2
Factor -4/3 - 2/3*q**2 + 7/3*q - 1/3*q**3.
-(q - 1)**2*(q + 4)/3
Let t = 25493/5 + -5093. Let -t*z**3 + 3/5*z**4 + 27/5 - 108/5*z + 18*z**2 = 0. What is z?
1/3, 3
Let r(h) be the third derivative of 0 + 0*h**5 + 0*h**3 + 0*h**4 - 1/40*h**6 + 23*h**2 + 0*h. Factor r(a).
-3*a**3
Let p(c) be the second derivative of -c**6/80 - 11*c**5/120 - c**4/8 + 11*c**2 + 9*c. Let j(q) be the first derivative of p(q). Factor j(k).
-k*(k + 3)*(3*k + 2)/2
Suppose 74 = 2*p + 72. Let o(v) = v**3 + 3*v**2 - 2. Let j be o(p). Suppose 0 + 4/3*d + 2/3*d**j = 0. Calculate d.
-2, 0
Let v(z) be the third derivative of z**9/141120 + z**8/15680 + z**5/30 + 3*z**2. Let p(a) be the third derivative of v(a). Determine x, given that p(x) = 0.
-3, 0
Find c, given that 3*c**4 - 3*c**5 + 36*c + 18*c**3 - 9*c**2 - 3*c - 9 - 33*c**2 = 0.
-3, 1
Let i(h) = 19*h**3 - h**2 - 10*h - 4. Let n(s) = 20*s**3 - 10*s - 5. Let r be 44/10 + 6/(-15) + 0. Let q(k) = r*n(k) - 5*i(k). Factor q(d).
-5*d*(d - 1)*(3*d + 2)
Factor 1/3*p**4 - 35/3*p**3 - 19208/3 + 98*p**2 + 1372/3*p.
(p - 14)**3*(p + 7)/3
Let t be 159/51 + 72/(-34) + 2. Let p(y) be the third derivative of -1/200*y**6 + 0*y + 3/100*y**5 + 3*y**2 + 0 - 3/40*y**4 + 1/10*y**t. Factor p(l).
-3*(l - 1)**3/5
Determine j, given that -26*j**2 - 2176/5*j - 2/5*j**3 - 2048/5 = 0.
-32, -1
Find q such that 6*q**4 + 5*q**2 + 12*q**3 + q**2 - 6*q**3 + 9*q**3 = 0.
-2, -1/2, 0
Let o(g) = 1. Let z(t) be the second derivative of -t**5/20 + t**4/12 + t**3/6 + t**2 + 7*t. Let y(j) = -6*o(j) + 2*z(j). Factor y(n).
-2*(n - 1)**2*(n + 1)
Let 12*v**4 - 18*v**2 - 16*v**5 + 84*v - 9*v**3 - 2*v**2 + 8*v**2 + 29*v**3 - 88*v = 0. Calculate v.
-1, -1/4, 0, 1
Suppose 4*o + 73 = -5*n + 70, o = 5*n + 18. Factor -2/5*z + 0 + 4/5*z**o + 0*z**4 + 0*z**2 - 2/5*z**5.
-2*z*(z - 1)**2*(z + 1)**2/5
Let m be (-2)/(-4)*0/(-28). Solve 0 - 3/2*y**2 + m*y = 0 for y.
0
Let b = 112 - 106. Factor -3*i**5 + b*i**4 - 3*i**2 - 10*i**2 + 3*i + 0*i + 7*i**2.
-3*i*(i - 1)**3*(i + 1)
Suppose -6 = -3*k - 2*w, -2*k - w = w - 4. Suppose 0 = k*j + d - 1, 4*j - 17 = -d + 2*d. Factor -4*b**4 + 0*b + 4*b**2 + j*b + b - 4*b**3.
-4*b*(b - 1)*(b + 1)**2
Factor -16*q**2 + 14/5*q**3 + 36/5 + 102/5*q.
2*(q - 3)**2*(7*q + 2)/5
Let f be 2/4 - 28/(-8). Let m be 60/16 + 1/f. Solve 5 - 6*q**2 + 2*q**m + 2*q + 10*q**3 - 1 - 12*q**3 = 0 for q.
-1, 1, 2
Let a(h) be the second derivative of 0*h**5 + 1/210*h**6 + 0*h**3 + 0 + 0*h**4 + 3*h - 3*h**2. Let p(u) be the first derivative of a(u). Factor p(g).
4*g**3/7
Let a(u) be the first derivative of u**3/6 - 113*u**2/4 + 524. Factor a(x).
x*(x - 113)/2
Let k(w) be the third derivative of -1/6*w**4 + 0 - 1/105*w**7 + 0*w**3 + 12*w**2 + 0*w + 1/30*w**6 + 1/30*w**5. Find x, given that k(x) = 0.
-1, 0, 1, 2
Determine r so that 3/2*r**2 + 15 + 21/2*r = 0.
-5, -2
Let f(m) be the third derivative of m**8/1848 + 2*m**7/165 + m**6/11 + 53*m**5/165 + 83*m**4/132 + 8*m**3/11 - 95*m**2. Find g such that f(g) = 0.
-8, -3, -1
Let b(s) be the first derivative of -s**8/1176 - 2*s**7/735 + s**5/105 + s**4/84 + 7*s**2 - 13. Let z(y) be the second derivative of b(y). Factor z(d).
-2*d*(d - 1)*(d + 1)**3/7
Let p be (-64)/(-416) + (-340)/(-325). Factor 3/5*a**2 + 0 + p*a.
3*a*(a + 2)/5
Factor 0*j + 0 + 60/13*j**2 - 2/13*j**4 - 2*j**3.
-2*j**2*(j - 2)*(j + 15)/13
Suppose -39 = -5*d + 2*x - 31, 10*d + 4*x = -16. Let 0*j**2 + 0*j + d + 5/6*j**3 = 0. Calculate j.
0
Let s(y) = 5*y**4 - 50*y**3 - 20*y**2 + 180*y + 130. Let o(i) = 5*i**4 - 53*i**3 - 19*i**2 + 181*i + 130. Let z(t) = -5*o(t) + 4*s(t). Factor z(j).
-5*(j - 13)*(j - 2)*(j + 1)**2
Let v be 0 + (36/70 - 4/(-14)). Let a(r) be the first derivative of 0*r - v*r**3 + 4 - 1/5*r**2 - 9/10*r**4. Factor a(o).
-2*o*(3*o + 1)**2/5
Let 4/9*o**3 - 2/9*o - 2 + 4*o**2 - 2/9*o**5 - 2*o**4 = 0. What is o?
-9, -1, 1
Let d(z) be the second derivative of -20*z - 16/21*z**4 + 0 - 4/7*z**2 + 1/5*z**5 + 22/21*z**3. Determine j so that d(j) = 0.
2/7, 1
Let v(m) be the second derivative of -m**5/4 - 5*m**4/12 + 5*m**3/6 + 5*m**2/2 - 74*m. Factor v(p).
-5*(p - 1)*(p + 1)**2
Let g(t) be the third derivative of 1/10*t**5 - t**3 + 1/8*t**4 + 0 + 0*t - 5*t**2 - 1/40*t**6. Determine n so that g(n) = 0.
-1, 1, 2
Let c(g) be the second derivative of 3 - 5/36*g**3 - 1/9*g**6 - 5/252*g**7 - 5/18*g**4 + 0*g**2 - 1/4*g**5 + 4*g. Factor c(m).
-5*m*(m + 1)**4/6
Let k be (-35)/(-21) - (-4)/3. Suppose k*g + 5*g = 2*g. Determine d, given that 0*d**2 + 2/3*d**3 + 0*d - 2/3*d**4 + g = 0.
0, 1
Find s such that -722/5 - 76/5*s - 2/5*s**2 = 0.
-19
Let p(l) be the second derivative of 0*l**3 + 0 + 0*l**5 - 7*l + 0*l**2 + 1/15*l**6 - 1/6*l**4. Factor p(v).
2*v**2*(v - 1)*(v + 1)
Suppose a + 12 = 5*a. Factor 9*v**3 + 9*v**a + 24*v**3 + 16*v + 10*v**3 + 24*v**4 + 48*v**2 + 4*v**5.
4*v*(v + 1)**2*(v + 2)**2
Let b(w) = w**3 - 11*w**2 - 14*w - 8. Let z be b(12). Let y = -29 - z. Solve 0 + 2/3*x**5 + 2/9*x**4 + 4/9*x - 2/9*x**2 - 10/9*x**y = 0 for x.
-1, 0, 2/3, 1
Let j(y) be the second derivative of y**6/165 - 3*y**5/55 - 25*y**4/66 - 6*y**3/11 - 31*y - 1. Factor j(w).
2*w*(w - 9)*(w + 1)*(w + 2)/11
Let z(g) be the third derivative of 1/15*g**4 - 1/150*g**5 - 4/15*g**3 + 0*g - 16*g**2 + 0. What is p in z(p) = 0?
2
Let y(k) be the second derivative of -k**5/20 + k**4/3 + 14*k - 3. Suppose y(b) = 0. Calculate b.
0, 4
Let z(a) be the third derivative of -a**8/168 + 4*a**7/105 - a**6/15 - 114*a**2. Determine q so that z(q) = 0.
0, 2
Suppose d - y = -d - 441, -3*y + 3 = 0. Let h be (24/d)/((-3)/10). Factor -6/11*q - h - 2/11*q**2.
-2*(q + 1)*(q + 2)/11
Let x = 431 - 428. Let q(w) be the third derivative of -1/180*w**5 + 0*w - 1/36*w**4 - 8*w**2 + 0 + 0*w**x. Factor q(s).
-s*(s + 2)/3
Suppose -3*y - 146 = -149. Let l(c) be the first derivative of -y + 2/3*c**3 - 4*c - c**2. Solve l(o) = 0 for o.
-1, 2
Let y(b) = b**4 - 115*b**3 + 1793*b**2 - 3248*b + 1566. Let f(r) = r**4 - r**3 + r**2 + 2. Let u(q) = -f(q) - y(q). Determine o so that u(o) = 0.
1, 28
Factor 389*p - 76*p + 203*p - 62658 - 2*p**2 + 386*p - 194*p.
-2*(p - 177)**2
Let r(w) = -w**2 + 12*w - 14. Let j be r(10). Suppose 2 = -5*h + j*h. Factor -10*q**3 + 4 + 8*q**h + 9*q + 12*q**3 + q.
2*(q + 1)**2*(q + 2)
Suppose v + 2*u = 0, -3*u + 7*u = 4*v - 36. Let i(o) = o**3 - 4*o**2 + 3*o - 2. Let p(q) = 1. Let a(s) = v*p(s) + 3*i(s). Factor a(k).
3*k*(k - 3)*(k - 1)
Let i(m) be the second derivative of 1/12*m**3 + 0 + 1/120*m**6 + 7*m + 0*m**2 - 5/48*m**4 - 1/168*m**7 + 3/80*m**5. Factor i(g).
-g*(g - 1)**3*(g + 2)/4
Factor -3/8*v + 1/4*v**3 - 1/2*v**4 + 1/2*v**2 + 1/8*v**5 + 0.
v*(v - 3)*(v - 1)**2*(v + 1)/8
Let u = 2734 + -2730. Factor -2/7*j**u + 50/7*j + 0 - 30/7*j**2 - 18/7*j**3.
-2*j*(j - 1)*(j + 5)**2/7
Let b(v) be the second derivative of v**5/60 + v**4/9 - 11*v**3/18 + v**2 - 2*v - 311. Solve b(s) = 0.
-6, 1
Let h(r) be the second derivative of -r**4/12 + 5*r**3/3 - 25*r**2/2 + 4*r. Suppose h(m) = 0. What is m?
5
What is m in 129*m - 68*m**2 + 6*m**4 - 129*m - 3*m**3 - 60*m - 2*m**4 - m**3 = 0?
-3, -1, 0, 5
Let i(m) be the second derivative of -m**3/6 - 4*m. Let o be i(-2). Factor -f**4 + f**o + f**2 + 9 - 10.
-(f - 1)**2*(f + 1)**2
Let w(n) be the first derivative of -n**6/6 + 23*n**5/15 + 2*n**4/3 + 793. Suppose w(i) = 0. Calculate i.
-1/3, 0, 8
Let u(y) = -4*y**2 + 15*y - 3. Let l(n) = n + 1. Let d(c) = 12*l(c) - 3*u(c). What is x in d(x) = 0?
1, 7/4
Find s, given that 72/17*s**2 + 0 + 26/17*s**4 + 2/17*s**5 + 96/17*s**3 + 0*s = 0.
-6, -1, 0
Suppose g = 5*c - 4, 3*c - 3*g = 6*c - 6. Let p = -79 + 85. Factor -c - 3 + 8*t + 8 + p*t**2 - 2*t**2.
4*(t + 1)**2
Let z = 24/133 - -23/399. Let k(j) be the second derivative of 1/14*j**4 + 0 + z*j**3 - 3*j + 2/7*j**2. Determine c, given that k(c) = 0.
-1, -2/3
Let z(u) = -u**3 - 9*u**2 - 3. Let m(a) = -3*a - 1. Let s be m(-1). Let y(w) = -8*w**2 - 2. Let r(l) = s*z(l) - 3*y(l). What is v in r(v) = 0?
0, 3
Let j(u) be the second derivative of 3/2*u**4 + 0 + 8*u + 0*u**2 + 9/2*u**3 + 3/20*u**5. Find b such that j(b) = 0.
-3, 0
Determine q so that -9*q**3 - 16/3*q**2 - 5/3*q**4 + 1/6*q**5 + 7 + 53/6*q = 0.
-3, -1, 1, 14
Let d = -2/221563 + 22378623/84193940. Let q = d - 3/190. Determine g so that 1/4 + 1/2*g + q*g**2 = 0.
-1
Let l(d) be the first derivative of d**7/70 + d**6/240 - d**