d**2 + 1/102*d**4 + 0*d**3. Solve a(z) = 0.
0
Let y(u) = -u**2 - 2. Let w(b) = b**2 - 130*b + 117. Let j(h) = -w(h) + 4*y(h). Factor j(k).
-5*(k - 25)*(k - 1)
Suppose -28 = -4*m - 4*f, 2*f - f - 19 = -5*m. Suppose 0*p = m*p - 144. Let -p*s**4 + 57*s**4 + 3*s**3 - 21*s**2 + 6*s + 3*s**3 = 0. Calculate s.
-2, 0, 1/3, 1
Let l(g) = -6*g**2 - 5*g + 11. Suppose 0 