+ 1)/11
Let h = -28 - -31. Factor 11*d**3 + 7*d**3 - h*d**3 - 5*d**5 - 10*d**2.
-5*d**2*(d - 1)**2*(d + 2)
Let u(r) be the third derivative of -r**6/120 + r**5/60 + r**4/6 - 2*r**3/3 - 2*r**2 + 16*r. Factor u(j).
-(j - 2)*(j - 1)*(j + 2)
Let z(f) be the second derivative of 3*f**6/10 - 12*f**5/5 + 7*f**4/2 + 12*f**3 - 27*f**2/2 + 18*f + 3. Suppose z(o) = 0. What is o?
-1, 1/3, 3
Factor -p + 241*p - p**4 + 110*p**3 - 16*p**2 - 154*p**3 - 3*p**4.
-4*p*(p - 2)*(p + 3)*(p + 10)
Let d be (5/(-2))/((-7)/14). Factor -d*x**3 + 12*x**3 + 3*x**4 - 10*x**3.
3*x**3*(x - 1)
Let b be -3 + 1 + -2 + (-42)/(-10). Factor -1/5*r**4 - b*r**5 + 0 + 0*r**3 + 0*r**2 + 0*r.
-r**4*(r + 1)/5
Let c(l) be the second derivative of -1/42*l**4 + 0 - 14*l + 0*l**3 + 4/7*l**2. Factor c(b).
-2*(b - 2)*(b + 2)/7
Let u(b) = b**3 - 8*b**2 + 15*b - 17. Let f be u(6). Let p(c) = -c - 1. Let r(q) = q**2 - 9*q. Let s(n) = f*r(n) - 4*p(n). Find i, given that s(i) = 0.
1, 4
Let o = 4725 - 14173/3. Determine a, given that 1/3*a**2 - 1/6*a**3 - 4/3 + o*a = 0.
-2, 2
Solve 0*s - 44/5*s**2 + 64/5 - 2/5*s**4 + 18/5*s**3 = 0.
-1, 2, 4
Let b(l) be the second derivative of 0 + 0*l**2 - 8*l + 1/30*l**4 + 1/15*l**3. Factor b(t).
2*t*(t + 1)/5
Suppose -18 = 3*u - 2*y - 38, -2*u + 14 = -y. Suppose -5 = k - u. Determine c, given that 2/3*c - 1/3*c**k - 1/3*c**2 + 0 = 0.
-2, 0, 1
Let b = -12 + 8. Let y(m) = m**3 + 3*m**2 - 4*m + 2. Let c be y(b). Determine t so that 22 + 14 + 12 - 24*t + 3*t**2 + 0*t**c = 0.
4
Determine f so that -271*f**3 - 18*f**2 + 6*f**2 + 280*f**3 = 0.
0, 4/3
Suppose 25 = 3*r + 4*k, 5*r - 5*k + 1 + 4 = 0. Factor -4*n**2 - 2*n**5 + n**5 - 17*n**3 - 7*n**r - 9*n**4 - 12*n**2.
-n**2*(n + 1)*(n + 4)**2
Let a = 21 - 15. Let h = -32 + 44. Factor -4*n**2 - 28 - 24*n - 2 + a - h.
-4*(n + 3)**2
Let t(z) be the first derivative of z**4/12 + 10*z**3/3 + 50*z**2 + 1000*z/3 - 153. What is d in t(d) = 0?
-10
Let i be (32/(-6) + 8 + -1)/5. Factor -i*c**4 + 5/3*c**2 + c**3 - 1/3*c**5 + 2/3*c + 0.
-c*(c - 2)*(c + 1)**3/3
Let r be 1209/156 - 14/8. Let i(x) be the second derivative of -7/20*x**r + 1/4*x**4 + 0*x**3 + 0 - 6*x + 0*x**2 + 3/8*x**5. Factor i(p).
-3*p**2*(p - 1)*(7*p + 2)/2
Suppose -2*t - 6 = 0, 2*t - 90 = 2*u + 2*u. Let g be ((-1)/(-3))/((-4)/u). Suppose 2*s**2 + 6*s - 6 + g*s - 4*s**2 = 0. What is s?
1, 3
Let m = 158 - 158. Let h be 2 + -5 + m - 57/(-15). Factor -4*b + 5*b**2 + h.
(5*b - 2)**2/5
Let k(s) be the third derivative of -11*s**6/600 - 3*s**5/25 - 31*s**4/120 - s**3/5 - 858*s**2. Determine u, given that k(u) = 0.
-2, -1, -3/11
Let o(f) be the third derivative of -f**5/30 + 37*f**4 - 16428*f**3 + 111*f**2. Suppose o(d) = 0. What is d?
222
Let h(u) be the second derivative of u**6/30 - 3*u**5/5 - u**4/3 + 8*u**3 + 28*u. Factor h(s).
s*(s - 12)*(s - 2)*(s + 2)
Let f(m) be the third derivative of -m**6/24 - 5*m**5/12 + 5*m**4/6 + 50*m**3/3 - m**2 + 32*m. Factor f(v).
-5*(v - 2)*(v + 2)*(v + 5)
Suppose 189 - 321 = -44*t. Let g(s) be the first derivative of 1/2*s**4 - 3 + 8*s - 14/3*s**t - 1/3*s**6 + 0*s**2 + 6/5*s**5. What is v in g(v) = 0?
-1, 1, 2
Let l(z) be the third derivative of -1/1470*z**7 + 5/84*z**4 - 1/14*z**3 - 1/35*z**5 + 0 + 29*z**2 + 0*z + 1/140*z**6. Factor l(c).
-(c - 3)*(c - 1)**3/7
Let o = 14044/3 - 4680. Factor -o*w + 1/3*w**2 + 0.
w*(w - 4)/3
Solve -1/4*t**5 + 1/4*t**4 - 1/4*t + 1/4 - 1/2*t**2 + 1/2*t**3 = 0.
-1, 1
Let h(r) be the first derivative of 7*r**4/9 - 244*r**3/27 - 4*r**2 + 902. Let h(l) = 0. Calculate l.
-2/7, 0, 9
Let z(o) = 41*o - 857. Let l be z(21). Factor 4/3*j**2 + 0*j**l + 0*j + 2/3*j**5 + 0 - 2*j**3.
2*j**2*(j - 1)**2*(j + 2)/3
Suppose 74/15*p**3 - 2/15*p**4 - 14*p**2 - 68/15 + 206/15*p = 0. What is p?
1, 34
Let r(y) be the second derivative of y**6/10 + 3*y**5/20 - 23*y**4/4 + 39*y**3/2 - 27*y**2 - 5*y - 46. Factor r(v).
3*(v - 3)*(v - 1)**2*(v + 6)
Let m(k) be the second derivative of k**4/2 + 23*k**3/3 - 8*k**2 + 10*k - 1. Factor m(i).
2*(i + 8)*(3*i - 1)
Let z(r) = -r**2 - 4*r. Let p be z(-2). Suppose p*u - 13 = -3*o, 4*o + u = 21 - 8. Let 2*y**2 - 2*y**3 + 3*y**2 - y - 4*y**o + 2*y**3 = 0. Calculate y.
0, 1/4, 1
Let f(l) = 12*l**3 - 78*l**2 + 66*l + 12. Let k(x) = x**4 - 13*x**3 + 79*x**2 - 67*x - 16. Let b(w) = 4*f(w) + 3*k(w). Solve b(y) = 0.
-7, 0, 1, 3
Let x(k) be the third derivative of 11*k**5/420 + k**4/7 + 2*k**3/21 - 30*k**2. Factor x(r).
(r + 2)*(11*r + 2)/7
Let r = 29 - 23. Let k(x) = -100*x**3 - 325*x**2 - 170*x. Let z(d) = -11*d**3 - 36*d**2 - 19*d. Let a(m) = r*k(m) - 55*z(m). Solve a(q) = 0.
-5, -1, 0
Let v(y) be the third derivative of -y**6/1020 + 7*y**5/510 + y**4/12 + 3*y**3/17 - 5*y**2 + 77. Determine z, given that v(z) = 0.
-1, 9
Let h be (-3)/2 - 18/12. Let s(z) = -z**3 - z**2 + z + 1. Let y(c) = -2*c**2 - c**2 - 2*c**3 - 1 + 2. Let r(j) = h*y(j) + 3*s(j). Factor r(o).
3*o*(o + 1)**2
Let a = 2 + 0. Let t = 8 - -5. Factor t*r**a - 13*r**2 + 5*r**3.
5*r**3
Suppose -7*q + 2*q + o = -q, -o = 0. Factor 0*w - 2/15*w**3 + q - 4/15*w**2.
-2*w**2*(w + 2)/15
Let -6*o - 523*o**3 - 23*o**2 + 30*o**4 + 558*o**3 - 34*o - 7*o**2 - 4*o**5 + 9*o**5 = 0. What is o?
-4, -2, -1, 0, 1
Factor 4/9*a**2 + 76/9*a + 136/9.
4*(a + 2)*(a + 17)/9
Let p(o) be the third derivative of 0*o - 1/1260*o**7 + 0*o**6 + 0*o**3 + 0 - 1/2016*o**8 - 14*o**2 + 0*o**4 + 0*o**5. What is h in p(h) = 0?
-1, 0
Let j = 2155 + -15065/7. Suppose -j*w**3 + 8/7*w**2 + 20/7*w - 8/7 = 0. What is w?
-1, 2/5, 1
Let n(b) = -b**3 - 6*b**2 - 7*b - 11. Let s be n(-4). Let t be -2 + (-24)/s - 4/(-10). Suppose -6/5*v**3 - 3/5*v**2 + t + 0*v + 9/5*v**4 = 0. What is v?
-1/3, 0, 1
Let n(j) = 10*j**3 - 10*j. Suppose 3 = 13*a - 12*a. Let q(x) = 0*x**2 + 5*x - 2*x**3 + 0*x**2 - 3*x**a. Let u(h) = -3*n(h) - 7*q(h). What is b in u(b) = 0?
-1, 0, 1
Factor 62*r + 77*r**2 + 20 - 11*r**2 + 26*r**3 - 51*r**4 + 53*r**4.
2*(r + 1)**3*(r + 10)
Let l(g) be the first derivative of 20 + 9/5*g + 1/15*g**3 - 3/5*g**2. Solve l(p) = 0.
3
Let b(a) = 2*a**2 - 42*a + 14. Let l be b(21). Let j be (-48)/(-26) - l/(-91). Factor 2/5*p**3 - 2/5*p - 2/5*p**4 + 2/5*p**j + 0.
-2*p*(p - 1)**2*(p + 1)/5
Solve 0 + 1/5*x**2 - 7*x = 0.
0, 35
Find y such that -4/3 + 0*y + y**2 - 1/3*y**3 = 0.
-1, 2
Let v(x) be the first derivative of -2*x**3/39 + 2*x**2/13 - 9. What is h in v(h) = 0?
0, 2
Suppose 0 = -2*z - 3*s - 0*s - 3, -3*s = z + 9. Factor 8/3*h**3 - 4/3 - 2*h**2 - z*h.
2*(h - 2)*(h + 1)*(4*h + 1)/3
Let y be (-8 + (-375)/(-20) - 10)*2/2. Determine z, given that 5/8*z + y + 1/8*z**2 = 0.
-3, -2
Let h be (-3 + -1)*-2*2/8. What is b in -1 + 49*b**h + 11 - 10*b - 5*b - 44*b**2 = 0?
1, 2
Let z(c) be the second derivative of 0 + 0*c**4 - 7*c + 2/195*c**6 - 3/130*c**5 + 0*c**3 + 0*c**2 + 1/273*c**7. What is a in z(a) = 0?
-3, 0, 1
Let m(w) be the first derivative of w**4/4 + 2*w**3/3 - 2*w**2 - 8*w - 83. Factor m(b).
(b - 2)*(b + 2)**2
Let -645*v**3 + 3135*v**2 - 3/2*v**5 - 9075/2*v + 105/2*v**4 + 3993/2 = 0. What is v?
1, 11
Let j(t) be the third derivative of t**6/780 - 2*t**5/195 + 51*t**2. Factor j(r).
2*r**2*(r - 4)/13
Suppose -18*v**3 - 3*v - 5*v**3 + 3*v - 110*v**2 + 21*v**3 = 0. Calculate v.
-55, 0
Let r(t) = 7*t**3 + 205*t**2 + 8*t - 820. Let m(p) = 2*p**3 - 2*p. Let j(x) = -6*m(x) + r(x). Find b such that j(b) = 0.
-2, 2, 41
Let u(v) = 6*v**3 + 36*v**2 + 15*v + 15. Let p = -20 - -25. Let x(g) = -p*g**2 + g - 3*g - 2*g - g**3 - 2 + 2*g. Let s(d) = 2*u(d) + 15*x(d). Factor s(n).
-3*n**2*(n + 1)
Let d = -2/4167 - -12511/20835. Find c such that d*c + 0*c**4 + 0 - 6/5*c**3 + 3/5*c**5 + 0*c**2 = 0.
-1, 0, 1
Let l(w) be the second derivative of -w**7/26460 - w**6/945 - 4*w**5/315 + w**4/3 - 13*w. Let j(o) be the third derivative of l(o). Factor j(b).
-2*(b + 4)**2/21
Suppose 1392*g - 1394*g + 6 = 0. Factor 4/3*z**2 - 2/3*z - 2/3*z**4 - 2/3 - 2/3*z**5 + 4/3*z**g.
-2*(z - 1)**2*(z + 1)**3/3
Suppose -1 = -4*j + 3*j. Let p(n) = n**2 + 4*n - 2. Let s be p(j). Factor 0 + 4/5*i**2 + 12/5*i**s + 0*i - 7/5*i**4.
-i**2*(i - 2)*(7*i + 2)/5
Suppose 47*n - 65*n + 36 = 0. Let j(t) be the second derivative of -1/5*t**5 + 2/3*t**3 - 5*t + 0 + 0*t**4 + 0*t**n. Factor j(p).
-4*p*(p - 1)*(p + 1)
Suppose 37*t - 12*t = 75. Let b(p) be the third derivative of p**2 + 1/5*p**t + 0 - 1/40*p**4 + 0*p - 1/100*p**5. Factor b(v).
-3*(v - 