m + 1)**2/11
Let r = 5877 + -2815081/479. Let s = r + 7181/958. Determine m so that -15*m**2 + 12*m**4 - 3/2*m - 6*m**3 + s*m**5 + 3 = 0.
-1, 2/5, 1
Let q(h) be the third derivative of -h**9/3024 - h**8/840 + h**6/180 + h**5/120 + h**3/3 + 2*h**2. Let c(n) be the first derivative of q(n). Factor c(x).
-x*(x - 1)*(x + 1)**3
Let n(x) be the first derivative of -x**4/4 - 7*x**3/12 - x**2/4 + x/4 - 6. Factor n(f).
-(f + 1)**2*(4*f - 1)/4
Let o(i) = i. Let z = 2 + 0. Suppose 6*t - 3*t = -2*n - 21, 0 = 3*n - t + 59. Let y(h) = -h**2 + 13*h - 4. Let q(u) = n*o(u) + z*y(u). What is f in q(f) = 0?
2
Find m, given that 108/5 + 147/5*m**2 - 468/5*m - 12/5*m**3 = 0.
1/4, 6
Let o be 1 + (-2)/4*-2. Suppose 2*q**4 + 3*q**2 - 5*q**o + 3*q**2 + 0*q**3 + 3*q**3 = 0. Calculate q.
-1, -1/2, 0
Suppose -2*n**4 - 1/3*n + 0*n**2 + 7/3*n**3 + 0 = 0. Calculate n.
-1/3, 0, 1/2, 1
Let a = -4028/5 + 806. Factor -1/5*n**5 - a*n**2 - 2/5*n**3 + 3/5*n**4 + 3/5*n - 1/5.
-(n - 1)**4*(n + 1)/5
Suppose 3*u - 4 = u. Factor 3*l**2 + 0*l**2 + 3*l + l**2 - 3*l**u + 2.
(l + 1)*(l + 2)
Let j(n) be the third derivative of -1/156*n**4 - 1/1365*n**7 - 2*n**2 + 0 + 0*n + 0*n**3 - 1/130*n**5 - 1/260*n**6. Factor j(r).
-2*r*(r + 1)**3/13
Let k be 22/15 - 34/(-170). Determine d, given that -1/3*d**3 - k*d - 2/3 - 4/3*d**2 = 0.
-2, -1
Suppose -24/7*z**2 + 2/7*z**3 - 2/7*z + 24/7 = 0. Calculate z.
-1, 1, 12
Let c(d) = d - 5. Let f be c(3). Let j be 18/12 + 2/f. Factor 0 + j*t - 1/2*t**2.
-t*(t - 1)/2
Let n(b) = -b**3 - b**2 - b + 3. Let r be n(0). Solve -9*j**4 - j**3 - 15*j**2 + 5*j**3 + 17*j**r + 3*j = 0.
0, 1/3, 1
Let a(x) be the first derivative of -1/3*x**2 + 1/9*x**6 + 4/15*x**5 + 1 - 4/9*x**3 + 0*x**4 + 0*x. Suppose a(k) = 0. What is k?
-1, 0, 1
Let d(x) be the first derivative of -3 - 2*x - 4/3*x**3 + 3*x**2. Let d(t) = 0. Calculate t.
1/2, 1
Let j(x) = 2*x + 16. Let b be j(-7). Let d(i) be the first derivative of 0*i - 5/12*i**3 - 1/4*i**b - 1 - 3/16*i**4. Factor d(o).
-o*(o + 1)*(3*o + 2)/4
Let q(u) be the first derivative of 3/4*u**4 + 7 + 0*u - 2*u**3 + 3/2*u**2. Let q(z) = 0. Calculate z.
0, 1
Let v(a) be the third derivative of 5*a**2 + 0 + 1/120*a**5 + 0*a - 1/12*a**3 - 1/32*a**4. Find m, given that v(m) = 0.
-1/2, 2
Determine o so that 14/9*o - 10/9*o**2 - 4/9 = 0.
2/5, 1
Let t = -2 - -9/4. Factor 0*c - 1/4 + t*c**2.
(c - 1)*(c + 1)/4
Let t(h) = h**4 + h**3 - h**2 - h. Let v(w) = 2*w**4 + 94*w**3 + 866*w**2 + 3458*w + 5184. Let j(y) = -2*t(y) - v(y). Suppose j(b) = 0. Calculate b.
-6
Let x(k) be the first derivative of -k**4/6 - 4*k**3/9 + k**2/3 + 4*k/3 + 6. Solve x(a) = 0.
-2, -1, 1
Let z(y) = y**3 - y**2 + y + 2. Let m be z(0). Factor 2*i**m - i**4 - 1 - 20*i + 20*i.
-(i - 1)**2*(i + 1)**2
Let v(a) be the first derivative of a**8/112 - a**7/105 - a**6/40 + a**5/30 + a**2 + 1. Let m(k) be the second derivative of v(k). Factor m(j).
j**2*(j - 1)*(j + 1)*(3*j - 2)
Let u(n) be the first derivative of n**5/100 - n**4/30 + n**3/30 - n - 2. Let y(g) be the first derivative of u(g). Factor y(d).
d*(d - 1)**2/5
Let 0*u - 4*u**5 + 3*u**5 + 2*u**3 - u + 0*u**5 = 0. Calculate u.
-1, 0, 1
Find m, given that 0 + 2/5*m + 0*m**2 - 2/5*m**3 = 0.
-1, 0, 1
Let w = 70/53 + 2/159. Solve -14/3*j**3 - w + 14/3*j + 4/3*j**2 = 0 for j.
-1, 2/7, 1
Let z(d) be the first derivative of -4 - 1/5*d**3 - 3/20*d**4 + 3/5*d**2 + 0*d. Solve z(j) = 0.
-2, 0, 1
Let q = 1 + 4. Let t(x) = 2*x**2 - x - 1. Let a be t(-1). Factor -4/3*i**4 + a*i**3 + 1/3*i + 0 + 1/3*i**q - 4/3*i**2.
i*(i - 1)**4/3
Factor 301 + 5*m**3 - 301 + 5*m**2.
5*m**2*(m + 1)
Let a be (2 + -4)*1 + 5. Let v = -23 + 25. Solve -1/4*m**v - 1/4*m**a + 1/4 + 1/4*m = 0.
-1, 1
Let w be (-20)/6*(-6)/4. Let q(k) = -3*k**3 - 2*k**2 + 5. Let h(s) = -4*s**3 - 3*s**2 + 7. Let m(b) = w*h(b) - 7*q(b). Factor m(t).
t**2*(t - 1)
Factor -6/5*b**2 + 8/5*b**3 - 9/5*b + 0 + 6/5*b**4 + 1/5*b**5.
b*(b - 1)*(b + 1)*(b + 3)**2/5
Let i = 1037521/360 - 2882. Let k(n) be the third derivative of -n**2 - i*n**6 + 1/72*n**4 + 0*n + 0 - 1/18*n**3 + 1/180*n**5. Factor k(u).
-(u - 1)**2*(u + 1)/3
Let l be (-4)/22 - (-138)/33. Let b = -2 + 4. Factor 2 + 2*h**b + l*h - 1 - 1.
2*h*(h + 2)
Let y(o) = -o**2 - 9*o - 5. Let k be y(-8). Find m, given that 35*m - 35*m + k*m**2 - 3 = 0.
-1, 1
Solve n**3 + 4*n**2 + n**3 - 272 + 272 = 0.
-2, 0
Let s be 34/168 - 10/(-120). Determine m so that s*m**2 + 2/7 + 4/7*m = 0.
-1
Suppose -y - u = -2, -5*y + 3*u = 2*u - 16. Let v(t) be the second derivative of -1/30*t**4 - t + 0 + 0*t**y + 1/50*t**5 + 0*t**2. Factor v(k).
2*k**2*(k - 1)/5
Factor -3*s**2 + 7*s**2 - 2*s + 6*s - 8.
4*(s - 1)*(s + 2)
Let o be (2 - -6 - 3) + (-34)/8. Suppose -o*g + 3/4*g**2 - 1/4*g**3 + 1/4 = 0. What is g?
1
Let i(l) = -2*l**2 - l + 4. Let t(z) = -3*z**2 - 2*z + 5. Let r(a) = 2*a - 3. Let h be r(3). Let v(c) = h*t(c) - 4*i(c). Let v(n) = 0. What is n?
-1
Determine o so that o**3 - 6*o + 14*o - 4*o - 4 - 3*o**3 + 3*o**2 - o**4 = 0.
-2, 1
Let i(o) be the second derivative of o**4/20 + o**3/15 - o**2/10 + o. Find d, given that i(d) = 0.
-1, 1/3
Let b(k) = -k**5 + k**3 + k**2 + k. Suppose -12 = 4*t - 2*l - 2*l, 5*t = -5*l - 25. Let g(o) = o**5 - 2*o**2 - 3*o. Let s(d) = t*b(d) - 2*g(d). Factor s(w).
2*w*(w - 1)**2*(w + 1)**2
Let w(m) = -m**2 - 7*m - 3. Let l be w(-3). Factor 6*r - l + 19 - 9 + 5*r**2.
(r + 1)*(5*r + 1)
Determine q, given that q**3 + 10*q**3 - 33*q**3 + 2*q - 4*q**2 + 288*q**5 + 48*q**4 - 24*q**3 = 0.
-1/3, 0, 1/4
Let f(s) = 3*s**2 + 3*s + 3. Let t be f(-2). Suppose -5*h + 2*h - 3*h - 3*h**3 - t*h**2 = 0. What is h?
-2, -1, 0
Suppose -13 = -5*v + 7. Let u(c) be the first derivative of -1/3*c**2 + 0*c + 0*c**3 - 1 + 1/6*c**v. Solve u(k) = 0.
-1, 0, 1
Let r(z) = 15*z**2 - 178*z - 22. Let g be r(12). Factor -3/2*k + 3/2*k**3 + 3/2*k**g + 0 - 3/2*k**4.
-3*k*(k - 1)**2*(k + 1)/2
Suppose 2*b = 3*b - s + 1, s + 2 = 4*b. Factor 3*u**3 + 1 - 4*u**3 - 6 + b - 5*u**2 - 8*u.
-(u + 1)*(u + 2)**2
Let k(f) be the first derivative of -3*f**5/5 + f**3 + 15. Factor k(h).
-3*h**2*(h - 1)*(h + 1)
Let v(h) = -h**2 - 4*h + 2. Let t be v(-4). Let q = 1 + t. Factor 2*u**3 - 2*u - 1 + 4*u + u**4 - 4*u**q.
(u - 1)**3*(u + 1)
Let j(r) be the third derivative of 0*r**4 - 1/90*r**5 + 0 + 0*r + 0*r**3 + 2*r**2 + 1/180*r**6. Factor j(l).
2*l**2*(l - 1)/3
Let x(m) = m**2 - m + 1. Let f(a) = 3*a**2 - a + 2. Suppose -2*o = -3*i + 12, 0*o = 4*o - i + 4. Let k = o + -2. Let p(t) = k*x(t) + f(t). Factor p(b).
b*(b + 1)
Let p(t) = 21*t**5 - 27*t**4 - 27*t**3 + 27*t**2 + 6. Let m(r) = r**5 + r**4 - r**3 - r**2 + r - 1. Let a(j) = -6*m(j) - p(j). Solve a(y) = 0.
-1, -2/9, 0, 1
Let y = -2/2269 + 1236611/6807. Let n = y + -179. Determine t, given that n + 2*t**2 - 16/3*t = 0.
2/3, 2
Let g = -10 + 15. Let c = g - 5. Factor c*r + 2/3*r**2 + 0.
2*r**2/3
Let b be 14/(-91) + 140/234. Suppose 0*n**2 + 2/9*n**5 + 0 - b*n**4 + 0*n + 2/9*n**3 = 0. Calculate n.
0, 1
Let k(u) be the first derivative of 0*u**2 + 0*u + 1/6*u**4 + 2 + 0*u**3 - 1/15*u**5. Find i, given that k(i) = 0.
0, 2
Let z be 3/(-20) - (-4)/10. Let o be 1/(-2) - 15/(-12). What is v in -1/2*v**2 - z + o*v = 0?
1/2, 1
Let i be 13 + 0/(-2 - -1). Let m be i/2 - (-3)/(-6). Factor 6 + 2*s**3 - m.
2*s**3
Let x(v) = v**3 + 5 + 0*v**5 - v**5 - 4 + v. Let a = 0 + 1. Let m(u) = -4*u**5 + 6*u**4 - 4*u**3 + 2*u**2 + 2*u + 2. Let s(p) = a*m(p) - 2*x(p). Factor s(r).
-2*r**2*(r - 1)**3
Let o(m) = -m**2 + 26*m - 69. Let z be o(3). Solve z - 1/9*c**2 + 2/9*c = 0 for c.
0, 2
Suppose 2*z = 2*b + 3*b + 9, -5*b = 5. Let l(k) be the first derivative of 2 - k**z + 2/3*k**3 + 0*k. Factor l(c).
2*c*(c - 1)
Let f(c) be the second derivative of 3*c**5/16 + c**4/8 + 9*c. Solve f(v) = 0 for v.
-2/5, 0
Let q(y) be the third derivative of -y**7/420 + y**6/120 - y**4/24 + y**3/12 - 3*y**2. Factor q(i).
-(i - 1)**3*(i + 1)/2
Let u(g) = g**2 + g + 7. Let y be u(0). Solve -2 - 15*a - 3*a**2 - 2*a**2 + 3*a**3 + 2*a**2 - y = 0.
-1, 3
Let j = 22 - 87/4. Suppose -1 = -5*x + 4. Solve -j*r**2 - r - x = 0 for r.
-2
Let k(l) = 8*l**2 + 6*l - 11. Let n(y) = 3*y**2 + 2*y - 4. Let h(j) = 4*k(j) - 11*n(j). Solve h(c) = 0 for c.
0, 2
Factor 13*s**2 - 2*s**4 - s + 12*s**2 - 30*s**2 + 7*s**2 + s**5.
s*(s - 1)**3*(s + 1)
Let 5/3*c**2 + 0 + 50/3*c = 0. What is c?
-10, 0
Let o(i) be the third