2 + 14*k. Let c(u) be the first derivative of i(u). Factor c(n).
2*n*(n + 1)**2/11
Let w be (-15)/((-230)/20 - -4). Solve w*t**2 - 2/3*t**3 + 2/3*t - 2 = 0 for t.
-1, 1, 3
Let z(d) be the third derivative of -1/24*d**4 - 1/4*d**3 + 3*d**2 + 1/120*d**5 + 0*d + 0. Determine l so that z(l) = 0.
-1, 3
Let u be ((-4)/6)/(2 + -8). Let h(i) be the second derivative of 1/9*i**2 + 0 + 1/18*i**4 + u*i**3 + 1/90*i**5 + 5*i. Factor h(a).
2*(a + 1)**3/9
Let u(r) be the second derivative of 0*r**2 + 0*r**4 + 0 + 0*r**3 - 1/4*r**5 + 32*r. Factor u(h).
-5*h**3
Let a(o) be the first derivative of o**4/8 - o**3/3 - 13*o**2/4 - 5*o - 63. Solve a(n) = 0.
-2, -1, 5
Let i(b) be the first derivative of -9*b**4/4 - 13*b**3 - 39*b**2/2 - 9*b - 25. Let i(q) = 0. What is q?
-3, -1, -1/3
Let v(w) be the first derivative of w**2/2 + 17*w - 6. Let h be v(-15). Find a, given that -2*a - 5 + 1 + h + 3*a + a**2 = 0.
-2, 1
Let i(h) be the first derivative of -25*h**4/2 - 460*h**3/3 + 196*h**2 - 80*h + 82. Let i(o) = 0. Calculate o.
-10, 2/5
Let h be 22/(-165) - (-134)/30 - (-8 + 11). Factor h*n**3 + 12*n**2 + 64/3 + 32*n.
4*(n + 1)*(n + 4)**2/3
Let t(d) be the first derivative of 2*d**3/9 + 14*d**2/3 + 98*d/3 + 19. Solve t(g) = 0.
-7
Let h(k) = -k**3 + 22*k**2 + 24*k - 23. Let i be h(23). Let c be (-2)/(-4)*6 - i - 1. Let -19/2*d**3 - 25/2*d**c - 1/2*d**5 - 2 - 8*d - 7/2*d**4 = 0. What is d?
-2, -1
Suppose m = 2*m, 0 = 2*x - m - 4. Let 2*t - 4*t**2 - 11*t**x + 9*t + 5*t**3 + 4*t - 5 = 0. What is t?
1
Factor 0 - 6*i**2 + 1/6*i**3 + 54*i.
i*(i - 18)**2/6
Suppose -2*x - 8 = -5*m + 2*x, -2*m = 2*x - 14. Factor 64*a**2 - m*a - 4*a**5 - 64*a**2 + 8*a**3.
-4*a*(a - 1)**2*(a + 1)**2
Let g(s) be the first derivative of -1/20*s**5 + 2/3*s**3 + 1/6*s**4 - 2 - 4*s**2 - 2*s. Let d(l) be the first derivative of g(l). Factor d(x).
-(x - 2)**2*(x + 2)
Let g be 230/161 - (2 - 54/21). Let r(d) be the second derivative of -1/18*d**4 + 1/9*d**3 + 1/3*d**g + 0 + 7*d - 1/30*d**5. Determine m so that r(m) = 0.
-1, 1
Let u(l) be the first derivative of 0*l**2 + 0*l**3 - 1/3*l**6 - 1/8*l**4 + 1/2*l**5 + 0*l + 12. Find a, given that u(a) = 0.
0, 1/4, 1
Let l(j) be the second derivative of 1/18*j**4 + 0*j**2 - 1/9*j**3 - 8*j - 1/45*j**6 + 1/30*j**5 + 0. Factor l(k).
-2*k*(k - 1)**2*(k + 1)/3
Determine l, given that -3/7*l**3 + 3/7*l + 9/7*l**2 - 3/7*l**4 - 6/7 = 0.
-2, -1, 1
Factor 20*c + c**3 - 32/3 - 32/3*c**2 + 1/3*c**4.
(c - 2)**2*(c - 1)*(c + 8)/3
Let j be (1/(-2))/((8/(-4))/12). Factor -21*l**2 - 5 + 9 - 14 - 3*l**j - 45*l - 17.
-3*(l + 1)*(l + 3)**2
Let c(p) be the first derivative of 2*p**3/45 - 2*p**2/3 + 32*p/15 - 7. Factor c(t).
2*(t - 8)*(t - 2)/15
Let l be 32/24 - 5338/(-24). Let n = -223 + l. Let 9/4*z**3 - n*z**4 - 9/4*z**2 + 0 + 3/4*z = 0. Calculate z.
0, 1
Factor 64/7 - 2/7*c**2 + 62/7*c.
-2*(c - 32)*(c + 1)/7
Let h(o) = 2*o**3 - 3*o - 17*o**2 + 196 - 2*o**2 - 183. Let u(p) = -p**3 + 6*p**2 + p - 4. Let v(z) = 4*h(z) + 14*u(z). Solve v(t) = 0.
-2/3, 1
Let o(p) be the first derivative of p**6/24 - 7*p**5/10 - 31*p**4/16 - 4*p**3/3 + 41. Find g such that o(g) = 0.
-1, 0, 16
Suppose -3 = -u, 3*g = 6*g + 3*u - 24. Suppose 4*v - g*s + 8 = 34, -14 = -4*v - s. Find y such that 3/2*y**v + 0*y**2 - 3/2 - 3*y + 3*y**3 = 0.
-1, 1
Let 8*p + p**2 - 8*p**3 - 4*p**4 - 4*p**2 + 7*p**2 = 0. Calculate p.
-2, -1, 0, 1
Factor 27*w**2 + 8*w**4 + w - 26*w**3 - 101*w**2 - 7*w + 26*w + 0*w**3.
2*w*(w - 5)*(w + 2)*(4*w - 1)
Suppose -3*t + 0*q + 4*q = 8, 2*t + 5*q = 33. Determine s so that 27*s**5 - 4*s**2 - s**3 + 4*s**t + 3*s**3 - 29*s**5 = 0.
-1, 0, 1, 2
Let f(n) be the first derivative of 2*n**5/5 - 7*n**4/2 - 8*n**3 + 176*n**2 - 640*n - 105. Find g, given that f(g) = 0.
-5, 4
Let l be -5 - (1/(-3))/(10/150). Let 3/5*y**3 + 6/5*y**4 + 0*y - 3/5*y**5 + l - 6/5*y**2 = 0. What is y?
-1, 0, 1, 2
Let v(n) be the third derivative of n**8/3360 - n**7/700 - 3*n**6/80 - 27*n**5/200 - 122*n**2 + 4. Factor v(x).
x**2*(x - 9)*(x + 3)**2/10
Let t(p) be the second derivative of p**5/60 + p**4/12 - p**3/3 - 4*p**2/3 + 20*p. Factor t(z).
(z - 2)*(z + 1)*(z + 4)/3
Let r = -1647 + 1647. Let h(k) be the second derivative of 1/72*k**4 + 0 - 1/12*k**3 + 5*k + r*k**2. Factor h(t).
t*(t - 3)/6
Let n be 3/(-2)*(-3 + (-3)/(-3)). Determine f so that 88*f + n*f**5 - 85*f - 14*f**2 - 12*f**4 + 2*f**2 + 18*f**3 = 0.
0, 1
Let r(f) be the first derivative of -f**7/6300 + f**5/300 + f**4/90 - 11*f**3/3 - 8. Let w(x) be the third derivative of r(x). Factor w(n).
-2*(n - 2)*(n + 1)**2/15
Let b(l) = -l**3 - 8*l**2 - 6*l + 9. Let s be b(-7). Let f be s/(-10) - 16/(-5). Solve 3*p + 6*p - p**2 - f*p - 4*p = 0.
0, 2
Let f = 1 + -1. Let m be f - (-6)/21*6. Factor 0 - 8/7*o**4 - 2/7*o**5 - 8/7*o**2 - 2/7*o - m*o**3.
-2*o*(o + 1)**4/7
Let b(d) be the second derivative of -8*d**6/35 + 174*d**5/35 + 17*d**4/4 + 15*d**3/14 + 276*d. Determine x, given that b(x) = 0.
-1/4, 0, 15
Let q(i) = 2*i**2 + 4*i + 2. Let a be q(-2). Factor 3*s**2 + 6*s - 2462 + 2464 + 3*s**2 + a*s**3.
2*(s + 1)**3
Find c, given that -50/7 + c**3 - 72/7*c**2 + 195/7*c = 0.
2/7, 5
Let m = 2/6489 - -7414/6489. Factor -m + 2/7*k**2 - 6/7*k.
2*(k - 4)*(k + 1)/7
Solve -1/3*x**2 - 1/3*x**3 + 16/3*x + 16/3 = 0 for x.
-4, -1, 4
Factor 19*o**4 + 6*o**5 + o**2 + 49*o**3 - 34*o**3 + o**2.
o**2*(o + 1)*(o + 2)*(6*o + 1)
Let o(x) = -x**4 - x**3 - 2. Let a(i) = 7*i**4 - 123*i**3 + 3072*i**2 - 32768*i + 131082. Let h(z) = 2*a(z) + 10*o(z). Factor h(j).
4*(j - 16)**4
Let b(h) = -h**3 + 10*h**2 + 15*h + 96. Let p(k) = k**3 - 6*k**2 - 15*k - 97. Let a(c) = 3*b(c) + 4*p(c). Let a(v) = 0. Calculate v.
-5, 4
Factor -2*b**3 + 30*b - 27*b**2 + 92 + 3*b**3 - 36 - 2*b**3 + 0*b**3.
-(b - 2)*(b + 1)*(b + 28)
Let c(x) = -4*x - 1. Let l(s) = s**2 - 6*s - 5. Let z(h) = 2*c(h) - l(h). Factor z(t).
-(t - 1)*(t + 3)
Find n, given that -8*n + 5*n**2 - 90 - 28*n + n = 0.
-2, 9
Let n(o) = 10*o + 60. Suppose 21 = 5*t + 51. Let a be n(t). Suppose 2/7*f**2 + 0*f + a = 0. Calculate f.
0
Let d be (12/(-26))/((-12)/156). Let j(l) be the second derivative of 0*l**3 + 1/45*l**d + 0 + 12*l + 1/30*l**5 + 0*l**4 + 0*l**2. Factor j(x).
2*x**3*(x + 1)/3
Let x = -132923/5 - -26699. Factor 0 + 242/5*u**4 - x*u**3 - 16/5*u + 184/5*u**2.
2*u*(u - 2)*(11*u - 2)**2/5
Let b = 1829 - 9103/5. Let n = 44/5 - b. Let 6/5*d**2 + n*d**3 + 4/5*d + 0 = 0. Calculate d.
-2, -1, 0
Let v(y) be the third derivative of -y**7/945 + y**5/45 - 2*y**4/27 + y**3/9 + 173*y**2. Factor v(u).
-2*(u - 1)**3*(u + 3)/9
Suppose f + 2 = 0, x - 4*f = 7 + 6. Suppose x*i - 3*i = p + 10, 4*p + 31 = 5*i. Factor -h + 18*h**4 - 5*h + 3*h**5 + 10*h**2 + h**5 - 4 + 0 + 26*h**i.
2*(h + 1)**3*(h + 2)*(2*h - 1)
Suppose -16*a = 4*j - 11*a - 31307, a + 39112 = 5*j. Let -5*v**3 - 5*v**4 + 10*v**2 + j*v - 7823*v = 0. What is v?
-2, 0, 1
Let k be ((-152)/(-66))/4*5 + -1. Let c = k - 6/11. Factor 0*u**2 - 2/3 + 2/3*u**4 + 4/3*u - c*u**3.
2*(u - 1)**3*(u + 1)/3
Let q = -35704 + 35704. Let 8/7*y**4 + 4/7*y**3 - 32/7*y**2 + q - 16/7*y = 0. Calculate y.
-2, -1/2, 0, 2
Factor -2/5*o - 8/5*o**2 + 4/5 + 6/5*o**3.
2*(o - 1)**2*(3*o + 2)/5
Let u(m) = -8*m**5 + 13*m**4 + 15*m**3 - 20*m**2 - 20*m + 3. Let n(o) = -o**5 + o**4 + 1. Let x = 82 + -81. Let y(v) = x*u(v) - 3*n(v). Factor y(t).
-5*t*(t - 2)**2*(t + 1)**2
Let a(k) = 4*k**2 - 4*k - 8. Let b be (-3 - (-2 - -4))*1. Let g(s) = 2*s**2 - 2*s - 4. Let i(u) = b*g(u) + 2*a(u). Factor i(o).
-2*(o - 2)*(o + 1)
Let y = 597/4 - 148. Let n = -2709 - -2711. Factor 1/4 + n*c**2 - c**3 - y*c.
-(c - 1)*(2*c - 1)**2/4
Find v, given that -152/11*v - 2/11*v**2 - 150/11 = 0.
-75, -1
Let v be 2/(-1 - -5) - 155/(-10). Suppose -z + 2*f + 7 = 0, 5*f + v = -0*z + 2*z. Solve 0 - 2/5*d**4 - 2/5*d - 6/5*d**z - 6/5*d**2 = 0 for d.
-1, 0
Suppose -3*k = -4*k + 3. Let h(g) be the first derivative of -2/3*g**k - 4*g - 3*g**2 + 4. Find z such that h(z) = 0.
-2, -1
Let d be (25 + -25)/(1 - (5 + -2)). Let q be ((-12)/45)/((-18)/30). Determine o, given that q*o + 2/9*o**3 + 2/3*o**2 + d = 0.
-2, -1, 0
Let o(j) = 3*j**2 - 6*j + 12. Suppose -5*y = -7*y + 4. Let z(t) = -3*t. Let h(i) = -7*i. Let x(w) = y*h(w) - 5*z(w). Let v(c) = -o(c) + 6*x(c). Factor v(d).
-3*(d - 2)**2
Suppose 100 - 35 = 5*f. Factor f*d**3 - d**2 - 16*d**3 + 7*d**2 + 0*d**2.
-3*d**2*(d - 2)
Suppose 29