et n = 61371/8 - 7671. Let 0 - n*f**2 + 3/4*f = 0. What is f?
0, 2
Let g(z) be the first derivative of -z**4/16 - 3*z**3/4 + z**2/8 + 9*z/4 - 193. Suppose g(r) = 0. What is r?
-9, -1, 1
Let o(u) = 8*u**3 - 34*u**2 + 30*u - 2. Let l(j) = 10*j**3 - 35*j**2 + 31*j - 3. Let t(g) = 2*l(g) - 3*o(g). Factor t(d).
-4*d*(d - 7)*(d - 1)
Let g(v) be the first derivative of -1/24*v**4 + 1/2*v**3 - 11/12*v**2 + 2/3*v - 1/30*v**5 - 1. Find n such that g(n) = 0.
-4, 1
Let k(w) = -3*w**3 - 5*w**2 + 125*w + 123. Let f(z) = -80*z**3 - 135*z**2 + 3375*z + 3320. Let q(v) = -2*f(v) + 55*k(v). Determine h so that q(h) = 0.
-5, -1, 5
Let h(a) be the second derivative of -a**4/6 + 2*a**3/3 - a**2 - 4*a - 8. Factor h(t).
-2*(t - 1)**2
Let h(d) be the first derivative of d**4/16 + 16*d**3/3 + 128*d**2 - 191. Let h(m) = 0. Calculate m.
-32, 0
Let h(c) be the first derivative of -c**3/12 + 23*c**2/8 + 6*c + 20. Factor h(k).
-(k - 24)*(k + 1)/4
Factor -2/3*g**2 + 332/3*g - 13778/3.
-2*(g - 83)**2/3
What is p in -2*p**2 + 2/11*p**4 + 6*p - 10/11*p**3 - 36/11 = 0?
-3, 1, 6
Find d such that 0*d - 2/7*d**4 - 6/7*d**2 + 0 + 10/7*d**3 - 2/7*d**5 = 0.
-3, 0, 1
Let z(c) = 6*c**2 + 8*c + 5. Let r(w) = -9*w**2 - 11*w - 7. Let m(q) = 5*r(q) + 7*z(q). Find k such that m(k) = 0.
0, 1/3
Let v = -78 + 80. Suppose 0 = -2*s - s. Suppose -1/4*q - 1/8*q**v + s = 0. Calculate q.
-2, 0
Let d(o) = -341*o**3 - 773*o**2 + 2088*o - 883. Let k(n) = 114*n**3 + 258*n**2 - 699*n + 294. Let w(v) = 6*d(v) + 17*k(v). Factor w(i).
-3*(i + 4)*(6*i - 5)**2
Let l(k) be the third derivative of -3/280*k**7 + 0*k + 20*k**2 - 1/80*k**6 + 0*k**4 + 0*k**5 + 0 + 0*k**3 - 1/448*k**8. Factor l(s).
-3*s**3*(s + 1)*(s + 2)/4
Suppose 3*f = -3*s - s - 7, -5*f - 23 = s. Factor -3*d**4 - 293*d**3 - 7*d**s - 5*d**2 + 305*d**3.
-3*d**2*(d - 2)**2
Let a(x) be the first derivative of x**7/2520 - x**5/120 - x**4/36 - 2*x**3/3 + 32. Let v(t) be the third derivative of a(t). What is n in v(n) = 0?
-1, 2
Let z be 2 - (-4 + 6) - 21568/14. Let p = z - -1544. Factor 48/7 + p*b + 3/7*b**2.
3*(b + 4)**2/7
Let p = 314 + -601/2. Let o be ((-2 - -3)*-2)/((-4)/4). What is v in 36*v + 3/2*v**3 + 24 + p*v**o = 0?
-4, -1
Let c(n) = -12*n**4 - 44*n**3 + 36*n**2 - 46*n + 22. Let q(j) = j**4 + j**3 - j**2 + 2*j - 1. Let a(m) = 2*c(m) + 44*q(m). Factor a(k).
4*k*(k - 1)**2*(5*k - 1)
Let n(o) = -o + 1. Let w(g) = -12*g**3 + 28*g**2 - 11*g + 3. Suppose 2*x - 72 = 4*x. Let a = -37 - x. Let j(m) = a*w(m) + 3*n(m). What is v in j(v) = 0?
0, 1/3, 2
Let z = 2410 + -2407. Suppose 0 + h**z + 1/3*h + 1/3*h**4 + h**2 = 0. Calculate h.
-1, 0
Let r be 3026/1173 - (-20)/230. Factor 4/3*l**4 + 0*l**3 - r*l**2 + 0*l + 4/3.
4*(l - 1)**2*(l + 1)**2/3
Let y = -10 + 22. Let a(q) = -q**2 - 46*q - 358. Let v be a(-10). Let -14*u**4 + 46*u**3 + 78*u - 78*u - y*u**v = 0. What is u?
0, 2/7, 3
Let v be 0/((-1 - -2) + -2). Let z = 282 + -219. Determine b, given that -59*b**3 - 2*b + v*b**5 - 2*b**5 + z*b**3 = 0.
-1, 0, 1
Let c(n) be the second derivative of -n**6/120 + 11*n**5/80 - 19*n**4/48 + 3*n**3/8 + 11*n - 9. Solve c(y) = 0 for y.
0, 1, 9
Let q(o) be the first derivative of -o**4/10 - 2*o**3/15 + 6*o**2/5 - 148. Determine k, given that q(k) = 0.
-3, 0, 2
Suppose 92*w = -8465 + 8649. Let g be (-18)/(-15)*(-20)/(-6). Factor -4/3*m**3 + 0 - 8/3*m - g*m**w.
-4*m*(m + 1)*(m + 2)/3
Let r = -16 + 11. Let n = 17 + r. Solve -n*g - 6*g**2 - 8 - g**3 + 5*g**2 - 5*g**2 = 0 for g.
-2
Let i be 6/(-2*(-3)/(-159)). Let o = -1111/7 - i. Find f, given that -2/7*f + o - 4/7*f**2 + 4/7*f**3 + 2/7*f**4 - 2/7*f**5 = 0.
-1, 1
Let b(a) be the second derivative of -1/12*a**4 - 1/40*a**5 + 1 + 0*a**3 - 5*a + 0*a**2. Determine s, given that b(s) = 0.
-2, 0
Let y(d) be the third derivative of -d**6/40 - 5*d**5/2 - 84*d**4 - 576*d**3 + 12*d**2 - 13*d. Factor y(c).
-3*(c + 2)*(c + 24)**2
Let z(t) be the second derivative of -t**5/60 + t**4/12 - t**3/6 - 8*t**2 - 8*t. Let r(g) be the first derivative of z(g). Factor r(q).
-(q - 1)**2
Suppose 5*m - 11*m + 12 = 0. What is f in 22*f**3 + 45*f**4 - f**3 - f**m + 28*f**5 - f**5 + 4*f**2 = 0?
-1, -1/3, 0
Let t be (-21)/231*11*(-1 - 0)*2. Factor 2/19*w**t + 4/19*w + 2/19.
2*(w + 1)**2/19
Suppose 0 - 2/5*b**2 + 6/5*b = 0. What is b?
0, 3
Let f(t) be the second derivative of 0 + 0*t**2 - 8/3*t**3 - 1/3*t**4 - 35*t. Factor f(i).
-4*i*(i + 4)
Let v(z) be the first derivative of z**7/210 - z**6/75 + z**5/100 + 14*z + 2. Let u(b) be the first derivative of v(b). Factor u(f).
f**3*(f - 1)**2/5
Let j(o) = -42*o**3 + 1058*o**2 - 15589*o + 27051. Let y(w) = -8*w**3 + 212*w**2 - 3118*w + 5410. Let s(l) = 2*j(l) - 11*y(l). Find v, given that s(v) = 0.
2, 26
Suppose 0 = 2*z + s - 5, -4*z + 7*z - 4*s - 2 = 0. Solve 11*r + 0*r - 2*r**z - 5*r - 4 = 0 for r.
1, 2
Let h(s) be the second derivative of 9/17*s**2 + 0 + 1/102*s**4 + 24*s - 2/17*s**3. Factor h(a).
2*(a - 3)**2/17
Suppose 0*r = -5*r + 15. Let v be r/4*(3 - -5). Factor -4*o**4 - 2*o + 2*o**3 + 4*o**2 - v*o**3 + 6*o.
-4*o*(o - 1)*(o + 1)**2
Factor 4971 - f**3 - 12543*f - 61*f**2 + 2604 + 5194 - 123*f**2 - 41*f**2.
-(f - 1)*(f + 113)**2
Let s = -7838 + 7840. Solve 1/3 - 1/9*l**4 + 2/3*l**s + 8/9*l + 0*l**3 = 0 for l.
-1, 3
Let k(g) be the first derivative of -1 + 1/8*g**3 + 1/4*g + 7/16*g**2. Factor k(i).
(i + 2)*(3*i + 1)/8
Let g be (4/10)/(4/240). Factor -5*x + 0*x - 18*x**3 - 4*x + 3*x**5 + g*x**2.
3*x*(x - 1)**3*(x + 3)
Let t = 1192929/57589 + -2/8227. Let x = -683/35 + t. Factor -3/5*k**4 + 3/5*k**2 - 6/5*k + 0 + x*k**3.
-3*k*(k - 2)*(k - 1)*(k + 1)/5
Let t(q) = -9*q**2 + 14*q - 4. Let y(b) = 10*b**2 - 15*b + 5. Let f = -60 + 65. Let c(s) = f*t(s) + 4*y(s). What is z in c(z) = 0?
0, 2
Suppose 0*k - 26 = -k + x, -k - 3*x + 18 = 0. Suppose -6*f - 6 = -k. Find t such that 7*t + f*t**2 - 9*t + 2*t = 0.
0
Factor 2/5*g**3 - 18*g + 70 - 6/5*g**2.
2*(g - 5)**2*(g + 7)/5
Let r(p) be the first derivative of -p**7/126 + p**5/60 + 10*p - 7. Let d(m) be the first derivative of r(m). Let d(z) = 0. Calculate z.
-1, 0, 1
Let v = -3/27392 - -109589/191744. Factor 2*h**3 - v + 4/7*h**2 - 2*h.
2*(h - 1)*(h + 1)*(7*h + 2)/7
Suppose 54/5*j + 0 - 12/5*j**3 - 9/5*j**2 + 3/5*j**4 = 0. Calculate j.
-2, 0, 3
Suppose 2*d + d = 2*r + 14, 5*d - 4*r - 26 = 0. Let -2/5*p**3 + 8/5*p**d + 4/5 - 2*p = 0. Calculate p.
1, 2
Suppose 5*v - 7*v = -8. Factor 3*w**2 - w**2 + 4*w - 5*w**3 - 6*w**2 + w**3 + 4*w**v.
4*w*(w - 1)**2*(w + 1)
Let a be (5 - 1)/(-4 + 5). Suppose k = 5*z - 13, 2*z + a*k = 4 + 10. Solve 3*w**z + 0*w**2 + 4*w**3 + 4*w**4 + w**3 - 8*w - 4*w**2 = 0.
-2, -1, 0, 1
Let n(u) be the first derivative of -u**6/72 - u**5/4 + 35*u**4/24 - 10*u**3/3 - 2. Let y(h) be the third derivative of n(h). Factor y(r).
-5*(r - 1)*(r + 7)
Let s be 2 + 5 + 3 + -5. Factor -4*x + 6*x + 21*x**2 + 25*x**3 + s*x**4 + 13*x + 14*x**2.
5*x*(x + 1)**2*(x + 3)
Factor -5*x**2 - 913 + 188 + 603*x + 111*x + 16*x.
-5*(x - 145)*(x - 1)
Let h(x) be the third derivative of 0*x**3 + 0*x + 1/90*x**5 + 0 - 31*x**2 + 2/9*x**4. Let h(z) = 0. What is z?
-8, 0
Factor 0*u**2 - 27*u + 81/2 + 3*u**3 - 1/2*u**4.
-(u - 3)**3*(u + 3)/2
Let n be 1/2 + -13 + (-2928)/(-224). Let l(y) be the first derivative of 1/14*y**4 + 0*y - 8/21*y**3 + n*y**2 - 2. Suppose l(o) = 0. Calculate o.
0, 2
Let f(v) = v**3 + 2*v**2 - 14*v - 23. Let p be f(-2). What is d in 0 - 8/3*d**2 + 4/3*d - 4/3*d**p + 0*d**3 + 8/3*d**4 = 0?
-1, 0, 1
Let o(j) be the second derivative of 1/2*j**5 + 7/3*j**3 + 0 - 2*j**2 - 3/2*j**4 + 21*j - 1/15*j**6. Determine m, given that o(m) = 0.
1, 2
Let h(s) be the third derivative of -29/96*s**6 - 1/1344*s**8 + 9*s**3 - 6*s**2 - 45/8*s**4 + 15/8*s**5 + 0 + 0*s + 1/42*s**7. Determine z, given that h(z) = 0.
1, 6
Factor -82/7*x**2 + 2/7*x**3 + 0 - 172/7*x.
2*x*(x - 43)*(x + 2)/7
Let d be (-2)/8 + (-561)/(-68). Determine l so that d*l**2 - 32*l + 15*l - 4*l**3 + 17*l = 0.
0, 2
Let d(n) be the third derivative of -n**7/4200 + n**6/600 + 15*n**3/2 - 50*n**2. Let x(j) be the first derivative of d(j). Factor x(c).
-c**2*(c - 3)/5
Let h = 2011/1342 + 1/671. Factor 0*s**3 + 0 - h*s**2 + 1/2*s**4 + s.
s*(s - 1)**2*(s + 2)/2
Let v(y) = -21*y - 228. Let k be v(-11). Solve 0 + 1/7*f**k + 6/7*f**2 - f = 0.
-7, 0, 1
Suppose 30 = 5*l - 0*l. Factor 2*p**2 + 15*p**3 + 0*p**2 + 0*p**2 - l*p*