 first derivative of 5*w**4/4 - 20*w**3/3 - 10*w**2 + 80*w - 11. Suppose g(c) = 0. Calculate c.
-2, 2, 4
Let b(p) = -p**2 + 1. Let j(z) = -z**2 - 3*z**2 + 3 + 0*z**2 + 3*z. Let a(c) = 3*b(c) - j(c). Factor a(q).
q*(q - 3)
Let w = -2339/196 - -793/49. Solve -1 + m**3 - w*m**2 + 5*m = 0.
1/4, 2
Let d(t) be the first derivative of 35*t**6/4 - 244*t**5/5 - 2341*t**4/24 - 69*t**3 - 71*t**2/3 - 4*t + 11. What is i in d(i) = 0?
-2/5, -1/3, -2/7, 6
Let b(u) be the third derivative of u**7/4200 + u**6/900 - u**5/600 - u**4/60 - 19*u**3/6 - 6*u**2. Let k(h) be the first derivative of b(h). Factor k(y).
(y - 1)*(y + 1)*(y + 2)/5
Factor 26/5*w**3 - 48/5 - 212/5*w**2 + 344/5*w.
2*(w - 6)*(w - 2)*(13*w - 2)/5
Suppose -7 = -5*s + 429*f - 428*f, -s - 3*f = -11. Solve 14/5*c - 28/5*c**3 + 8/5*c**s - 4/5*c**4 + 14/5*c**5 - 4/5 = 0 for c.
-1, 2/7, 1
Let z(t) = 7*t**3 + 2*t**2 - 5*t - 6. Let h(p) = -6*p**3 - 2*p**2 + 4*p + 5. Let f = 147 + -141. Let u(l) = f*h(l) + 5*z(l). Find g such that u(g) = 0.
-1, 0
Factor -240*n - 2*n**3 + 260*n - 3*n**3.
-5*n*(n - 2)*(n + 2)
Let i(p) be the third derivative of -2*p**7/735 - p**6/70 - p**5/105 + p**4/14 + 4*p**3/21 - 47*p**2. Determine l, given that i(l) = 0.
-2, -1, 1
Factor 2/7*o**2 - 232/7*o + 6728/7.
2*(o - 58)**2/7
Let b(x) be the third derivative of x**8/63840 - x**6/6840 - 11*x**4/24 + 11*x**2. Let u(t) be the second derivative of b(t). Factor u(d).
2*d*(d - 1)*(d + 1)/19
Let z(y) = y**4 + 62*y**3 - 291*y**2 + 432*y - 196. Let j(h) = -60*h**3 + 291*h**2 - 432*h + 195. Let k(p) = -4*j(p) - 3*z(p). Determine n, given that k(n) = 0.
1, 8
Let o(t) be the second derivative of -t**5/70 - 2*t**4/21 - 4*t**3/21 - 14*t - 5. Factor o(x).
-2*x*(x + 2)**2/7
Let j = 1594 - 4622/3. Factor 5/6*d**2 - 40/3*d + j.
5*(d - 8)**2/6
Let r(k) be the third derivative of 3*k**6/40 - k**5/4 + k**4/4 - 47*k**2. Factor r(t).
3*t*(t - 1)*(3*t - 2)
Let s be (-21 + 20)*(-2 + -1). Let x(m) be the third derivative of -3/40*m**5 - 1/80*m**6 + 0 + 0*m - 3/16*m**4 - 1/4*m**s + 7*m**2. Factor x(y).
-3*(y + 1)**3/2
Factor -24*a + 288 + 1/2*a**2.
(a - 24)**2/2
Let b be -1 + (-844)/8 - 12/4. Let g = -105 - b. Factor 7/2*u**2 + g*u + 1.
(u + 1)*(7*u + 2)/2
Suppose -7*d + 9*d = -w + 9, -4*d - 10 = -2*w. Suppose w*l - 2 = 19. Factor -22/9*k**2 + 10/9*k**5 + 14/3*k**l + 0 - 34/9*k**4 + 4/9*k.
2*k*(k - 1)**3*(5*k - 2)/9
Let 28*c**2 + 33*c - 27*c - 27*c**2 = 0. Calculate c.
-6, 0
Suppose -4*z + f = 440, -f - 3*f = -5*z - 550. Let a be (-44)/z*(1 - -9). Factor 2/5*j**a - 2/5*j**2 + 0*j + 0*j**3 + 0.
2*j**2*(j - 1)*(j + 1)/5
Let i(t) be the first derivative of 3*t**5/25 + 51*t**4/20 - 97. Factor i(n).
3*n**3*(n + 17)/5
Let y be (4 - 3) + 3*(-2)/(-12). Factor -6*c**2 - 3 - 15/2*c - y*c**3.
-3*(c + 1)**2*(c + 2)/2
Let q = 796 + -790. Let t(f) be the second derivative of -f + 3/40*f**5 + 1/12*f**3 + 0*f**2 + 0 + 1/8*f**4 + 1/60*f**q. What is y in t(y) = 0?
-1, 0
Let n(j) = -j**4 + 84*j**3 - 109*j**2 - 11*j + 11. Let c(q) = 28*q**3 - 36*q**2 - 4*q + 4. Let g(u) = 11*c(u) - 4*n(u). Factor g(o).
4*o**2*(o - 5)*(o - 2)
Suppose -3*y + 6*y + a - 7 = 0, -4*y + 5*a = -3. Find d, given that 1/3*d**y + 64/3 + 16/3*d = 0.
-8
Let q(z) be the first derivative of -z**3/6 + 3*z**2/4 + 2*z + 56. Factor q(x).
-(x - 4)*(x + 1)/2
Let b = 10355 - 10355. Factor 2/3*z**3 + 0*z**4 + b*z**2 + 0*z - 2/3*z**5 + 0.
-2*z**3*(z - 1)*(z + 1)/3
Let i(j) be the second derivative of 2*j**6/105 + 3*j**5/5 + 38*j**4/21 - 6*j - 15. Determine m, given that i(m) = 0.
-19, -2, 0
Factor 1681/2*t + 0 - 41*t**2 + 1/2*t**3.
t*(t - 41)**2/2
Let o be (-1 - 5/(-2))*(-58 - -60). Let d(v) be the first derivative of 0*v**2 - 3/5*v**5 + 0*v**4 + 0*v + v**3 + o. Factor d(b).
-3*b**2*(b - 1)*(b + 1)
Let i = 68494/3 - 22822. Suppose 5*r - 29 = 31. Find p such that -8/3 - i*p + r*p**2 = 0.
-2/9, 1
Let j be ((-4)/5)/(-2*(-1)/5). Let l(y) = 2*y**2 + 3*y. Let o be l(j). Factor 1/4*i**4 + 1/2*i**o + 0*i + 0 + 3/4*i**3.
i**2*(i + 1)*(i + 2)/4
Let c(t) be the third derivative of -t**6/90 + 2*t**4/3 - 32*t**3/9 - 19*t**2. Suppose c(m) = 0. Calculate m.
-4, 2
Let p(s) = -s**2 + 12*s + 28. Let o be p(14). Let y(i) be the third derivative of -i**2 - 1/120*i**6 - 2/3*i**3 + 0*i + 1/20*i**5 + 0*i**4 + o. Factor y(b).
-(b - 2)**2*(b + 1)
Factor -15*t**4 + 15*t**2 - 1652*t**5 - 10*t + 2*t**3 + 3*t**3 + 1657*t**5.
5*t*(t - 2)*(t - 1)**2*(t + 1)
Let w be ((-24)/(-30))/((-1)/(-5)). Suppose x + 5*l - 7 = 0, -3*x - 3*l + w = -5. Suppose 2*k - 2*k**x + 5*k - 4*k + k**2 = 0. What is k?
0, 3
Let k(y) be the first derivative of y**8/6720 + y**7/3360 - y**6/1440 - y**5/480 - 4*y**3 + 8. Let t(j) be the third derivative of k(j). Factor t(v).
v*(v - 1)*(v + 1)**2/4
Suppose -z - 309 = -311. Factor -94*o**3 + 15*o - 24*o**z + 79*o**3 - 2*o - o.
-3*o*(o + 2)*(5*o - 2)
Let w(i) = 2*i - 9. Let r be w(4). Let b = 3 + r. Factor -2*f**4 - 5*f**3 + 5*f + b*f**2 + 3*f**3 - 3*f + 0*f**2.
-2*f*(f - 1)*(f + 1)**2
Let z be (-716)/(-24) - 1/6*-1. Let o be 10*((-146)/z - -5). Factor 0 + 2/3*p + 2/3*p**3 - o*p**2.
2*p*(p - 1)**2/3
Suppose f - 5 = 2. Suppose -3*g + f = -5. Factor -12*c**g - 4*c + 4*c**3 + 108 + 12*c**2 - 108.
-4*c*(c - 1)*(c + 1)*(3*c - 1)
Let a = 46 + -41. Let f(r) = r**3 - r - 1. Let h(s) = 7*s**3 + 24*s**2 + 67*s - 5. Let q(p) = a*f(p) - h(p). Let q(b) = 0. Calculate b.
-6, 0
Let q(a) = a**2 + 15*a + 59. Let t be q(-9). Factor 0 - 6/7*i**3 + 3/7*i**t + 3/7*i + 0*i**4 + 0*i**2.
3*i*(i - 1)**2*(i + 1)**2/7
Let p(k) be the third derivative of k**6/30 + k**5/2 + 2*k**4 - 16*k**3/3 - 235*k**2. Let p(r) = 0. What is r?
-4, 1/2
Let a(p) = p**2 + 39691 - 39691 - 6*p. Let j be a(0). Find o, given that 1/5 - 1/5*o**2 + j*o = 0.
-1, 1
Let b(k) be the first derivative of -k**7/1960 + k**6/210 - 20*k**3/3 + 19. Let f(n) be the third derivative of b(n). Factor f(d).
-3*d**2*(d - 4)/7
Suppose 12*z = 25*z - 39. Let i(j) be the third derivative of 0*j + 0 + 0*j**z + 1/20*j**5 - 1/70*j**7 + 12*j**2 + 1/20*j**6 - 1/4*j**4. Factor i(v).
-3*v*(v - 2)*(v - 1)*(v + 1)
Let c = 20 + -14. Let h(r) be the first derivative of 25/9*r**c - 28/9*r**3 + 2*r**5 + 3*r**2 - 17/3*r**4 - 3 - 2/3*r. Find z such that h(z) = 0.
-1, 1/5, 1
Let l be 1 - (-5)/(25/5). Factor -20*y**2 + 30*y**l + 0*y**3 + 4*y - 14*y**2 + y**3.
y*(y - 2)**2
Suppose -6*h + 218 - 106 = 100. Factor -2/13 + 2/13*x**h + 0*x.
2*(x - 1)*(x + 1)/13
Let g(b) = -b**3 + b. Let i(q) = 6*q**3 - 13*q**2 + 43*q - 28. Let z(y) = -18*g(y) - 2*i(y). Factor z(s).
2*(s - 2)*(s + 7)*(3*s - 2)
Let u(j) be the third derivative of 0*j**3 - 10*j**2 + 0*j + 1/120*j**5 + 1/48*j**4 + 0. Let u(q) = 0. What is q?
-1, 0
Let k(w) be the second derivative of -w**5/140 + w**4/56 + 7*w**2 - 2*w. Let b(s) be the first derivative of k(s). Factor b(y).
-3*y*(y - 1)/7
Let m be (19 + -10)*(-2)/(-6). Factor 1/3*t**4 + t + 0 - 1/3*t**2 - t**m.
t*(t - 3)*(t - 1)*(t + 1)/3
Suppose 0 = 4*m - 3*i + 6, -3*m = -3*i + 18 - 12. Suppose 0 + m*z - 1/7*z**2 - 2/7*z**3 - 1/7*z**4 = 0. Calculate z.
-1, 0
Let h(y) = -30*y - 2726. Let o be h(-91). Determine c, given that -44/5*c + 28/5*c**4 - o + 8*c**3 - 8/5*c**2 + 4/5*c**5 = 0.
-5, -1, 1
Let z be ((-2)/4)/(7 + (-145)/20). Determine f so that 0*f + 115*f**2 - z - 3*f - 116*f**2 = 0.
-2, -1
Suppose 7*q = 2*q + 30. Suppose -q*r**3 + 0*r**5 - 10*r**4 + 4*r + 2*r**5 + 12*r**4 - 3*r**2 + r**2 = 0. Calculate r.
-2, -1, 0, 1
Let n(g) be the first derivative of -11 + 3/2*g**5 + 35/8*g**4 + 5/4*g**2 + 0*g + 25/6*g**3. Solve n(l) = 0.
-1, -1/3, 0
Let s(o) = o**3 - o**2. Let d(a) = 1 + 2*a - 4*a**2 - 6*a**3 - a + 8*a**3. Let u(g) = -4*d(g) + 12*s(g). Factor u(f).
4*(f - 1)*(f + 1)**2
Let t be 1*-3*62/(-93). Let -33*y + 5*y + 25 + 34*y**2 - 38*y**t + 7 = 0. What is y?
-8, 1
Let j = -16 + 15. Let v be (j/(-3))/((-10)/(-120)). What is d in 47*d**2 - 35*d**2 - v*d - 12*d + 4*d**3 = 0?
-4, 0, 1
Let k(d) be the first derivative of -d**4/34 + 46*d**3/17 - 1587*d**2/17 + 24334*d/17 - 31. Determine l, given that k(l) = 0.
23
Let y(o) be the first derivative of o**5/15 + o**4/6 - o**3/3 - 4*o**2/3 - 4*o/3 + 27. Factor y(s).
(s - 2)*(s + 1)**2*(s + 2)/3
Find i such that 6*i**5 + 75*i**3 - i**5 - 60*i**3 + 15*i**4 + 5*i**2 = 0.
-1, 0
Suppose 0 = 3*y + 2*x - 10, 5 = -5*y + 7*y + x. Let a = 0 - -2. Let -2*c**2 + 1 + y*c**3 + 3*