 -z - 1/3*a**3 - a**2 - a = 0. Calculate a.
-1
Let o(g) be the third derivative of -1/84*g**4 - 3*g**2 - 1/420*g**5 + 0*g + 0 + 0*g**3. Let o(t) = 0. What is t?
-2, 0
Let -2/9*c + 2/9*c**3 + 2/9*c**2 - 2/9 = 0. Calculate c.
-1, 1
Factor -1148*p**3 + 1148*p**3 - 5*p**5.
-5*p**5
Let s = 1/61 - -117/305. Let h(y) = -y**3 - y**2 + y. Let p be h(-2). What is o in -s - 6*o**p + 14/5*o + 18/5*o**3 = 0?
1/3, 1
Suppose -5*k - 17 = -0*n - n, k = 3*n - 9. Factor -2/5*u**4 + n*u**3 + 0 + 8/5*u - 16/5*u**2.
-2*u*(u - 2)**2*(u - 1)/5
Let o be (-110)/(-4)*4/(-2). Let y be o/(-15)*1 - 3. Solve -2/3*f - y + 2/3*f**2 + 2/3*f**3 = 0 for f.
-1, 1
Factor 2*r + 2*r - 20*r**3 - 3*r + 4*r + 15*r**2.
-5*r*(r - 1)*(4*r + 1)
Let r(k) be the third derivative of 0 + 0*k + 1/180*k**5 + 0*k**4 - 4*k**2 + 0*k**3. Solve r(l) = 0 for l.
0
Let c(n) be the third derivative of -11*n**7/7560 - n**6/1080 + n**4/6 + 5*n**2. Let k(t) be the second derivative of c(t). Let k(a) = 0. Calculate a.
-2/11, 0
Let i = 26 + -28. Let c(v) = -v**2 - 2*v + 5. Suppose p + 5*w - 15 = w, 0 = 5*p - w - 12. Let m(j) = -3*j + 6. Let l(t) = i*m(t) + p*c(t). Factor l(x).
-3*(x - 1)*(x + 1)
Let x(o) be the first derivative of o**5/10 - o**4/8 - o**3/6 + o**2/4 + 4. What is r in x(r) = 0?
-1, 0, 1
Let l(q) be the first derivative of -2*q**7/21 + 4*q**6/15 - 2*q**4/3 + 2*q**3/3 + 3*q + 3. Let o(i) be the first derivative of l(i). Factor o(t).
-4*t*(t - 1)**3*(t + 1)
Factor 2/5*z + 2/5*z**2 + 2/15*z**3 + 2/15.
2*(z + 1)**3/15
Let q(p) be the third derivative of p**5/60 - p**4/6 + p**3 + 2*p**2. Let r be q(4). What is x in r*x**3 - 6*x**2 + x**4 - 2*x - 3*x**4 + 4*x = 0?
0, 1
Factor 12*h**2 + 6 - 11*h - h**3 - 4*h - 2*h**3.
-3*(h - 2)*(h - 1)**2
Let s(k) be the first derivative of 1/5*k**2 + 8/25*k**5 + 8/15*k**3 + 3/5*k**4 + 1/15*k**6 + 2 + 0*k. Factor s(v).
2*v*(v + 1)**4/5
Let z(l) = 3*l. Let n be z(1). Let d(i) = i**2 - 3*i + 3. Let g be d(2). Factor -3*f**3 - f**n - g + f**4 + 2*f + 2*f**3.
(f - 1)**3*(f + 1)
Let r(g) be the first derivative of -g**5/20 - 13*g**4/16 - 5*g**3 - 14*g**2 - 16*g + 9. Factor r(t).
-(t + 1)*(t + 4)**3/4
Let s = -310 + 310. Factor 0 + 2/7*n**2 + s*n - 2/7*n**3.
-2*n**2*(n - 1)/7
Suppose -2*c = 2*n - 4 - 0, 0 = 2*n + 3*c - 4. Find i, given that 0 + i**n - 2*i**2 + 0 = 0.
0
Factor 0*l**5 - 179*l**3 - 3*l**4 + 181*l**3 + l**5.
l**3*(l - 2)*(l - 1)
Let s(r) be the first derivative of 7*r**4/4 - 26*r**3/3 + 10*r**2 + 8*r + 1. Let s(p) = 0. Calculate p.
-2/7, 2
Suppose 0 = -5*r - 2*o, -4*r + 2*r + 24 = -4*o. Factor 0*m + 16/7 - 4/7*m**r.
-4*(m - 2)*(m + 2)/7
Let u(x) be the third derivative of 1/6*x**4 + 4*x**2 - 1/60*x**5 + 0*x + 0 + 1/6*x**3 - 1/30*x**6. Determine a so that u(a) = 0.
-1, -1/4, 1
Factor -2/5*c**2 + 0 + 2/5*c.
-2*c*(c - 1)/5
Let q = -51/4 - -53/4. Factor 3/2*j**3 + q*j + 3/2*j**2 + 1/2*j**4 + 0.
j*(j + 1)**3/2
Let i = -688735/91 + 7568. Let z = -3/13 - i. Find q such that z*q - 2/7*q**2 + 0 = 0.
0, 1
Let d(f) be the first derivative of 3*f**4/10 - 2*f**3/3 + 2*f**2/5 - 3. Factor d(j).
2*j*(j - 1)*(3*j - 2)/5
Let m(w) = -w - 5. Let p be m(-5). Let s be p - -1 - (-14)/(-18). Factor 8/9 + s*j**2 - 8/9*j.
2*(j - 2)**2/9
Let r = 319/2 + -158. Find h, given that 0*h**2 + 0 - r*h**3 + 3/2*h = 0.
-1, 0, 1
Suppose -5*b = 2*o - 11, -3*b = 2*o - 8*b - 1. Factor 35*d + 13*d + 27*d**o - 16*d**2 - 12 - 47*d**2.
3*(d - 1)*(3*d - 2)**2
Let w(h) be the second derivative of 0*h**3 + 0 + 4*h**2 - 7/6*h**4 + 3/10*h**5 + h. Factor w(x).
2*(x - 2)*(x - 1)*(3*x + 2)
Let p(f) be the first derivative of -5*f**4/12 - 22*f**3/9 - 4*f**2/3 - 21. Factor p(r).
-r*(r + 4)*(5*r + 2)/3
Let z(d) be the third derivative of -d**6/780 + d**5/130 - 15*d**2. Suppose z(r) = 0. Calculate r.
0, 3
Solve -2/5*s**3 + 0*s**2 + 6/5*s + 4/5 = 0 for s.
-1, 2
Let v(q) be the first derivative of 0*q - 4/35*q**5 + 4 + 0*q**3 - 3/14*q**4 + 1/7*q**2. Factor v(c).
-2*c*(c + 1)**2*(2*c - 1)/7
Suppose 6 = -2*q, -4*s = -2*q + q - 15. Let t be s - 0/(1 + -4). Factor 2*d + 0*d + d**3 + 4*d**2 + d**t.
2*d*(d + 1)**2
Let l(h) be the second derivative of -2*h**5/5 + 5*h**4/6 + 7*h**3/3 - 2*h**2 - 4*h. Let l(i) = 0. Calculate i.
-1, 1/4, 2
Let g(o) be the first derivative of -o**3/12 - 3*o**2/2 - 9*o - 39. Solve g(r) = 0 for r.
-6
Let m(d) = -15*d**3 + 2*d**2 + 40*d + 23. Let y(g) = -45*g**3 + 5*g**2 + 120*g + 70. Let l(n) = -10*m(n) + 3*y(n). Find r, given that l(r) = 0.
-1, -2/3, 2
Let c(x) = 5*x**4 - 8*x**2 + 3. Let n(d) = -6*d**4 + 9*d**2 - 3. Let o be 2 + -3 + 4 + 0. Let q(a) = o*c(a) + 2*n(a). Factor q(v).
3*(v - 1)**2*(v + 1)**2
Let g(h) be the second derivative of -h**8/840 + h**7/140 - h**6/60 + h**5/60 + h**3/2 + 2*h. Let a(d) be the second derivative of g(d). Solve a(k) = 0 for k.
0, 1
Factor 2*j**3 - 5/2*j - 2*j**4 + j**2 + 1 + 1/2*j**5.
(j - 2)*(j - 1)**3*(j + 1)/2
Suppose 0 = 2*u - 5*f + 11, -5*u - f = -5*f + 2. Find a such that 2/3*a**3 + 0*a**2 - u*a - 4/3 = 0.
-1, 2
Let k(m) be the third derivative of -7*m**5/20 + 43*m**4/4 - 12*m**3 - m**2 + 16. Find i, given that k(i) = 0.
2/7, 12
Suppose -4*i = -370 - 98. Let l be (-18)/i - (-88)/234. Determine c, given that 4/9*c - 2/9 - l*c**2 = 0.
1
Let a be (-2 + (-27)/(-15))/(24/(-60)). Factor h**2 + 1/2*h + 0 + a*h**3.
h*(h + 1)**2/2
Factor 0 + 2/5*k**2 + 2/5*k.
2*k*(k + 1)/5
Let d = 8 - 4. Factor 0*q**d + 5*q**2 + q**4 + 4*q - 2*q + 4*q**3.
q*(q + 1)**2*(q + 2)
Suppose 2*v - b + 2*b = -6, 0 = -2*b. Let z be -3*(1 + 1 + v). Factor -k**4 + 27*k**2 + 6 + z*k**3 - 18*k**3 + 4*k**4 + 0 - 21*k.
3*(k - 2)*(k - 1)**3
Let t(x) be the third derivative of -5/72*x**4 - 1/6*x**3 + 1/360*x**6 + 0 - 1/180*x**5 + 0*x + x**2. Factor t(m).
(m - 3)*(m + 1)**2/3
Let b(a) be the third derivative of a**6/40 + 21*a**5/20 + 147*a**4/8 + 343*a**3/2 - 6*a**2. Factor b(j).
3*(j + 7)**3
Let m(z) be the third derivative of z**9/12096 + z**8/3360 + z**7/3360 - z**3/2 - 3*z**2. Let k(b) be the first derivative of m(b). Factor k(n).
n**3*(n + 1)**2/4
Factor -5*b**4 - 17*b**2 + 27*b**2 + 0*b**4 + 5*b**3.
-5*b**2*(b - 2)*(b + 1)
Let u(z) be the second derivative of -2*z**6/3 - 12*z**5/5 - 3*z**4 - 4*z**3/3 - 8*z. Let u(t) = 0. Calculate t.
-1, -2/5, 0
Let i(f) be the third derivative of -f**4/24 - f**3/2 + 2*f**2. Let z be i(-3). Factor 1/2*d**5 + d**4 + 1/2*d**3 + 0 + 0*d + z*d**2.
d**3*(d + 1)**2/2
Let r be (-13)/(-91)*-2 - (-50)/28. Factor -11/2*f**2 - 1/2*f + r - 7/2*f**3.
-(f + 1)**2*(7*f - 3)/2
Suppose 40/11*u**3 - 40*u - 156/11*u**2 - 2/11*u**4 - 22 = 0. What is u?
-1, 11
Let i(m) = 10*m + 12. Let x be i(-9). Let p be (-40)/x + (-4)/(-26). Find t, given that -4/3*t + p*t**2 + 2/3 = 0.
1
Let c be 6/21 + (-4)/14. Suppose -4*b - 4*m + 40 = 0, b - 18 = -c*b - 3*m. Factor -b*r**2 - r - 3*r - 3*r**3 + 0*r + r**3.
-2*r*(r + 1)*(r + 2)
Let x(b) be the third derivative of 1/630*b**7 - 1/90*b**5 - 4*b**2 + 0*b**6 + 0*b + 0*b**4 + 1/18*b**3 + 0. Factor x(g).
(g - 1)**2*(g + 1)**2/3
Let i(l) be the first derivative of 1/10*l**5 + 2*l**2 - 1/3*l**3 - 1/3*l**4 + 2 + l. Let f(s) be the first derivative of i(s). Factor f(x).
2*(x - 2)*(x - 1)*(x + 1)
Factor 0 - 2/5*v**2 - 6/5*v.
-2*v*(v + 3)/5
Let g(h) = h - 4. Let q be g(6). Suppose -i + 0*i = -q. Factor m**4 - 6*m + m + m**2 + 8*m**i + 2 + 12*m + 5*m**3.
(m + 1)**3*(m + 2)
Let n(o) be the third derivative of 0*o - 7/120*o**4 - 1/600*o**6 - 1/60*o**5 + 6*o**2 - 1/10*o**3 + 0. Factor n(y).
-(y + 1)**2*(y + 3)/5
Suppose -2*a = -0*a. Suppose a = -2*r + 4 + 2. Find y such that 4/5 + 2/5*y**r + 6/5*y**2 - 2/5*y**4 - 2*y = 0.
-2, 1
Suppose -5*v + 12 = 2. Find h, given that 2*h**v - 307 + 307 = 0.
0
Let k(n) be the first derivative of -n**3/6 - 9*n**2/4 - 4*n - 74. Factor k(a).
-(a + 1)*(a + 8)/2
Factor z**2 - 4*z - 4*z**4 - 37*z**3 + 35*z**3 + 9*z**2.
-2*z*(z - 1)*(z + 2)*(2*z - 1)
Let w(q) be the first derivative of -1/4*q**2 - 1/3*q**3 + 3 + 1/5*q**5 + 1/12*q**6 + 0*q**4 + 0*q. Factor w(t).
t*(t - 1)*(t + 1)**3/2
Let -2/9 - 2/9*t**4 - 4/3*t**2 - 8/9*t**3 - 8/9*t = 0. Calculate t.
-1
Let p = 0 + 2. Suppose a + 2 = 3*a - t, -5*t + 4 = -3*a. Factor 2*h + h - 3*h**p + h + 2*h**a - 4.
-(h - 2)**2
Suppose 18*u - 5*o = 19*u - 27, -3*o + 19 = 2*u. Factor 24*d - 135/4*d**4 + 27/4*d**5 - 56*d**u - 4 + 63*d**3.
(d - 2)*(d - 1)*(3*d - 2)**3/4
Let b(h) = 3*h**3 - h**2 - h