*3 + 90*o**2 + 3*o. Suppose z(t) = 0. Calculate t.
51
Factor -784 - 168*d - 2/7*d**3 - 12*d**2.
-2*(d + 14)**3/7
Let o(y) be the third derivative of y**5/20 + 9*y**4/8 + 9*y**3 + 12*y**2 - 10. Factor o(h).
3*(h + 3)*(h + 6)
Let x(d) be the third derivative of 1/40*d**6 - 1/8*d**4 + 0*d**3 + 0 + 0*d + 14*d**2 + 0*d**5. Factor x(o).
3*o*(o - 1)*(o + 1)
Suppose 113*a**2 + 5*a**3 - 2*a**3 - 219*a**2 + 112*a**2 = 0. What is a?
-2, 0
Let v be (-6)/((-24)/(-84) + (-88)/14) - -2. Factor -1/2*w**4 - w + 0 - 5/2*w**2 - 2*w**v.
-w*(w + 1)**2*(w + 2)/2
Suppose 197*m = 201*m + 16. Let f be m*(-1)/(-2)*4/(-10). Factor -2/5*x**2 + 0 - f*x**3 + 2/5*x**4 + 4/5*x.
2*x*(x - 2)*(x - 1)*(x + 1)/5
Let b(s) = s**2 - 4*s - 8. Let w be b(6). Let c(f) = 3*f + 5. Let d be c(0). Factor -17*m - w*m**2 + d*m - 2*m**2 + 2*m**2.
-4*m*(m + 3)
Let y(o) = -o**2 - 2*o. Let l be y(-2). Factor -3*f + f**2 + l*f**2 + 1 - 3 + 4*f.
(f - 1)*(f + 2)
Let x(p) be the second derivative of -p**8/43680 + p**7/5460 - p**6/1560 + p**5/780 - 5*p**4/3 + 10*p. Let f(i) be the third derivative of x(i). Factor f(b).
-2*(b - 1)**3/13
Let l = -13091/4 - -3284. Determine w so that -l*w**3 - 1/2 + 3*w**2 + 7/4*w = 0.
-2/5, 1/3
Let t(k) be the first derivative of -6*k**2 - 11 + 2*k + 37/6*k**3 + 3/8*k**4 + 7/4*k**6 - 41/10*k**5. What is n in t(n) = 0?
-1, 2/7, 2/3, 1
Let i(p) be the first derivative of -p**6/15 + 14*p**5/25 - 3*p**4/2 + 26*p**3/15 - 4*p**2/5 + 67. What is d in i(d) = 0?
0, 1, 4
Let 24/5*h - 6/5*h**3 - 8/5*h**2 + 0 + 2/5*h**4 = 0. What is h?
-2, 0, 2, 3
Let m(b) be the second derivative of b**8/10080 + b**7/2520 - 29*b**3/6 - 10*b. Let c(t) be the second derivative of m(t). Factor c(n).
n**3*(n + 2)/6
Let m(u) be the third derivative of -u**8/12 + 6*u**7/35 + 13*u**6/15 - 12*u**5/5 + 4*u**4/3 + 82*u**2. Let m(d) = 0. Calculate d.
-2, 0, 2/7, 1, 2
Let f = -414 - -1569. Let g = f + -5751/5. Factor 54/5*j**2 - 21/5*j**3 - 12*j + 3/5*j**4 + g.
3*(j - 2)**3*(j - 1)/5
Let v be (-38 - -44) + (-264)/55. Determine z so that 24/5 - 9/5*z**3 + v*z**2 + 36/5*z - 3/5*z**4 = 0.
-2, -1, 2
Let j(x) be the first derivative of 20/9*x**3 + 4 + 7/36*x**6 + 1/3*x + 25/12*x**4 + x**5 + 5/4*x**2. Factor j(w).
(w + 1)**4*(7*w + 2)/6
Let j(h) = -h**3 + h**2 - 3*h + 1. Let w(o) = 8*o**3 - 40*o**2 - 28*o - 60. Let r(s) = 12*j(s) + w(s). What is g in r(g) = 0?
-3, -2
Factor 0 + 2/3*l**3 + 0*l**2 - 2/3*l.
2*l*(l - 1)*(l + 1)/3
Suppose -2 = -3*h + 2*h. Suppose -21*l + 24 = -9*l. Suppose 6*g + l*g**2 + g**2 + 0*g**h + 3 = 0. What is g?
-1
Suppose 2*c - 10 = -3*n, -2*n + 2*c + 6 = -14. Determine w so that -10*w**3 - 3*w**3 + w**4 + n*w**3 + 5*w**3 = 0.
0, 2
Let o(l) be the third derivative of l**7/420 - 2*l**6/15 + 7*l**5/5 - 20*l**4/3 + 52*l**3/3 - 595*l**2. Let o(w) = 0. Calculate w.
2, 26
What is u in 1/4*u + 1/2*u**2 + 0*u**3 - 1/4*u**5 + 0 - 1/2*u**4 = 0?
-1, 0, 1
Factor 647*s**3 - 31*s**2 - 644*s**3 - 5*s**2 - 12*s**2.
3*s**2*(s - 16)
Factor 1/3*k**3 - 17*k**2 + 225*k - 625/3.
(k - 25)**2*(k - 1)/3
Let b(o) be the first derivative of -2*o**6/9 + 28*o**5/15 - 5*o**4 + 52*o**3/9 - 8*o**2/3 - 271. Find p such that b(p) = 0.
0, 1, 4
Let g = 12789 - 12789. What is d in 8/11 + g*d + 2/11*d**3 - 6/11*d**2 = 0?
-1, 2
Let r = 2254 - 6761/3. Let t(k) be the second derivative of -r*k**3 - 12*k + 0 + 1/14*k**4 + 2/7*k**2. Let t(m) = 0. What is m?
1/3, 2
Let b(f) be the first derivative of -7*f**6/30 + 2*f**5/15 + 7*f**4/6 - 4*f**3/3 + 8*f**2 - 3. Let v(g) be the second derivative of b(g). Factor v(c).
-4*(c - 1)*(c + 1)*(7*c - 2)
Solve -2/5*s**2 - 8/5*s + 2 = 0.
-5, 1
Let i(r) be the first derivative of -r**6/14 + 29*r**5/35 - 57*r**4/28 - r**3/21 + 30*r**2/7 - 4*r + 445. Solve i(u) = 0.
-1, 2/3, 1, 2, 7
Let c(g) = 2*g**2 + 503*g + 495. Let z(y) = -7*y**2 - 1508*y - 1485. Let q(r) = 8*c(r) + 3*z(r). Factor q(o).
-5*(o + 1)*(o + 99)
Let n(z) be the third derivative of -2/3*z**4 + 0 + 0*z - z**3 + 4*z**2 - 17/30*z**5 - 2/45*z**6. Let p(o) be the first derivative of n(o). Factor p(d).
-4*(d + 4)*(4*d + 1)
Let k(n) be the second derivative of -n**7/840 + n**6/216 - n**5/180 + 7*n**3/6 - 4*n - 6. Let o(m) be the second derivative of k(m). Factor o(d).
-d*(d - 1)*(3*d - 2)/3
Let n be (1354/(-10))/(-1) - (-12)/(-4). Let o = -131 + n. What is r in -4/5*r**2 + 2/5 - o*r = 0?
-2, 1/4
Let w(y) be the second derivative of y**5/50 + y**4/6 - 61*y**3/15 + 11*y**2 - y + 24. Factor w(z).
2*(z - 5)*(z - 1)*(z + 11)/5
Let a(k) be the second derivative of k**6/1080 + k**5/360 - k**4/36 + 11*k**3/6 + 3*k. Let u(y) be the second derivative of a(y). Find w such that u(w) = 0.
-2, 1
Suppose 5*j + 0 - 9 = -3*g, 0 = -j - 3*g - 3. Let z(u) = -2*u**2 + 7*u - 1. Let a be z(j). Factor 2/7*n**a + 0 - 2/7*n.
2*n*(n - 1)/7
Let h(l) = 3*l**3 + 3*l**2 - 6*l + 9. Let b(s) = -10 - 4*s**2 + 67*s**3 - 70*s**3 + 4*s + s. Let u(v) = 3*b(v) + 4*h(v). Factor u(m).
3*(m - 1)**2*(m + 2)
Factor -18*c - 23*c - 101*c**2 + c**3 + 141*c**2.
c*(c - 1)*(c + 41)
Let t = 7 - 7. Let l(v) = v**3. Let g be l(t). Let g - 3 + 5 + 8*x**3 - 6*x = 0. Calculate x.
-1, 1/2
Let c(u) be the first derivative of -u**6/7 + 2*u**5/5 + 9*u**4/7 + 16*u**3/21 + 45. What is l in c(l) = 0?
-1, -2/3, 0, 4
Let t(z) = -3*z**4 + 8*z**3 + 179*z**2 + 484*z + 396. Let p(l) = -l**3 - l**2 - 2*l. Let q(d) = -4*p(d) + t(d). Suppose q(f) = 0. What is f?
-3, -2, 11
Let z be (-9)/36*0 - (1 + -14). Let f(t) be the first derivative of -4/3*t - 1/24*t**4 + 1/9*t**3 + 1/3*t**2 + z. Factor f(w).
-(w - 2)**2*(w + 2)/6
Let h(a) be the second derivative of a**7/21 + 6*a**6/5 + 42*a**5/5 + 77*a**4/3 + 41*a**3 + 36*a**2 + 214*a. Factor h(v).
2*(v + 1)**3*(v + 3)*(v + 12)
Let x(l) = -l**2 + l - 2. Let a(n) = -2*n**3 - 2*n**2 - 5*n + 6. Let o(w) = 2*a(w) + 6*x(w). Factor o(q).
-2*q*(q + 2)*(2*q + 1)
Let j(l) be the second derivative of -3*l**5/160 + 11*l**4/32 - 5*l**3/8 - 23*l. Factor j(t).
-3*t*(t - 10)*(t - 1)/8
Solve 8/3*w**3 + 2/3 + 4*w**2 + 2/3*w**4 + 8/3*w = 0.
-1
Let h be 2*2/4*-3 + 5. Factor -87 + 2*f**h + 87 + 3*f**3 + f**4.
f**2*(f + 1)*(f + 2)
Let p(d) be the third derivative of -1/36*d**4 + 0 + 4/105*d**7 + 12*d**2 - 1/56*d**8 + 1/90*d**6 - d - 2/45*d**5 + 0*d**3. Suppose p(u) = 0. What is u?
-1/3, 0, 1
Let a = -253/15 - -1921/105. What is v in -12/7 + a*v - 2/7*v**2 = 0?
2, 3
Let o be (9 + -5 - -8)*(-4 - 65/(-15)). Factor 0 - 2/11*a**5 - 8/11*a**o + 0*a - 10/11*a**3 - 4/11*a**2.
-2*a**2*(a + 1)**2*(a + 2)/11
Let h = 808 - 423. Let f be (-6)/(-21) - 40/h. Solve f*u**2 + 6/11 + 8/11*u = 0 for u.
-3, -1
Let 3/2 + 1/4*l**2 - 5/4*l = 0. Calculate l.
2, 3
Let g = 2380/13 + -4565/26. Let 0*a**3 + 0 - 5*a - 5/2*a**4 + g*a**2 = 0. Calculate a.
-2, 0, 1
Let j(m) be the first derivative of 3/4*m**3 + 1/24*m**6 + 0*m**2 + 0*m - 1/4*m**5 - 13 + 3/16*m**4. Determine q, given that j(q) = 0.
-1, 0, 3
Let v be ((6 - 12) + 5)/(-12). Let z(f) be the second derivative of 0 + 0*f**2 + 1/30*f**6 - v*f**4 - 1/6*f**3 + 1/20*f**5 - 6*f. Factor z(p).
p*(p - 1)*(p + 1)**2
Factor 11*i**3 + 0*i**2 + 14*i**3 - 40*i**3 + 17*i**3 - 4*i**2.
2*i**2*(i - 2)
Let y(v) = v**2 + 29*v + 27. Let m be y(-28). Let k be 130/45 + 2 + m + -3. What is t in -2/9 + 10/9*t - k*t**2 = 0?
1/4, 1
Let x = -25/11 + 419/165. Let m(b) be the first derivative of 0*b - 1/5*b**2 + 6 + 1/15*b**6 - x*b**3 + 0*b**4 + 4/25*b**5. Factor m(a).
2*a*(a - 1)*(a + 1)**3/5
Let t(g) be the third derivative of 1/4*g**5 + 0*g + 5/24*g**4 - 31*g**2 + 0 - 5/3*g**3. Let t(o) = 0. Calculate o.
-1, 2/3
Let z = 36822550/11 - 3343857. Let b = -3643 + z. What is i in -278/11*i**3 - 64/11*i - 190/11*i**4 - 194/11*i**2 - b*i**5 - 8/11 = 0?
-1, -2/5
Let y(h) be the second derivative of 15*h + 0 + 2/9*h**3 + h**2 - 1/18*h**4. Factor y(a).
-2*(a - 3)*(a + 1)/3
Find l, given that 3/2*l**2 + 0 - 3/2*l**4 - 3/2*l**3 + 0*l + 3/2*l**5 = 0.
-1, 0, 1
Let k be (6/10)/((-7)/(-35)). Suppose 0 = l - 3*q + 6, 3*l - q - 3*q = -k. Find z, given that -24*z**3 - 3*z**5 - z**4 + 10*z**l + 5*z**3 - 8*z**4 - 3*z**2 = 0.
-1, 0
Let n(c) be the first derivative of -4/3*c**3 + 2 - 8*c**2 - 16*c. Suppose n(m) = 0. What is m?
-2
Find b, given that 10*b - 20*b**3 + 10*b - 30*b**2 + 25*b**4 - 7 + 0*b + 12 = 0.
-1, -1/5, 1
Suppose 79*x + 21*x - 500 = 0. Let 2*t**3 - 2*t**4 + 0 - 2/3*t**2 + 2/3*t**x + 0*t = 0. What 