- 1/1344*c**8 + 1/30*c**5. Find u such that s(u) = 0.
-1, 2
Suppose 11*a - 20 = 15*a. Let o be ((-6)/60*a)/(0 - -2). Factor 0 + o*x + 1/4*x**2.
x*(x + 1)/4
Let i(u) = 2*u + 4. Let d be i(2). Let f = 11 - d. Factor -3/2*b**2 + 0 - 1/2*b**f - b.
-b*(b + 1)*(b + 2)/2
Let x(w) be the third derivative of -26*w**2 + 0*w**3 + 0 - 1/20*w**5 + 0*w - 1/4*w**4 + 1/40*w**6. Solve x(z) = 0 for z.
-1, 0, 2
Let h(o) be the second derivative of o**9/1728 + 5*o**8/5376 - o**7/1008 - o**4/12 + 10*o. Let f(w) be the third derivative of h(w). Factor f(z).
5*z**2*(z + 1)*(7*z - 2)/4
Suppose 10 = 2*u + 2*h - 0*h, 3*u + 4*h = 18. Find t, given that u*t**2 + 6*t - 2 + 4 + 2*t + 6 = 0.
-2
What is j in 69 - 15 - 23*j**3 + 117*j - 18*j**3 + 6 + 54*j**2 + 38*j**3 = 0?
-1, 20
Let a(k) = k**4 - k**3 - k**2 - 2*k - 1. Let o(v) = -5*v**4 - 4*v**3 + 5*v**2 + 10*v + 2. Let j(l) = -2*a(l) - o(l). Let j(s) = 0. Calculate s.
-2, -1, 0, 1
Suppose l - 4 = -3*a - 2, 4*l + 10 = -3*a. Suppose d + 3*z - 5 = 4*z, -4*d - 3*z = 1. Factor 20 + b - 22 - 5*b - a*b**d.
-2*(b + 1)**2
Suppose 2*l - 3*l = 2*r, -4*l - 2*r = -12. Suppose -76*s = -73*s. Determine n so that -3/4*n**2 + 3/4*n**l + s*n + 0*n**3 + 0 = 0.
-1, 0, 1
Let f be ((-6)/(-15))/(12/(-75))*-4. Let j be 8/f + 10/(-25). Factor -1/5*q**2 + j*q + 0.
-q*(q - 2)/5
Let u(a) = -a**2 - 675*a - 5334. Let l be u(-8). Factor 2/3*t + 1/6*t**3 + 2/3*t**l + 0.
t*(t + 2)**2/6
Factor -290/3*b**2 + 0 - 5/3*b**3 - 95*b.
-5*b*(b + 1)*(b + 57)/3
Let c(b) be the second derivative of 1/70*b**5 + 0 + 1/21*b**3 - 1/21*b**4 + 0*b**2 - 13*b. Factor c(h).
2*h*(h - 1)**2/7
Let u be 18/((-144)/(-20))*((-107)/(-95) + -1). Factor 0*h**2 + 2/19*h**4 + 0*h + 0 + u*h**3.
2*h**3*(h + 3)/19
Suppose 0 = -6*j + 9*j - 48. Suppose -2*k = -4, -m + j*k = 11*k + 8. Factor 6/5*b**m + 2/5*b - 6/5 - 2/5*b**3.
-2*(b - 3)*(b - 1)*(b + 1)/5
Let b be (7/(-245))/(24/(-5)). Let m(y) be the second derivative of 0 - 1/16*y**5 - b*y**7 + 4*y + 1/24*y**4 + 0*y**3 + 0*y**2 + 1/30*y**6. Factor m(t).
-t**2*(t - 2)*(t - 1)**2/4
Let j(v) = v**3 + 7*v**2 + 6. Let i be j(-7). Suppose -i = -y + 5. Factor -4*q**3 - 23*q**5 + 2*q**4 + 14*q**5 + y*q**5.
2*q**3*(q - 1)*(q + 2)
Let x(d) be the third derivative of 2*d**7/35 - 3*d**6/40 - d**5/4 + 3*d**4/8 + d**3/2 - 54*d**2. Factor x(k).
3*(k - 1)**2*(k + 1)*(4*k + 1)
Find n, given that -228*n**2 - 6*n - 8*n + 223*n**2 - 116*n - 845 = 0.
-13
Let w(s) = -11*s**2 + 6. Let o(r) = -5*r**2 + 3. Let d be (0 + -105)/(-5)*1. Let l = d + -16. Let a(y) = l*o(y) - 2*w(y). Factor a(k).
-3*(k - 1)*(k + 1)
Let p(l) = -2*l**2 + 8*l + 3. Let u(g) = -g**2 + 6*g + 2. Let t(o) = -2*p(o) + 3*u(o). Suppose t(i) = 0. Calculate i.
-2, 0
Let s(p) = -p**2 - 16*p + 21. Let d be s(-17). Let 7*l**2 + 0*l**2 - d + 16*l**3 + 8*l + 21*l**2 = 0. What is l?
-1, 1/4
Let l(m) be the second derivative of m**6/255 - 2*m**5/85 + 5*m**4/102 - 2*m**3/51 + 37*m. Suppose l(z) = 0. What is z?
0, 1, 2
Suppose 3*g - 5*d = -14, -14 = -g - 2*d - d. Let u be (10 - 38/4)/1. What is a in 5/4*a**4 + 0 + 1/4*a - u*a**5 - 1/4*a**g - 3/4*a**3 = 0?
-1/2, 0, 1
Let p(u) be the second derivative of 30*u + 0*u**2 + 2/75*u**6 + 0*u**3 + 1/5*u**4 + 2/105*u**7 + 0 - 1/5*u**5. Factor p(t).
4*t**2*(t - 1)**2*(t + 3)/5
Suppose 3*r + 2*d - 5*d = 24, -4*d = -r + 20. Factor 16 - 16*c**2 + 48*c**5 - 49*c**5 + 4*c**3 - c**4 + r*c**4.
-(c - 2)**3*(c + 1)*(c + 2)
Let a = 3541/12369 - 1/1767. Factor j**3 + 0 + a*j**2 + 0*j.
j**2*(7*j + 2)/7
Let o(t) be the third derivative of 0*t + 1/8*t**6 - 27*t**2 - 1/42*t**7 + 0*t**3 + 0 + 0*t**5 - 5/6*t**4. Factor o(m).
-5*m*(m - 2)**2*(m + 1)
Suppose -2*p - 2*d + 4 = 0, -110*p + 10 = -105*p - 5*d. Let 3/2*q**p + 0 - 3/2*q - 3/8*q**3 = 0. What is q?
0, 2
Let b(s) = -5*s**2 - 38*s - 101. Let v(q) = -5*q**2 - 41*q - 102. Let z(m) = -3*b(m) + 4*v(m). Factor z(u).
-5*(u + 3)*(u + 7)
Let g be (-5)/(-20)*(-8 - -14). Determine a, given that -3/2*a + g*a**2 + 0 = 0.
0, 1
Let v(l) be the second derivative of 0*l**2 + 1/140*l**5 - 1/70*l**6 + 0 - 1/42*l**3 + 1/28*l**4 - 17*l. Determine q, given that v(q) = 0.
-1, 0, 1/3, 1
Let p(h) = 7*h**2 + 9*h + 10. Let d(v) = -6*v**2 - 9*v - 9. Suppose -7*r = -5*r + 6. Let w(t) = r*p(t) - 4*d(t). Factor w(y).
3*(y + 1)*(y + 2)
Let 41*d**3 - 12 + 0*d**4 + 9*d**4 + 36*d - 33*d**2 - 29*d**3 - 9*d**3 - 3*d**5 = 0. Calculate d.
-2, 1, 2
Let n = 10737/5 + -2147. Factor -2/5 - n*p**2 - 4/5*p.
-2*(p + 1)**2/5
Let n(y) = -y + 13. Let x(z) = 1. Let u(g) = -n(g) + 5*x(g). Let k be u(12). Factor -2*v**3 + 2*v**k + 5*v**2 + 8*v**3 - v**2.
2*v**2*(v + 1)*(v + 2)
Let z(u) be the third derivative of -5/24*u**5 - 35/48*u**4 - 20*u**2 + 0 + 0*u - 5/6*u**3. Suppose z(g) = 0. What is g?
-1, -2/5
Suppose -4*s - 8 + 108 = 0. Let n = -95 - -97. Solve -19*a - 8*a**2 - s*a + 19 - 4*a**n - 3 = 0 for a.
-4, 1/3
Let s(q) be the second derivative of -3*q**5/40 - q**4 - 7*q**3/4 + q - 57. Factor s(u).
-3*u*(u + 1)*(u + 7)/2
Let k(w) = -w**3 - w - 1. Let n(z) = -2*z**3 - 19*z**2 - 45*z - 3. Let i(m) = -3*k(m) + n(m). Factor i(d).
d*(d - 21)*(d + 2)
Let i(f) be the third derivative of -f**8/3192 + f**7/665 + f**6/190 - 13*f**5/285 + 9*f**4/76 - 3*f**3/19 + 2*f**2 - 13*f. Determine s so that i(s) = 0.
-3, 1, 3
Let q(d) be the third derivative of d**8/5880 - d**6/630 + d**4/84 + 11*d**3/6 + 10*d**2. Let r(s) be the first derivative of q(s). Factor r(w).
2*(w - 1)**2*(w + 1)**2/7
Let 81/2*x - 87/2*x**4 + 147*x**3 + 81/2 - 189*x**2 + 9/2*x**5 = 0. What is x?
-1/3, 1, 3
Let f = 69 + -66. Determine n so that -3*n**f + 4*n**4 - 8*n**2 - 6*n**2 + 6*n**2 - n**3 = 0.
-1, 0, 2
Let x = 616 - 608. Let u(p) be the third derivative of 0*p**3 + 0*p**5 + x*p**2 - 1/120*p**6 + 1/48*p**4 + 0*p + 1/672*p**8 + 0*p**7 + 0. Factor u(n).
n*(n - 1)**2*(n + 1)**2/2
Find g, given that 361/4 - 19/2*g + 1/4*g**2 = 0.
19
Let f(y) = 2*y + 27. Let h be f(-14). Let d(o) = o**3 - o**2. Let l(w) = -4*w**3 + 22*w**2 + 32*w. Let b(j) = h*l(j) - 6*d(j). Determine t, given that b(t) = 0.
-4, 0
Let v(k) be the first derivative of -3/5*k**5 + 12*k + 3*k**4 - 6*k**2 - 3*k**3 + 9. Factor v(h).
-3*(h - 2)**2*(h - 1)*(h + 1)
Let f(w) be the third derivative of -2/3*w**3 + 0 + 0*w + 11*w**2 + 1/4*w**4 + 1/180*w**6 + 1/15*w**5. Let q(v) be the first derivative of f(v). Factor q(d).
2*(d + 1)*(d + 3)
Factor -6/5*k + 1 + 1/5*k**2.
(k - 5)*(k - 1)/5
Let c be (6/12)/((-1)/(-6)). Factor 4*m**c - 3*m**2 - m**3 - 6*m**5 + 3*m**5 + 3*m**4.
-3*m**2*(m - 1)**2*(m + 1)
Let r = -14/11 - -111/44. Let g = 23/4 - r. Solve -3*i**3 + 3/4 - 3*i + g*i**2 + 3/4*i**4 = 0.
1
Factor -3*m**4 - 18*m + m**4 - 29*m**2 - 9*m**2 - 3*m**4 - 22*m**3 + 3*m**4.
-2*m*(m + 1)**2*(m + 9)
Let p(s) = -102*s**5 - 172*s**4 - 48*s**3 + 20*s**2 - 6*s + 4. Let w(h) = -h**5 - h**4 - h**3 - h**2 - h + 1. Let y(t) = -p(t) + 4*w(t). Factor y(f).
2*f*(f + 1)**2*(7*f - 1)**2
Suppose -2*c = 8, -3*c = -2*f - 2*c + 24. Let x be (-24)/14 + (-3)/((-15)/f). Solve 0 + x*v**2 - 2/7*v = 0 for v.
0, 1
Let x(b) be the first derivative of 2*b**5/85 + 15*b**4/17 + 128*b**3/17 - 512*b**2/17 - 189. Determine c so that x(c) = 0.
-16, 0, 2
Let c(m) be the second derivative of -m**10/15120 + m**9/7560 + m**4/4 - 7*m. Let x(k) be the third derivative of c(k). Solve x(h) = 0.
0, 1
Let b(i) be the second derivative of -i**6/135 + i**5/30 + i**4/18 - 7*i**3/27 - 2*i**2/3 + 11*i + 2. What is v in b(v) = 0?
-1, 2, 3
Let r be -20*16/(800/(-10)). Let -5/2*b - 3/2*b**2 + 2 - 1/2*b**r + 5/2*b**3 = 0. What is b?
-1, 1, 4
Let y = -37 - -39. Suppose y*n - 10 + 30 = -4*f, n - 3*f - 15 = 0. Factor -1/2*q + 1/4 + 1/2*q**3 + n*q**2 - 1/4*q**4.
-(q - 1)**3*(q + 1)/4
Let z(j) be the first derivative of 3/20*j**5 - 3/16*j**4 - 3/2*j + 15/8*j**2 - 3/4*j**3 - 35. Factor z(d).
3*(d - 1)**3*(d + 2)/4
Let r(t) = -17*t**2 - t - 2 + 4*t**2 - 2*t**3 - 4*t - 8*t. Let v(p) = -12*p**2 - p - 13*p - 2 + 2*p - 2*p**3. Let g(s) = 6*r(s) - 7*v(s). Factor g(a).
2*(a + 1)**3
Let r(j) be the first derivative of -5*j**3/3 - 45*j**2/2 - 100*j + 223. Factor r(k).
-5*(k + 4)*(k + 5)
Factor 60*n**2 + 52*n**3 + 24*n**4 + 11*n**4 + 28*n + 4 - 37*n**4 + 18*n**4.
4*(n + 1)**3*(4*n + 1)
Let w(i) be the first derivative of -i**6/40 + 7*i**5/20 - i**4 - 8*i**3 + 9*i**2 - 1. Let a(c) be the second derivative of w(c). Factor a(n).
-3*(n - 4)**2*