, -1, 2
Let y(j) be the third derivative of -2*j**7/735 - 2*j**6/105 + j**5/105 + 2*j**4/21 + j**2 + 11. Factor y(u).
-4*u*(u - 1)*(u + 1)*(u + 4)/7
Let v(y) be the third derivative of -y**7/945 - y**6/108 - 4*y**5/135 - y**4/27 - y**2 - 8. Suppose v(b) = 0. What is b?
-2, -1, 0
Let o be (-14)/70*0/1. Solve o*g - 8/7*g**2 + 2/7 = 0 for g.
-1/2, 1/2
Let b(p) be the first derivative of 5*p**8/672 + p**7/84 - p**6/48 - p**5/24 - 21*p**2/2 + 17. Let z(h) be the second derivative of b(h). Factor z(s).
5*s**2*(s - 1)*(s + 1)**2/2
Suppose 254*l - 28*l + 4*l**2 - 43*l + 1600 - 23*l = 0. What is l?
-20
Let k be (6*(-21)/14)/(-21). Factor 0*v**4 - k*v + 6/7*v**3 - 3/7*v**5 + 0 + 0*v**2.
-3*v*(v - 1)**2*(v + 1)**2/7
Let r(m) be the first derivative of -m**4/14 - 4*m**3/3 - 44*m**2/7 - 80*m/7 + 102. Find a, given that r(a) = 0.
-10, -2
Let c(q) be the second derivative of 3*q**5/100 - 2*q**4/5 + 13*q**3/10 - 9*q**2/5 + 25*q. Solve c(g) = 0 for g.
1, 6
Let n(h) = 3*h**3 - 8*h**2 - 20*h. Let z(u) = 10*u**2 + 8 - 2*u**2 - 4*u**3 + 21*u - 8. Let p(t) = 5*n(t) + 4*z(t). Factor p(w).
-w*(w + 4)**2
Let l(z) be the first derivative of -z**6/39 + 2*z**5/65 + 11*z**4/26 + 14*z**3/39 - 10*z**2/13 - 16*z/13 + 452. Suppose l(f) = 0. What is f?
-2, -1, 1, 4
Let b(z) be the second derivative of -z**6/3 + 3*z**5/4 + 5*z**4/4 - 5*z**3/3 + 20*z. Factor b(t).
-5*t*(t - 2)*(t + 1)*(2*t - 1)
Let t = 5528 + -16552/3. Factor -80/3*s + 26/3*s**4 + t + 7/3*s**5 - 8/3*s**3 - 112/3*s**2.
(s - 2)*(s + 2)**3*(7*s - 2)/3
Let g(b) be the third derivative of b**6/90 + b**5/10 - 2*b**4/3 - 5*b**3/6 - 2*b**2. Let w(v) be the first derivative of g(v). Factor w(q).
4*(q - 1)*(q + 4)
Let n(k) be the third derivative of -k**5/20 - 19*k**4/2 - 722*k**3 + 126*k**2. Factor n(x).
-3*(x + 38)**2
Find t, given that -1/10*t**2 + 13/10*t - 21/5 = 0.
6, 7
Factor -544/5 + 536/5*o - 128/5*o**2 - 2/5*o**3.
-2*(o - 2)**2*(o + 68)/5
Let u be (-6)/51 + 248/85. Let a be 1*(72/(-135) + (-12)/(-9)). Let u*q - 8/5*q**3 - 2*q**2 + a = 0. Calculate q.
-2, -1/4, 1
Let h be (2 + -8)*(5 - (-321)/(-63)). Find y such that 2/7*y**2 + 2/7*y - h = 0.
-2, 1
Let w(p) = p**3 + 3*p**2 - 7*p + 3. Let g be w(-4). Solve 10*t + 12*t**3 + g*t**4 - 9*t**3 - 8*t**3 - 15*t**2 - 2*t**5 - 3*t**5 = 0.
-1, 0, 1, 2
Let n(j) be the second derivative of -j**6/10 + 21*j**5/20 - j**4/2 - 32*j**3 + 144*j**2 + 18*j - 7. Factor n(d).
-3*(d - 4)**2*(d - 2)*(d + 3)
Let m(g) be the third derivative of -g**8/45360 + g**7/4536 - g**6/1620 + 2*g**5/5 + 19*g**2. Let i(c) be the third derivative of m(c). Factor i(r).
-2*(r - 2)*(2*r - 1)/9
Let a(g) be the first derivative of 1/3*g**3 - 1/10*g**5 + 1/8*g**4 + 42 + 0*g + 0*g**2. Suppose a(o) = 0. What is o?
-1, 0, 2
Let p(c) be the third derivative of 0*c**3 + 0*c**5 + 0*c**4 - 1/300*c**6 - 30*c**2 + 0*c + 0. Let p(b) = 0. Calculate b.
0
Let -1/4*r**2 + 33/4 - 8*r = 0. Calculate r.
-33, 1
Suppose i - 5 = -44*r + 49*r, 2*r + 2 = -4*i. Let y be (i - 3/7)/((-52)/91). Suppose y*n**2 + 9/4*n + 0 = 0. Calculate n.
-3, 0
Let i(x) = -x**2 + 10*x. Let o(j) = 2*j. Let u(l) = -i(l) - 6*o(l). Let u(g) = 0. What is g?
0, 22
Let m(r) = -2*r + 14. Let i be m(-3). Let -28*p**2 + 0 - 44*p**3 + 2*p**5 + 18*p + 10*p + i*p**4 + 14*p**5 + 8 = 0. Calculate p.
-2, -1, -1/4, 1
Factor 0 + 18/7*p - 12/7*p**2 + 2/7*p**3.
2*p*(p - 3)**2/7
Let y be ((-7)/2)/((-3)/(-48)). Let m be (y/(-12) + -5)*0. Factor 8/5*z**3 - 2/5*z**2 + m*z + 0.
2*z**2*(4*z - 1)/5
Let z(c) be the third derivative of -7*c**6/810 - c**5/30 - c**4/27 - 5*c**3/6 + 12*c**2. Let g(m) be the first derivative of z(m). Factor g(d).
-4*(d + 1)*(7*d + 2)/9
Let m(v) be the third derivative of -v**6/600 + v**4/40 - v**3/15 + 11*v**2 - 1. Factor m(h).
-(h - 1)**2*(h + 2)/5
Let x = -6 - -6. Let o be -2*(0 + x + -1). Find g, given that g**2 - 3*g**3 - 9*g**o - 24 + 14*g**2 + 12*g = 0.
-2, 2
Suppose 13*y = 18*y - 20. Suppose y*b + 2*r + 1 = 11, 2*b - r + 5 = 0. Factor 2/5 - 2/5*m**2 + b*m.
-2*(m - 1)*(m + 1)/5
Let q(k) be the first derivative of -18 - 5/8*k**2 - 1/12*k**3 + 3/2*k. Suppose q(n) = 0. Calculate n.
-6, 1
Let x(i) be the third derivative of 9*i**7/280 - 3*i**6/32 - 2*i**5/5 - 3*i**4/8 + 13*i**2 - 9. Factor x(a).
3*a*(a - 3)*(3*a + 2)**2/4
Let a(m) be the second derivative of -m**4/48 + 15*m**3/8 - 5*m - 4. Factor a(t).
-t*(t - 45)/4
Let o(p) be the first derivative of -5*p**3/3 - 13*p**2 - 5*p - 104. Determine v, given that o(v) = 0.
-5, -1/5
Let b(x) be the third derivative of -x**5/360 + x**4/24 - 5*x**3/36 + 112*x**2. Factor b(q).
-(q - 5)*(q - 1)/6
Determine m, given that -16/3*m - 22/5*m**2 - 4/3*m**3 - 2/15*m**4 - 32/15 = 0.
-4, -1
Let s(a) be the third derivative of a**6/1020 + 4*a**5/255 - 206*a**2. Factor s(c).
2*c**2*(c + 8)/17
Let m(c) be the third derivative of -c**5/30 + 25*c**4/12 + 26*c**3/3 - 14*c**2 + 15*c. Factor m(v).
-2*(v - 26)*(v + 1)
Suppose -2/7*f**4 - 12/7*f + 0 - 2/7*f**5 + 2/7*f**2 + 2*f**3 = 0. Calculate f.
-3, -1, 0, 1, 2
Let r(g) be the first derivative of -2*g**5/5 + 21*g**4/2 - 274*g**3/3 + 279*g**2 - 324*g - 85. What is f in r(f) = 0?
1, 2, 9
Suppose 0 = 18*n + 2 - 74. Factor -3*z + 2*z**n - 6*z**2 - 7*z + 6*z.
2*z*(z - 2)*(z + 1)**2
Let q = -28/11 - -95/33. Let n(h) be the third derivative of -7/24*h**4 + 5*h**2 + 0 + 0*h - 1/12*h**5 - q*h**3. Factor n(y).
-(y + 1)*(5*y + 2)
Let u = -10839 + 10843. Solve 24/23*q**2 - 4/23 - 20/23*q**3 - 2/23*q + 6/23*q**5 - 4/23*q**u = 0.
-2, -1/3, 1
Let x(n) = 4*n**3 - 24*n**2 + 66*n - 60. Let y(l) = -l**3 + l**2 - l + 2. Let h(v) = x(v) + 2*y(v). Suppose h(t) = 0. Calculate t.
2, 7
Let h(q) = -82*q + 159*q - 6 - 81*q + 6*q**2. Let k(c) = c**2. Let r(i) = -h(i) + 4*k(i). Factor r(p).
-2*(p - 3)*(p + 1)
Let j(k) be the second derivative of -1/6*k**4 + 0 + 1/30*k**6 - 1/12*k**3 - 1/84*k**7 + 8*k + 1/2*k**2 + 1/20*k**5. Find f such that j(f) = 0.
-1, 1, 2
Let n = 1674 + -1672. Factor -w - 2/3 - 1/3*w**n.
-(w + 1)*(w + 2)/3
Suppose 4*b + 0*k = -3*k - 9, 9 = -3*k. Suppose 0 = -m + 2*n, 0 = 6*n - 5*n. What is t in 2/3*t**2 + m - 1/3*t**3 + b*t = 0?
0, 2
Let t(z) = z**3 - 5*z**2 - 4*z - 10. Suppose 3*b - 6 = 3*a, 0 = a + 3*a - 16. Let i be t(b). Factor -2/3*n**5 + 2/3*n**4 + 0*n**3 + 0*n**i + 0 + 0*n.
-2*n**4*(n - 1)/3
Suppose 0 = 2*u + 10, u + 20 = -268*v + 273*v. Solve 1/3*t**v + t**2 + 0 + 0*t = 0 for t.
-3, 0
Solve 139*j**2 - 140*j**2 + 3 - 12 + 10*j = 0 for j.
1, 9
Let a = 48952/5 - 9788. Factor -9/5 + a*u - 3/5*u**2.
-3*(u - 3)*(u - 1)/5
Suppose -5*k + 13 = -17. Let d(f) = -f**3 + 5*f**2 + 6*f + 2. Let w be d(k). Factor -32*m**4 - 8*m**w + 54*m**2 + 4*m - 10*m - 80*m**3.
-2*m*(m + 3)*(4*m - 1)**2
Let j = -77 + 77. Suppose 12*r - 8*r - 8 = j. Factor -2 + 7/2*z**4 + 27/2*z**r - 13*z**3 - 2*z.
(z - 2)*(z - 1)**2*(7*z + 2)/2
Let r(k) be the first derivative of -28 + 55*k - 5/3*k**3 - 25*k**2. Factor r(l).
-5*(l - 1)*(l + 11)
Factor 42*z**4 + 1395*z**2 + 980*z - 429*z**2 + 2*z**5 - 1914*z**3 + 2228*z**3.
2*z*(z + 2)*(z + 5)*(z + 7)**2
Let x(l) be the third derivative of -5*l**6/6 + 43*l**5/12 - 5*l**4/6 - 10*l**3/3 - 412*l**2. Find p such that x(p) = 0.
-1/4, 2/5, 2
Find s such that 0 - 1/3*s**3 + 0*s + 2/3*s**5 + 0*s**2 + 1/3*s**4 = 0.
-1, 0, 1/2
Let z be (20/60)/((-10)/(-6)). Factor -3/5*o**2 - z + 3/5*o + 1/5*o**3.
(o - 1)**3/5
Suppose -3/4*r**4 - 3/4 + 1/4*r - 1/2*r**3 + 1/4*r**5 + 3/2*r**2 = 0. What is r?
-1, 1, 3
Let d = 1387 - 1384. Determine b, given that 1/5*b**d + 2/5*b**5 - 3/5*b**4 + 0*b**2 + 0 + 0*b = 0.
0, 1/2, 1
Suppose 2*a = 18 - 2. Suppose 0 = 3*f - 10 - a. Determine g so that -2*g - 2 - 3*g + 3*g + f*g - 2*g**2 = 0.
1
Let d be (-2)/2*189/(-9). Let k be ((-12)/42)/((-15)/d). Solve 2/5 + 6/5*w**2 - 6/5*w - k*w**3 = 0 for w.
1
Let m be (2 - (6/3 - -1))*0. Suppose 4*x + 4 - 12 = m, -5*v + 3*x + 9 = 0. Factor 0*s**2 + 2/5*s**v + 4/5*s**4 + 2/5*s**5 + 0 + 0*s.
2*s**3*(s + 1)**2/5
Let a(o) = 5*o**2 + 354*o - 31686. Let r(q) = 3*q**2 - q - 1. Let g(d) = 5*a(d) - 10*r(d). Solve g(c) = 0.
178
Let f(b) be the first derivative of 3 - 1/3*b**3 + 0*b**2 - 1/20*b**5 + 0*b - 1/120*b**6 + 0*b**4. Let n(x) be the third derivative of f(x). Factor n(z).
-3*z*(z + 2)
Let q(n) be the third derivative of n**7/350 - 3*n**6/50 + 43*n**5/100 - 3*n**4/2 + 14*n**3/5 + 89*n**2. Let q(u) = 0. What is u?
1, 2, 