r k(n).
n*(n - 1)/3
Determine h, given that 66*h - 51 + 54 - 27*h + 66*h**2 = 0.
-1/2, -1/11
Suppose 0 = -4*a - a. Suppose z + 3*z - 20 = 4*p, -4*z + p + 11 = a. Let -88*d**z + 10*d - d + 85*d**2 = 0. What is d?
0, 3
Let f(i) be the third derivative of -i**8/112 + i**7/70 + i**6/8 - i**5/20 - i**4 - 2*i**3 - 4*i**2. Factor f(t).
-3*(t - 2)**2*(t + 1)**3
Suppose 3*i - 17 = 1. Let q = -3 + i. Let -p**3 + 0*p**4 + 4*p**3 + q*p**4 = 0. What is p?
-1, 0
Let -11/7*n + 3/7 - 5/7*n**3 + 13/7*n**2 = 0. Calculate n.
3/5, 1
Let j = 6236 - 6236. Factor 2/7*v**3 + 16/7*v + j + 18/7*v**2.
2*v*(v + 1)*(v + 8)/7
Let b(n) be the third derivative of -2*n**2 + 0 - 1/30*n**5 - 8/3*n**4 - 256/3*n**3 + 8*n. Factor b(l).
-2*(l + 16)**2
Let c(x) be the first derivative of -2*x**3/63 - x**2/21 - 6. Factor c(b).
-2*b*(b + 1)/21
Let r = 27621 + -27619. Factor 40*j + 400/3 + 2/15*j**3 + 4*j**r.
2*(j + 10)**3/15
Let 6 + 7*h**2 + 2 + 4 + 3*h**4 - 22*h**2 = 0. What is h?
-2, -1, 1, 2
Let o(a) = -33*a**2 + 124*a - 107. Let c(y) = -12*y**2 + 42*y - 36. Let z(i) = -8*c(i) + 3*o(i). What is v in z(v) = 0?
1, 11
Let m be -27*(-3 - 4/(-2)). Suppose 0 = 12*a - m - 9. Find y such that 3/2*y**2 + 0 + 3/2*y**3 + 0*y - a*y**4 = 0.
-1/2, 0, 1
Suppose 4 = z - 0. Suppose 3*i + 13 = r - 2, 16 = -z*i. Find t, given that -10*t**2 - 8*t**2 + 21*t**2 + r*t = 0.
-1, 0
Suppose 162 = 143*n - 89*n. Let z(v) be the first derivative of 9 + 1/6*v**2 - 1/15*v**5 - 2/3*v + 1/3*v**n - 1/12*v**4. Factor z(i).
-(i - 1)**2*(i + 1)*(i + 2)/3
Let w(g) be the third derivative of -g**7/168 + 7*g**6/480 + 3*g**5/40 - 7*g**4/24 + g**3/3 + 5*g**2 + 7. Let w(k) = 0. What is k?
-2, 2/5, 1, 2
Suppose -3*p = 3*y - 4 - 8, -2*p + 14 = 5*y. Find z such that -267*z**y + 533*z**2 + 3*z**3 - 272*z**2 = 0.
0, 2
Let d(b) = 23*b**4 - 35*b**3 - 60*b**2. Let m(c) = -4*c**4 + 6*c**3 + 10*c**2. Let p(j) = -6*d(j) - 34*m(j). Factor p(h).
-2*h**2*(h - 5)*(h + 2)
Let b(o) = -o**3 - 10*o**2 + 24*o + 3. Let k be b(-12). Factor -3*c**k - 51*c - c**3 + 99*c - 64.
-4*(c - 2)**2*(c + 4)
Factor 5*j + 2 + 1/8*j**4 + 5/4*j**3 + 33/8*j**2.
(j + 1)**2*(j + 4)**2/8
Determine z so that 2/5*z**2 - 1/5 - 1/5*z**4 - 3/5*z**5 - 3/5*z + 6/5*z**3 = 0.
-1, -1/3, 1
Let i(v) be the third derivative of 1/15*v**5 + 0*v + 0*v**3 + 17/180*v**6 + 0 + 1/63*v**7 + 0*v**4 + 13*v**2. Let i(r) = 0. Calculate r.
-3, -2/5, 0
Let i(g) be the third derivative of -1/3*g**4 - 1/168*g**8 + 1/20*g**6 + 7*g**2 + 0*g**3 - 2/105*g**7 + 0*g + 0 + 2/15*g**5. Find y such that i(y) = 0.
-2, 0, 1
Determine a so that 40*a**2 + 175*a - 3 - 27 - 156*a**2 - 124*a**2 - 45*a**3 = 0.
-6, 1/3
Find y, given that -102*y**2 - 1/2*y**4 - 17*y**3 - 207*y - 243/2 = 0.
-27, -3, -1
Suppose 8*b**3 - 128/3*b + 32/3*b**2 + 0 - 10/3*b**4 + 1/3*b**5 = 0. Calculate b.
-2, 0, 4
Let l(t) be the second derivative of -2*t**6/15 - t**5 + t**4/3 + 10*t**3/3 + 2*t - 10. Let l(b) = 0. What is b?
-5, -1, 0, 1
Let q be (29/(-116))/(2/(-48)). Let c be (5 + -2)*(q + 1246/(-231)). Let 6/11*f**4 - c*f**2 - 18/11 - 42/11*f + 12/11*f**3 - 2/11*f**5 = 0. Calculate f.
-1, 3
Let k(c) = -18*c**2 + 241*c - 149. Let r(u) = -3*u**2 + 48*u - 30. Let z(t) = 2*k(t) - 11*r(t). Determine s so that z(s) = 0.
-16, 2/3
Let w be -11*(14/(-21))/((-11)/(-3)). Factor 0*v + 1/7*v**w - 1/7.
(v - 1)*(v + 1)/7
Let z(t) be the second derivative of t**4/12 - 23*t**3/3 + 529*t**2/2 - 150*t. Factor z(a).
(a - 23)**2
Factor 0 - 2*n + 8/7*n**3 - 54/7*n**2.
2*n*(n - 7)*(4*n + 1)/7
Let z be (-8)/(-6) + 2 + 8/(-6). Find y, given that -576 - 8*y**z - 7*y + 4*y**2 - 36*y - 53*y = 0.
-12
Suppose 0 = 3*h + 5*k - 43, 0 = 4*h - 4*k + 3*k - 65. Let v be h/(-4)*2/(-2). Find x such that -v*x**3 - x**2 + 4*x - 2 + 2*x**4 + 0 + x**2 = 0.
-1, 1
Let n = -2/14639 + 409910/131751. Factor 40/9*b - n*b**2 - 16/9 + 2/3*b**3.
2*(b - 2)**2*(3*b - 2)/9
Let v = -2/681 - -685/1362. Factor v*x + 0 + 1/4*x**2.
x*(x + 2)/4
Let v(c) = 7*c**3 - 16*c**2 + 17*c - 2. Let b(s) = 8*s**3 - 15*s**2 + 19*s - 3. Let m(x) = 2*b(x) - 3*v(x). Factor m(g).
-g*(g - 1)*(5*g - 13)
Let f(t) be the first derivative of -5*t**3/3 - 7*t**2/2 + 6*t + 40. Factor f(w).
-(w + 2)*(5*w - 3)
Let -12*q - 4*q**2 + 4*q**2 - q - 4*q + 16 + q**2 = 0. What is q?
1, 16
Suppose 6*j + 83 = 5*t + 26, -3*t - 5*j - 26 = 0. Find n such that 3*n**2 - 3/2*n - t + 3/2*n**3 = 0.
-2, -1, 1
Let w(s) be the first derivative of -s**6/240 - 3*s**5/80 - s**4/8 + 13*s**3/3 + 7. Let i(j) be the third derivative of w(j). Determine u, given that i(u) = 0.
-2, -1
Let q be 9/(-10)*100/(-60). Let l(n) be the second derivative of 0 - q*n**2 - 1/4*n**4 + 5*n - n**3. Factor l(w).
-3*(w + 1)**2
Let x = 5 - 17/4. Let j(m) be the first derivative of -x*m**2 - 2*m**3 + m - 7 - 7/8*m**4. Suppose j(g) = 0. Calculate g.
-1, 2/7
Let k(o) be the first derivative of o**7/63 + o**6/18 + o**5/30 - o**4/9 - 2*o**3/9 - o**2/6 + 10*o - 12. Let l(g) be the first derivative of k(g). Factor l(p).
(p - 1)*(p + 1)**3*(2*p + 1)/3
Let r(l) = -l**2 + l. Let w(i) = -2*i - 42. Let o be w(-21). Let j be r(o). Factor 0*a**4 + 0 - 2/3*a**3 + 2/3*a**5 + j*a + 0*a**2.
2*a**3*(a - 1)*(a + 1)/3
Let m(y) be the third derivative of 5*y**8/1008 - y**7/14 + 7*y**6/24 - 19*y**5/36 + 5*y**4/12 + 587*y**2. Solve m(k) = 0.
0, 1, 6
Let l(y) = 2*y**5 + 2*y**4 + 1. Let h(t) = t**2 + t**5 + 2*t**4 - 2*t**4 + t**3 + t**4 + 1. Suppose 0 = 63*v - 52*v + 11. Let j(g) = v*h(g) + l(g). Factor j(n).
n**2*(n - 1)*(n + 1)**2
Let f(t) be the first derivative of -1/12*t**3 + 1/4*t - 6 + 0*t**2. Factor f(i).
-(i - 1)*(i + 1)/4
Let m be (146/(-172))/((-20)/6). Let h = -1/215 + m. Factor -h*u**2 + 1/4*u + 1/2.
-(u - 2)*(u + 1)/4
Let x be (-1)/(-3 + (-4)/((-128)/92)). Suppose -3*c + x*c - 15 = 0. Factor -6/5 + 3/5*f**4 + 9/5*f**c + 3/5*f**2 - 9/5*f.
3*(f - 1)*(f + 1)**2*(f + 2)/5
Let w(q) be the third derivative of -q**6/180 + 7*q**5/5 - 147*q**4 + 8232*q**3 - 4*q**2 + 3*q. Factor w(t).
-2*(t - 42)**3/3
Suppose 0 = 4*c + w - 14, -5*c + 0 + 9 = -3*w. Let u(j) be the second derivative of 3*j - 1/27*j**c + 0*j**2 - 1/54*j**4 + 0. Solve u(t) = 0.
-1, 0
Let q(d) = 7*d**3 + 114*d**2 + 347*d + 120. Let x(f) = f**3 - f. Let j(t) = -2*q(t) - 6*x(t). Let j(v) = 0. What is v?
-6, -5, -2/5
Let h(c) be the second derivative of c**6/255 + c**5/34 + 3*c**4/34 + 7*c**3/51 + 2*c**2/17 - 11*c - 2. Suppose h(x) = 0. Calculate x.
-2, -1
Let w(h) be the first derivative of 3*h**2 + 0*h + 10 - 2/3*h**3. Factor w(u).
-2*u*(u - 3)
Let d be 858/286 - 6*3/(-1*12). Factor 3/2*p - d + 9/2*p**2 - 3/2*p**3.
-3*(p - 3)*(p - 1)*(p + 1)/2
Let r(o) = -2*o. Let f(v) = 2*v**2 - 60*v + 338. Let m(h) = -f(h) + 4*r(h). Let m(g) = 0. Calculate g.
13
Let s(n) be the first derivative of 2*n**3/3 - 312*n**2 + 48672*n + 393. Factor s(k).
2*(k - 156)**2
Let x be 308/192 - (7/(-3) - -3). Let r = -13/48 + x. Let 4/3*g - 2/3 - r*g**2 = 0. Calculate g.
1
Let b be 2/4 - (-8)/(-16). Suppose 14 = -f - 2*v + 39, b = 2*f - 4*v - 58. Suppose f*u**3 + 50*u + 5 + 14*u**2 + 40*u**2 - 17*u + 1 = 0. What is u?
-1, -2/3, -1/3
Find u such that -42*u**2 + 20*u**2 + 28*u**2 + 14*u**2 - 5*u**3 - 5*u - 30 = 0.
-1, 2, 3
Suppose -89 = -5*v - 9. Factor -v + 52*k**2 + 20 + 12*k**3 + 12 + 61*k + 3*k.
4*(k + 2)**2*(3*k + 1)
Solve -5*r**5 + 31553*r + 29466*r**2 - 8438*r - 22445 + 675*r**4 - 7696*r**2 - 23110*r**3 = 0 for r.
-1, 1, 67
Suppose 48*s - 50*s - 12 = 0. Let v be -2 - (-3 - -2*(-3)/s). Solve 2/9*f**4 - 4/9*f + 4/9*f**3 + v*f**2 - 2/9 = 0.
-1, 1
Solve 125*o**2 + 20*o**3 - 6*o**5 - 125*o**4 + o**5 - 88*o**3 + 19*o - 47*o**3 + 101*o = 0.
-24, -1, 0, 1
Suppose -31 = -10*d - 1. Let b(a) be the second derivative of 0 + d*a + 1/24*a**3 + 1/80*a**5 + 0*a**2 + 1/24*a**4. Factor b(k).
k*(k + 1)**2/4
Let s(t) be the first derivative of -3*t**4/16 - 3*t**3 - 135*t**2/8 - 81*t/2 - 11. Determine b, given that s(b) = 0.
-6, -3
Let x = -41493/5 - -8304. Solve 0 - 21/5*z**4 - x*z**2 - 9*z**3 - 3/5*z**5 + 0*z = 0.
-3, -1, 0
Suppose 3*o - 2*h + 3 = h, -2*o - 4*h + 22 = 0. Let n be o*(2 + 2 + -1 + -2). Let -4/9*b**2 - 4/9*b**n + 2/9*b**5 + 2/9 + 2/9*b + 2/9*b**4 = 0. What is b?
-1, 1
Find c, given that -3*c - 934*c**3 - 9*c + 932*c**3 + 14*c**2 = 0.
0, 1, 6
Let d = -1/1330 + 669/5320. Let 1/2*a**2 - d*a**3 - 5/8*a + 1/4 = 0. Calculate a.
1, 2
Let f be (0 + -3)*(-2)/(-6)