j = -2*j - 28. Suppose -o + q*o = 152. Factor -6*p + o*p**2 - 41*p**3 + 7*p**2 + 32*p**3 - 5*p**2.
-3*p*(p - 2)*(3*p - 1)
Let d(j) be the third derivative of 0*j - 1/120*j**5 + 0 + 29*j**2 - 1/1344*j**8 + 1/420*j**7 + 1/480*j**6 + 0*j**4 + 0*j**3. Find p, given that d(p) = 0.
-1, 0, 1, 2
Let d = -138 + 152. Suppose 0 = -4*v + d*v - 50. Let 0*n**3 + 0*n + 0 + 16/7*n**2 + 4/7*n**v - 12/7*n**4 = 0. What is n?
-1, 0, 2
Factor 147 - 129*q**2 + 1914*q**3 + 909*q**2 + 624*q**2 + 363*q**4 + 285 + 327*q**2 - 2088*q.
3*(q + 3)**2*(11*q - 4)**2
Let p(g) be the second derivative of 0*g**3 - 3*g + 0*g**2 - 3/4*g**4 + 3/10*g**6 - 9 + 1/14*g**7 - 3/20*g**5. Factor p(d).
3*d**2*(d - 1)*(d + 1)*(d + 3)
Let y(q) be the first derivative of -10/3*q**3 - 5/12*q**4 - 19 + 0*q**2 - 6*q. Let i(j) be the first derivative of y(j). Factor i(z).
-5*z*(z + 4)
Let x(m) be the second derivative of -5*m**4/72 - 595*m**3/18 - 395*m**2/4 + 1227*m. What is b in x(b) = 0?
-237, -1
Let h(v) be the third derivative of -v**7/105 + v**6/5 + 23*v**5/30 - 23*v**4/2 + 104*v**3/3 - 2356*v**2 - 2*v. Let h(x) = 0. What is x?
-4, 1, 2, 13
Let a(b) be the first derivative of -b**5/90 + b**4/18 - b**3/9 - 16*b**2 - 101. Let g(i) be the second derivative of a(i). Solve g(y) = 0.
1
Let g(d) be the first derivative of d**4/18 - 32*d**3/9 - 17*d**2/3 + 196*d/9 + 2385. Determine w so that g(w) = 0.
-2, 1, 49
Let s(m) be the second derivative of -9*m**7/14 - 13*m**6/10 + 63*m**5/10 + 9*m**4 - 28*m**3 - 2*m - 931. Suppose s(c) = 0. Calculate c.
-2, 0, 1, 14/9
Let m = -11808 - -11808. Let q(d) be the third derivative of -2*d**3 + m*d + 1/60*d**6 + 6*d**2 + 0*d**5 + 0 - 7/12*d**4. Let q(h) = 0. What is h?
-2, -1, 3
Suppose 129 - 11 = 56*b + 6. Let 60/7 - 2/7*g**b + 26/7*g = 0. What is g?
-2, 15
Suppose -3*c + 41 + 7 = 0. Suppose 0 = -5*f - t + 11, -4*f + 4*t = 3*t - c. Solve x + 4*x**4 + 1 - 3*x**4 + 4 - 2*x**f - 4 + x**5 - 2*x**2 = 0.
-1, 1
Determine w, given that 26/7*w**2 - 68/7*w + 2/7*w**3 - 80 = 0.
-14, -4, 5
Let c(o) be the third derivative of -8/15*o**6 + 2/3*o**4 + 0*o - 185*o**2 + 0 - 2/105*o**7 + 104/3*o**3 - 13/5*o**5. Factor c(y).
-4*(y - 1)*(y + 2)**2*(y + 13)
Factor -363/4*o + 0 - 3/4*o**3 - 33/2*o**2.
-3*o*(o + 11)**2/4
Factor -1/2*n**3 + 169/2 + 171/2*n**2 - 339/2*n.
-(n - 169)*(n - 1)**2/2
Let n = -67183 + 604667/9. Let -1/3*c**2 + n*c - 2/3*c**3 + 1/9*c**4 - 4/3 = 0. Calculate c.
-2, 1, 6
Let n(q) be the first derivative of -q**3/18 - 203*q**2 - 247254*q + 1690. Factor n(s).
-(s + 1218)**2/6
Let a(s) be the third derivative of 0 - 1/360*s**5 - 1/360*s**6 + 0*s**4 - 125*s**2 + s - 1/1260*s**7 + 0*s**3. Factor a(k).
-k**2*(k + 1)**2/6
Let c(o) be the first derivative of 165 - 15/4*o**4 + 0*o**2 + 10/3*o**3 + 0*o - 12*o**5 - 35/6*o**6. Factor c(a).
-5*a**2*(a + 1)**2*(7*a - 2)
Let f(q) be the third derivative of -q**9/90720 + q**7/5040 - q**6/2160 + q**4/24 + q**3/2 + 2*q**2 + 2. Let h(r) be the second derivative of f(r). Factor h(o).
-o*(o - 1)**2*(o + 2)/6
Let n(p) be the first derivative of 51*p**4/4 + 108*p**3 + 567*p**2/2 + 162*p + 8878. Factor n(a).
3*(a + 3)**2*(17*a + 6)
Suppose 31*p = 32*p - 2*w + 340, 4*p + 1385 = 3*w. Let u = -348 - p. Factor 0 - 2/3*k**u - 2/3*k.
-2*k*(k + 1)/3
Factor 216*v**2 + 4/5 + 538/5*v**3 + 546/5*v.
2*(v + 1)**2*(269*v + 2)/5
Let w(j) be the second derivative of -87*j - 14*j**4 - 5*j**5 - 8/15*j**6 - 6*j**3 + 0 + 0*j**2. Factor w(z).
-4*z*(z + 3)**2*(4*z + 1)
Factor -5/4*r**3 - 27555/4*r**2 - 30995416265/4 - 50618535/4*r.
-5*(r + 1837)**3/4
Suppose -105*y - 274408 = -274408. Factor -405/2*u**3 + 150*u**4 - 125/4*u**5 - 81/4*u + y + 108*u**2.
-u*(u - 3)*(5*u - 3)**3/4
Factor 26*o**2 + 9 + 65/2*o + 5/2*o**3.
(o + 1)*(o + 9)*(5*o + 2)/2
Solve -14 - 180*t**3 - 992*t**4 - 22 + 972*t**4 - 39 - 465*t**2 - 340*t = 0 for t.
-5, -3, -1/2
Determine g so that 25164*g**2 - 25352*g**2 + 5*g + 188 - 4*g**3 + 7*g - 13*g + 5*g = 0.
-47, -1, 1
Let x(v) = v**3 + v**2 + 1. Let u(p) = 2*p**2 + 3*p - 11. Let m be u(-3). Let k(z) = -7*z**3 - 2*z**2 + 15*z + 8. Let y(r) = m*x(r) - k(r). Factor y(l).
5*(l - 2)*(l + 1)**2
Suppose 0 = -0*s - 5*s + 15. Suppose -3*i + 5 = s*u + 2, u + 2 = -4*i. Determine v so that 32/9*v**u + 2/9*v**4 - 16/9*v**3 + 0 + 0*v = 0.
0, 4
Factor -790/19*g - 64/19*g**2 - 2100/19 + 2/19*g**3.
2*(g - 42)*(g + 5)**2/19
Factor 3/4*h**2 + 468 - 75/2*h.
3*(h - 26)*(h - 24)/4
Let n(y) = 2*y**4 + 39*y**3 - 84*y**2 + 43*y - 7. Let w(l) = l**3 - 2*l**2 + l + 1. Let v(i) = -2*n(i) - 14*w(i). Factor v(k).
-4*k*(k - 1)**2*(k + 25)
Let c = 4 + 0. Let q = 46 + -31. Determine p so that -8*p**4 - 10*p**3 + 5 - 3*p**5 + 4*p**2 - 2*p**5 + 6*p**2 - 7*p**c + q*p = 0.
-1, 1
Let z be (-8 - (-570)/65)*(-8 + (-41)/(-5)). Determine k, given that -6/13*k**3 + 0 + z*k**5 + 8/13*k - 8/13*k**2 + 4/13*k**4 = 0.
-2, 0, 1
Let q(z) be the second derivative of 48*z + 2 + 1/7*z**4 + 5/21*z**3 + 1/70*z**5 + 0*z**2. Determine c so that q(c) = 0.
-5, -1, 0
Let y(i) = 4*i**4 + 42*i**3 - 52*i**2 - 92*i + 10. Let s(l) = 5*l**4 + 41*l**3 - 53*l**2 - 92*l + 15. Let b(g) = 2*s(g) - 3*y(g). Suppose b(m) = 0. What is m?
-23, -1, 0, 2
Let p = -16 - 2. Let v be ((-24)/p)/(6/9). Suppose k**3 - v*k - k + 3*k = 0. Calculate k.
0
Let h(j) be the third derivative of j**7/840 - 149*j**6/60 + 22201*j**5/15 - 1546*j**2 - 1. Factor h(o).
o**2*(o - 596)**2/4
Let v(n) be the first derivative of n**6/9 - 52*n**5/5 + 934*n**4/3 - 27536*n**3/9 + 13056*n**2 - 73984*n/3 + 4229. Find s, given that v(s) = 0.
2, 4, 34
Let s(p) be the second derivative of 14*p - 7203/2*p**2 - 1/4*p**4 - 49*p**3 + 0. Factor s(b).
-3*(b + 49)**2
Let b be 4/6 - (-4)/3. Factor b + n**2 - 35*n - 37*n + 69*n.
(n - 2)*(n - 1)
Let a be 19 - 48 - (-88 - -57). Let -1/2*u**a + 1 - 7/4*u = 0. Calculate u.
-4, 1/2
Let x(t) = 21*t**3 - 2*t**2 + 6. Let b be x(2). Find u, given that 18 + 53 - 3*u + 161*u**2 + 23*u - b*u**2 - 11 = 0.
-2, 6
Let q(u) = 2*u**4 + 54*u**3 + 196*u**2 + 12*u - 12. Let w(t) = t**3 + t**2 + 2*t - 2. Let l(v) = q(v) - 6*w(v). Solve l(a) = 0.
-19, -5, 0
Let i(m) be the third derivative of -m**6/24 + 19*m**5/20 - 19*m**4/4 - 88*m**3/3 - 9186*m**2. Solve i(n) = 0.
-1, 22/5, 8
Let v(a) = -2*a**3 + 10*a**2 + 47*a + 21. Let u be v(11). Let l = u + 2746/3. Factor -4/3*j + 1/3*j**3 + 1/3*j**2 - l.
(j - 2)*(j + 1)*(j + 2)/3
Let l be 33/(-3*(-2)/4). Let o(z) = -3 - l*z**2 + 20*z**2 - 15 - 14*z. Let b(h) = -h**2 - 13*h - 17. Let p(i) = -6*b(i) + 5*o(i). Find d such that p(d) = 0.
-1, 3
Let i(h) be the second derivative of -h**5/5 + 1525*h**4/3 - 1161286*h**3/3 - 1164338*h**2 - 18*h + 17. Factor i(m).
-4*(m - 763)**2*(m + 1)
Suppose 0 = 5071*l - 19 + 35 - 16. Let s = -3/77 + 1093/385. Determine y, given that 12/5*y**2 + 0*y**4 + s*y**3 - 2/5*y**5 + l + 0*y = 0.
-2, -1, 0, 3
Let z(o) be the second derivative of -1/3*o**6 - 5*o**4 - 5/2*o**2 + 0 - 65/12*o**3 - 17/8*o**5 + 6*o. Suppose z(k) = 0. What is k?
-2, -1, -1/4
Let n be 20/(-165)*162/(-2). Let o be 30/99*(((-6)/1)/(-30) - -19). Find a, given that -n*a**4 + 270/11*a**5 - 416/11*a + 928/11*a**2 + o - 720/11*a**3 = 0.
-2, 2/5, 2/3
Let h(y) be the first derivative of 0*y - 2/5*y**5 + 0*y**2 - 102 + 5/2*y**4 - 4*y**3. Factor h(b).
-2*b**2*(b - 3)*(b - 2)
Suppose 79*r - 77*r = 8. Let x(c) = c**3 - 22*c**2 - 83*c - 96. Let u(i) = 22*i**2 + 82*i + 96. Let g(v) = r*x(v) + 6*u(v). Solve g(s) = 0 for s.
-4, -3
Let y(d) = -375*d**4 - 14*d**3 - 8*d**2 - 24*d. Let h(i) = -500*i**4 - 18*i**3 - 11*i**2 - 33*i. Let z(b) = 8*h(b) - 11*y(b). Solve z(m) = 0 for m.
-2/25, 0
Factor -1696*r + 28201496*r**2 + 2*r**4 + 225 - 28200830*r**2 - 68*r**3 - 2657.
2*(r - 19)*(r - 8)**2*(r + 1)
Let f(w) = 3*w**2 + 183*w + 182. Let p be f(-1). Suppose -5*s - 10 = 5*l, p*l + 2 = 5*s - 8*s. Factor -2/5*q**s - 4/5*q + 6/5.
-2*(q - 1)*(q + 3)/5
Let g(o) be the second derivative of o**6/180 + 11*o**5/120 - o**4/24 - 35*o**3/36 - 11*o**2/6 + 323*o. Factor g(s).
(s - 2)*(s + 1)**2*(s + 11)/6
Suppose -g + 19*r = 22*r - 2, -4*g - 3*r = -8. Let q be ((-18)/(-108))/(((-2)/(-15))/g). Factor -q*h**3 - 10*h**2 - 15/2*h + 0.
-5*h*(h + 1)*(h + 3)/2
Let l(p) be the first derivative of p**9/1008 - 3*p**8/280 + 11*p**7/280 - p**6/20 + 49*p**3/3 - 189. Let y(b) be the third derivative of l(b). Factor y(q).
3*q**2*(q - 3)*(q - 2)*(q - 