se 22*y - 24*y = -2. Let c be (-77)/(-66) + y/3. Factor 0*t**4 + 0*t - 3*t**2 - c*t**5 + 9/2*t**3 + 0.
-3*t**2*(t - 1)**2*(t + 2)/2
Let r = -53/5 - -4453/420. Let n(h) be the third derivative of 0*h**3 + r*h**6 - 1/84*h**4 + 0 + 0*h + 0*h**5 - 6*h**2. Factor n(y).
2*y*(y - 1)*(y + 1)/7
Let q be 418/494 + 72/(-39) + 2. Let x(r) be the first derivative of q + 2/9*r**3 - 1/9*r**6 + 0*r + 2/5*r**5 - 1/2*r**4 + 0*r**2. Factor x(h).
-2*h**2*(h - 1)**3/3
Let c(g) be the first derivative of g**5/40 - 19*g**4/32 + 25*g**3/12 - 2*g**2 - 404. What is d in c(d) = 0?
0, 1, 2, 16
Let t(b) be the second derivative of b**6/90 + b**5/10 + b**4/3 - 5*b**3/2 + 8*b. Let z(m) be the second derivative of t(m). Factor z(q).
4*(q + 1)*(q + 2)
Let y(k) be the second derivative of 1/3*k**4 - 1/2*k**2 + 13*k + 1/2*k**3 + 0. Factor y(r).
(r + 1)*(4*r - 1)
Let d(w) be the second derivative of -w**5/30 - w**4/3 - w**3 - 4*w**2/3 + 803*w. Factor d(z).
-2*(z + 1)**2*(z + 4)/3
Let d(u) = -u**2 - 87*u - 152. Let i(b) = 4*b**2 + 260*b + 456. Let t(z) = -8*d(z) - 3*i(z). Factor t(l).
-4*(l + 2)*(l + 19)
Let w(j) = 6*j**3 + 18*j**2 - 2*j - 12. Let u(p) = p**3 + 3*p**2 + p. Let g(b) = -2*u(b) + w(b). Find y, given that g(y) = 0.
-3, -1, 1
Factor 5*k**2 + 18 + 70*k - 72 - 21.
5*(k - 1)*(k + 15)
Solve -46/7 - 90/7*g - 6*g**2 + 2/7*g**3 = 0.
-1, 23
Let o(k) be the third derivative of -k**8/30240 + k**6/1080 + k**5/20 - 8*k**2. Let u(m) be the third derivative of o(m). Determine g, given that u(g) = 0.
-1, 1
Let k(q) be the second derivative of -q**4/48 - q**3/2 - 27*q**2/8 + 253*q. Factor k(z).
-(z + 3)*(z + 9)/4
Let z(a) be the second derivative of -a**9/22680 - a**8/3360 + a**7/945 + a**4/3 + 5*a**2 - 3*a. Let c(q) be the third derivative of z(q). Factor c(i).
-2*i**2*(i - 1)*(i + 4)/3
Let w = -380 + 384. Let u(j) be the third derivative of 1/15*j**5 + 1/6*j**w + 0*j + j**2 + 0*j**3 + 0. What is o in u(o) = 0?
-1, 0
Suppose 36 - 16 = 4*s. Factor -4*j**2 + 4*j**2 + j**3 - 3 + 3*j**2 - s*j - 4*j**2.
(j - 3)*(j + 1)**2
Let o(y) = -y**3 - 6*y**2 + 3*y + 17. Let x be o(-6). Let j be x + 40/25 + (-7)/(-5). Factor 0 - 2/15*v**j + 4/15*v.
-2*v*(v - 2)/15
Let l(z) be the second derivative of 0*z**2 - 1/20*z**5 + 0*z**3 - 1/4*z**4 + 0 + 15*z. Factor l(y).
-y**2*(y + 3)
Let d = -1704 - -1707. Solve -2/3*g**d + 0 + 2/9*g**2 + 0*g + 2/3*g**5 - 2/9*g**4 = 0.
-1, 0, 1/3, 1
Factor -250/9 + 220/9*n**2 + 148/9*n**3 - 50/3*n + 10/3*n**4 + 2/9*n**5.
2*(n - 1)*(n + 1)*(n + 5)**3/9
Suppose -5*t + 12 = 4*d, -3*t + 16 = -4*d - 4. Let -1/4*o**3 - 1/4*o**t - 3/4*o + 0 + 5/4*o**2 = 0. What is o?
-3, 0, 1
Determine m, given that 10/11*m**2 + 6/11*m**4 + 0 + 2/11*m + 14/11*m**3 = 0.
-1, -1/3, 0
Let x(m) be the first derivative of -2*m**5/15 + m**4 + 14*m**3/9 + 163. Factor x(s).
-2*s**2*(s - 7)*(s + 1)/3
Let j(r) be the first derivative of 5*r**2 + 1/2*r**5 + 1 + 5/2*r**4 + 5/2*r + 5*r**3. Factor j(b).
5*(b + 1)**4/2
Let w be (17 + -112)/(-19) - 5. Let j = -41/3 - -208/15. Factor -x**4 + w - 4/5*x**2 + j*x**5 + 0*x + 8/5*x**3.
x**2*(x - 2)**2*(x - 1)/5
Let m(h) be the third derivative of 1/360*h**5 + 0 + 0*h - 33*h**2 - 1/6*h**4 + 4*h**3. Determine w so that m(w) = 0.
12
Factor -6*s**3 + 0*s**2 + 3 + 12*s + 6*s**2 + 9 + 3*s**3 - 9*s**2.
-3*(s - 2)*(s + 1)*(s + 2)
Let v = -8 + 16. Suppose -2*w - 2*w + v = 0. Determine q, given that 3*q - 24*q**3 - 3 - q**2 + 21*q**3 + 2*q**2 + w*q**2 = 0.
-1, 1
Let t = -49/138 + 757/966. Factor -12/7 - 9/7*f + t*f**2.
3*(f - 4)*(f + 1)/7
Let a(y) = -y**2 - 42*y + 20*y - 2 + 29*y. Let j be a(5). Let -j*f**2 + f + 4*f**3 + 7*f - 3*f - f = 0. What is f?
0, 1
Let w be 21/196*35/90. Let s(p) be the second derivative of -p + 0 + 0*p**2 + 1/48*p**4 - w*p**3. Factor s(o).
o*(o - 1)/4
Let l = 1955/3914 - -1/1957. Find v such that -3/2 + 2*v - l*v**2 = 0.
1, 3
Let d = 38 + -16. Factor -4*g**5 - 45*g + 23*g + 4*g**3 - 4*g**4 + 4*g**2 + d*g.
-4*g**2*(g - 1)*(g + 1)**2
Let k = 2413 + -506729/210. Let j(c) be the third derivative of 7*c**2 + 0*c - 1/20*c**5 - k*c**7 - 1/24*c**4 - 1/40*c**6 + 0*c**3 + 0. Factor j(d).
-d*(d + 1)**3
Suppose -3/7*r**2 - 4/7*r + 1/7*r**3 + 0 = 0. Calculate r.
-1, 0, 4
Let b(a) be the first derivative of -a**3/4 - 3*a**2/8 + 3*a/2 - 34. Let b(y) = 0. Calculate y.
-2, 1
Let w(x) be the second derivative of 0*x**2 + 1/12*x**4 + 0 + 3/20*x**5 - 1/2*x**3 + 10*x - 1/30*x**6. Let w(j) = 0. Calculate j.
-1, 0, 1, 3
Let f(o) be the first derivative of -o**3/15 + o**2 - 488. Solve f(g) = 0.
0, 10
Let q(i) be the second derivative of i**5/5 - 2*i**4/3 + 2*i**3/3 - 2*i - 8. Solve q(m) = 0.
0, 1
Factor -53067/5 - 7671/5*n**2 - 12/5*n**4 - 7182*n - 108*n**3.
-3*(n + 19)**2*(2*n + 7)**2/5
Let u(c) be the first derivative of c**4/28 - 5*c**3/42 - c**2/7 + 37*c + 45. Let x(n) be the first derivative of u(n). Factor x(i).
(i - 2)*(3*i + 1)/7
Let s(n) = n**4 + n**3 + n**2 + n + 1. Let x(z) = -6*z**4 - 24*z**3 - 26*z**2 + 16*z - 2. Let d(m) = 4*s(m) + 2*x(m). Factor d(y).
-4*y*(y + 3)**2*(2*y - 1)
Let y(g) = -5*g**3 - g**2 - 3*g - 2. Let i be y(-1). Let j(s) = s**4 + s - 1. Let t(v) = 5*v**4 + 2*v**3 + 4*v - 4. Let a(d) = i*t(d) - 20*j(d). Solve a(b) = 0.
-2, 0
Suppose 0 = 3*j + 5*y - 5, -3*j + 8 = 3*y + 5. Factor 0 + j*b**2 + 0*b + b**4 + 7/5*b**5 - 2/5*b**3.
b**3*(b + 1)*(7*b - 2)/5
Let s(z) be the third derivative of 0*z**3 - 1/25*z**5 - 13*z**2 + 0*z + 0 - 1/200*z**6 - 1/10*z**4. Factor s(y).
-3*y*(y + 2)**2/5
Factor 38 + 5*v**2 + 6*v - 2*v**2 + 0*v - 35.
3*(v + 1)**2
Suppose 36 = 3*v + 15. Suppose -48 + z - 3*z**2 - v*z - 18*z = 0. What is z?
-4
Suppose 0 = 55*t - 52*t + 9. Let k be 9 + -7 + t/((-54)/(-33)). Factor -1/6*i**2 + k*i + 1/3.
-(i - 2)*(i + 1)/6
Let n = 2217 - 2215. Determine j so that 0*j**3 + 2/13 + 2/13*j**4 - 4/13*j**n + 0*j = 0.
-1, 1
Let n(p) be the second derivative of -3/4*p**4 + 3/5*p**5 - 1/2*p**3 + 13*p + 0*p**2 + 0. Factor n(f).
3*f*(f - 1)*(4*f + 1)
Let q = 9471 + -66281/7. What is m in 16/7 + q*m**2 - 68/7*m = 0?
1/4, 4
Let s = -164 - -179. Determine g so that -3*g + s*g + 20*g**2 - 8 - 3*g + 3*g = 0.
-1, 2/5
Let b(m) be the second derivative of m**6/420 - m**4/84 + 3*m**2/2 + 23*m. Let u(l) be the first derivative of b(l). Suppose u(p) = 0. What is p?
-1, 0, 1
Let o = -63 - -70. Let -o*u + 8 - 4*u - 4*u**2 - u + 12*u**3 - 14*u**4 + 10*u**4 = 0. Calculate u.
-1, 1, 2
Let c(q) = q**2 + 6*q + 10. Let m be c(-2). Let v(z) be the third derivative of 0*z + 1/6*z**4 + 3*z**m + 0 - 2/15*z**5 + 2*z**3. Factor v(t).
-4*(t + 1)*(2*t - 3)
Let r(l) = 115*l**3 + 755*l**2 - 1180*l + 410. Let y(z) = -39*z**3 - 252*z**2 + 394*z - 137. Let m(c) = 3*r(c) + 10*y(c). Find t such that m(t) = 0.
-7, 2/3
Suppose 2*f + 21*f - 9*f - 28 = 0. Solve -1/5*g**f - 2/5 - 3/5*g = 0.
-2, -1
Let g = 347 + -344. Let y = -2 - -8. Find j, given that 0*j**3 + 3*j**3 - 3 - 11*j - 9*j**2 + 2*j - y*j**g = 0.
-1
Suppose 13*f = -250 - 465. Let k(w) = 5*w**2 + 20*w + 15. Let p(c) = -70*c**2 - 280*c - 210. Let h(o) = f*k(o) - 4*p(o). Let h(v) = 0. What is v?
-3, -1
Let o(l) be the first derivative of -2*l**2 - 4/25*l**5 + 8/5*l + 4/5*l**3 + 1/5*l**4 + 10. Find z such that o(z) = 0.
-2, 1
Suppose 3 = -10*k + 123. Suppose 0*r + 4*r - 16 = 0. Factor 11*y**3 + k*y**2 - 1 + 6*y + 3*y**r + 2 - y**3.
(y + 1)**3*(3*y + 1)
Let x(y) be the second derivative of 2*y**7/21 - 2*y**6/15 - 17*y**5/5 - 5*y**4 - 2*y - 193. Factor x(j).
4*j**2*(j - 5)*(j + 1)*(j + 3)
Let y be 6 + 5 - 15 - (0 - 9). Let a be (18/45)/(0 + 1/y). What is b in 1/5*b - 2/5*b**a + 2/5 - 1/5*b**3 = 0?
-2, -1, 1
Let p(j) = -j**3 - 4*j**2 - 11*j - 8. Let q be p(-4). Let s = -36 + q. Factor -1/7*h**4 - 1/7*h + s + 1/7*h**2 + 1/7*h**3.
-h*(h - 1)**2*(h + 1)/7
Let o(m) be the first derivative of -5*m**2 + 18 - 1/3*m**3 - 9*m. Solve o(j) = 0 for j.
-9, -1
Let m(g) be the third derivative of 3/56*g**4 + 1/84*g**5 + 1/21*g**3 - 3/280*g**6 + 6*g**2 + 0 - 1/210*g**7 + 0*g. Let m(h) = 0. What is h?
-1, -2/7, 1
Let f(b) be the third derivative of b**8/9240 + b**7/2310 + b**6/1980 - 16*b**3/3 + 33*b**2. Let d(o) be the first derivative of f(o). Factor d(r).
2*r**2*(r + 1)**2/11
Let i(x) = 4*x**3 - 17*x**2 + 49*x. Let l(b) = 5*b**3 - 18*b**2 + 49*b. Let g(a) = -4*i(a) + 3*l(a). Determine y so that g(y) = 0.
0, 7
Let c(a) be the second derivative of -a