t**4/8 + 8*t**3/3 + 15*t**2 - 431. What is q in b(q) = 0?
-10, -6, 0
Let c(r) be the third derivative of 0 - 2/1995*r**7 + 4/57*r**3 - 3/380*r**6 - 16*r**2 + 3/76*r**4 + 0*r - 1/285*r**5. Let c(t) = 0. What is t?
-4, -1, -1/2, 1
Let m = -640/23 - -1349/46. Determine c, given that -7/2*c**2 + 2*c + m = 0.
-3/7, 1
Let v(q) be the third derivative of 6/5*q**3 - 7/200*q**6 + 37/100*q**5 + 0*q - 13/10*q**4 + 0 + 20*q**2. Factor v(w).
-3*(w - 3)*(w - 2)*(7*w - 2)/5
Factor -64/5*f**3 - 324/5 - 4/5*f**4 - 184/5*f**2 + 576/5*f.
-4*(f - 1)**2*(f + 9)**2/5
Suppose -d + 43 = 5*l, -3764 = l - 3772. Let q = 161 + -1447/9. Determine y so that 0 + 2/9*y**2 + q*y**d + 0*y = 0.
-1, 0
Suppose -3*t - t + 32 = 0. Factor -14 + t + 4 + 2*h**2.
2*(h - 1)*(h + 1)
Factor 21*x**2 + 7*x**2 - 6*x**2 - 112 + 120 + 28*x + 5*x**3.
(x + 2)**2*(5*x + 2)
Let g(a) be the first derivative of -2*a**3/9 - 4*a**2 - 18*a + 9. Factor g(v).
-2*(v + 3)*(v + 9)/3
Let b be (2/8*8 - 4) + 54/24. Factor -1 - 13/4*a - 15/4*a**2 - 7/4*a**3 - b*a**4.
-(a + 1)**3*(a + 4)/4
Let k(d) be the third derivative of 27*d**7/70 + 891*d**6/40 + 504*d**5 + 5248*d**4 + 16384*d**3 + 63*d**2 - 3. Factor k(g).
3*(g + 1)*(3*g + 32)**3
Suppose 19 = 27*v - 36 - 26. Solve -2*l + 4/7 + 2*l**2 - 4/7*l**v = 0.
1/2, 1, 2
Suppose 133*n + 102*n - 993 = -53. Let -21/8*o**3 + 3/2*o + 0 + 9/8*o**n + 0*o**2 = 0. Calculate o.
-2/3, 0, 1, 2
Let x(u) be the second derivative of -u**7/63 + 26*u**6/45 - 47*u**5/10 - 182*u**4/9 - 196*u**3/9 - 7*u - 25. Factor x(s).
-2*s*(s - 14)**2*(s + 1)**2/3
Let c(d) be the first derivative of 1/4*d**3 + 0*d - 3/20*d**5 - 1 + 0*d**4 + 0*d**2. Factor c(w).
-3*w**2*(w - 1)*(w + 1)/4
Suppose -1/4*n**5 + 0 + 3*n**4 - 5/2*n**3 - 3*n**2 + 11/4*n = 0. Calculate n.
-1, 0, 1, 11
Let w(h) = h**2 + 6*h - 59. Let s be w(-12). Factor 28*z**3 - s*z**3 + 3 + z**2 - 5*z - 14*z**3.
(z - 1)**2*(z + 3)
Let d(f) be the third derivative of 1/6*f**4 + 0 + 0*f**3 + 0*f + 2/105*f**7 - 1/15*f**5 + 11*f**2 - 1/30*f**6. Factor d(o).
4*o*(o - 1)**2*(o + 1)
Let v(u) = -u + 8. Let h be v(-4). Suppose -2*s + h = s. Factor -3*m**3 - s*m + 8*m**2 - 10*m**2 + 9*m**3.
2*m*(m - 1)*(3*m + 2)
Let d(i) be the second derivative of -i**5/20 + 17*i**4/12 - 21*i**3/2 - 81*i**2/2 + 3*i - 7. Find b, given that d(b) = 0.
-1, 9
Let d(f) be the first derivative of f**4 + 8*f**3 + 6*f**2 - 40*f - 64. Find i such that d(i) = 0.
-5, -2, 1
Suppose 5*o = -5 + 15. Suppose 5*c = 4*p + 8, o*p + 0*c - 2 = c. Factor 3*t**3 + 12*t**2 + 21*t + p*t**2 + 10 - 1.
3*(t + 1)**2*(t + 3)
Let p be 0 + -3 - -6 - (-3)/(-1). Suppose -5*h - 25 + 50 = p. Factor 0 + 1/4*m**h - 1/2*m**3 + 1/4*m + 0*m**4 + 0*m**2.
m*(m - 1)**2*(m + 1)**2/4
Let z(u) be the third derivative of -u**6/1200 + 7*u**5/300 - 13*u**4/48 + 5*u**3/3 - 3*u**2 + 13*u. Factor z(r).
-(r - 5)**2*(r - 4)/10
Let v(x) = -x**3 - 5*x**2 - 6*x - 4. Let y be v(-4). Let z = -2 + y. Factor -1 + 18*o + 3 + 24*o**z + 1.
3*(2*o + 1)*(4*o + 1)
Let k(j) = 6*j**3 + 14*j**2 + 8*j + 14. Let g(d) = 2*d**3 + 5*d**2 + 3*d + 5. Let p = 40 - 35. Let r(a) = p*k(a) - 14*g(a). Factor r(h).
2*h*(h - 1)*(h + 1)
Let b be 0 - (-2)/3*39/26. Let p(r) be the first derivative of b + 8/9*r + 0*r**2 + 1/18*r**4 - 2/9*r**3. Solve p(q) = 0 for q.
-1, 2
Let m(u) be the first derivative of -u**7/210 + u**5/60 + u**2 + 7. Let x(p) be the second derivative of m(p). Factor x(s).
-s**2*(s - 1)*(s + 1)
Let z(a) be the third derivative of -a**9/9450 - a**8/8400 - 7*a**5/15 + 12*a**2. Let c(y) be the third derivative of z(y). Factor c(b).
-4*b**2*(8*b + 3)/5
Find r such that 15*r**2 - 82982*r**4 + 82977*r**4 + 10*r + 5*r**3 - 5*r**3 = 0.
-1, 0, 2
Let q(c) = c**3 - c + 2. Let x be q(1). Factor -x*v**2 - 8*v**4 + 7*v**2 + 3*v**4 - v - 4*v + 5*v**3.
-5*v*(v - 1)**2*(v + 1)
Let r(q) = -q**2 + 13*q - 2. Let a be r(12). Let n be 392/70 + (-6)/a. Factor -3*l**4 + 2*l**5 + l**2 + 2*l**4 - 4*l**5 + l**n + l**3.
-l**2*(l - 1)*(l + 1)**2
Let z = 1 + 1. Let a(h) = -h + 6*h**2 - 1 + 10*h**2 - 15*h**z. Let i(c) = -8*c**2 - 6*c - 12. Let o(q) = 6*a(q) + i(q). Solve o(d) = 0.
-3
Let m = -1911/695 - 7/139. Let x = m + 61/20. Factor 1/4*d - 1/4*d**2 - x*d**3 + 1/4.
-(d - 1)*(d + 1)**2/4
Let z(q) be the third derivative of 1/2*q**4 + 0 - 7*q**2 + 0*q**5 + 0*q - 3/40*q**6 + 1/70*q**7 + 0*q**3. Factor z(h).
3*h*(h - 2)**2*(h + 1)
Let d be (-3)/9*12/(-10). Let u(n) be the first derivative of -3 - d*n**3 + 0*n + 9/20*n**4 - 4/25*n**5 + 1/10*n**2. What is o in u(o) = 0?
0, 1/4, 1
Let c(t) = 8*t - 2*t + 4*t**5 + t**3 + 4*t**2 - 10*t**4 + t**5 - 2*t. Let d(y) = 5*y**5 - 10*y**4 + 5*y**2 + 5*y. Let a(s) = -5*c(s) + 4*d(s). Factor a(q).
-5*q**3*(q - 1)**2
Let v(m) be the second derivative of 0 - 21*m - 9/7*m**2 - 1/14*m**3 + 1/28*m**4. Factor v(z).
3*(z - 3)*(z + 2)/7
Let i(h) = 4*h**3 + 13*h**2 - 41*h + 11. Let r(s) = -2*s**3 - 6*s**2 + 20*s - 6. Let l(d) = 6*i(d) + 13*r(d). Factor l(m).
-2*(m - 2)*(m - 1)*(m + 3)
Let z(w) be the first derivative of -1/630*w**7 + 2 + 0*w**3 + 0*w**5 + 0*w**6 + 0*w + 0*w**4 - 2*w**2. Let r(h) be the second derivative of z(h). Factor r(k).
-k**4/3
Let l(a) = -168*a - 2529. Let p(i) = i**2 + 2*i - 2. Let z(w) = l(w) - 3*p(w). Solve z(d) = 0.
-29
Let f = 3557/360828 + -2/3341. Let o(a) be the second derivative of 1/45*a**5 + 0*a**3 - f*a**4 + 0 - 2/189*a**7 + 0*a**2 - 15*a + 1/270*a**6. Solve o(b) = 0.
-1, 0, 1/4, 1
Let p(t) be the first derivative of -t**6/2 + 3*t**5/5 + 9*t**4/2 - 73. What is f in p(f) = 0?
-2, 0, 3
Let h(n) be the first derivative of -5*n**4 - 26*n**2 - 56/3*n**3 - 16*n + 15. What is x in h(x) = 0?
-1, -4/5
Let c be 4 + (3 - 4)/((-5)/20). Suppose -r - 6 + c = 0. Factor 0 + 3/4*x**r - 3/4*x.
3*x*(x - 1)/4
Find b, given that 2/5*b**4 + 0*b**3 + 0 - 6/5*b**2 + 4/5*b = 0.
-2, 0, 1
Let r(c) = 6*c - 135. Let g be r(23). Determine f, given that -2/3*f**2 + 1/3*f**5 - 1/3*f + 0*f**g + 2/3*f**4 + 0 = 0.
-1, 0, 1
Let a(y) be the third derivative of -y**5/24 + 3*y**4/16 + 19*y**3/6 - 278*y**2 - y. Factor a(k).
-(k + 2)*(5*k - 19)/2
Let z(a) be the second derivative of -a**6/180 + 2*a**5/15 - a**4 + 15*a**2 - 24*a. Let l(i) be the first derivative of z(i). Solve l(n) = 0.
0, 6
Let y(k) be the third derivative of -1/108*k**4 + 0 + 0*k + 1/270*k**5 + 0*k**3 - 5*k**2. Determine l so that y(l) = 0.
0, 1
Let y(t) be the second derivative of -t**7/56 + 11*t**6/40 - 57*t**5/40 + 13*t**4/4 - 3*t**3 + 306*t. Determine a so that y(a) = 0.
0, 1, 2, 6
Let v be ((-12)/(-78) - 6/(-468))/4. Let s(y) be the second derivative of -1/80*y**5 + v*y**3 + 1/8*y**2 - 2*y + 0 - 1/48*y**4. Suppose s(o) = 0. What is o?
-1, 1
Let h(w) be the first derivative of 4*w**5/5 - 11*w**4 + 68*w**3/3 + 142*w**2 + 168*w + 451. Determine d, given that h(d) = 0.
-1, 6, 7
Let y(b) be the first derivative of -b**5/80 + b**4/16 - b**3/8 + b**2/8 + 2*b - 19. Let x(o) be the first derivative of y(o). Let x(i) = 0. What is i?
1
Let u(c) = c - 3. Let x be u(8). Let o = -3 + x. Factor 2*n**5 - 3*n**5 + 2*n**2 + n**3 - o*n**4 - n**3 + n.
-n*(n - 1)*(n + 1)**3
Suppose -14 + 3 = 3*h + d, -h - 4*d - 11 = 0. Let n = h - -2. Let z(q) = 2*q**2 - 2*q - 12. Let v(t) = -1. Let b(x) = n*z(x) + 8*v(x). Let b(p) = 0. What is p?
-1, 2
Factor 7*i**4 - 4000 - 800*i - 56*i**3 + 9*i**4 + 8*i**4 - 22*i**4 + 480*i**2.
2*(i - 10)**3*(i + 2)
Find j, given that 2/7*j - 6/7*j**2 - 2/7*j**3 + 4/7 + 2/7*j**4 = 0.
-1, 1, 2
Let g(p) be the first derivative of p**4/2 + 38*p**3 + 783*p**2 - 1682*p - 73. Factor g(a).
2*(a - 1)*(a + 29)**2
Let v(w) be the first derivative of 1/15*w**5 - 1/12*w**4 + 0*w**3 + 0*w**2 + 0*w - 13. Determine i so that v(i) = 0.
0, 1
Let m be (-20)/(-15)*(-3)/(-2). Let q(k) be the third derivative of 0*k**3 - 1/12*k**6 + 0*k + 0*k**4 - 4*k**m + 0 - 1/15*k**5. Factor q(t).
-2*t**2*(5*t + 2)
Let m be 5/(-2)*(-462)/385. Let l(b) be the first derivative of 1/2*b**4 + 5 - 4/5*b**5 + 2*b**m - b**2 - 2*b. Solve l(p) = 0.
-1, -1/2, 1
Let l(p) = 5*p**3 + 20*p**2 - 5*p - 25. Let t(g) = -48*g + 24 - 5*g**3 + 96*g - 44*g - 19*g**2. Let f(r) = -4*l(r) - 5*t(r). Find h, given that f(h) = 0.
-2, 1
Let x = 16546/45 - 1834/5. Factor 10/9*d + x*d**2 + 2/9*d**3 + 4/9.
2*(d + 1)**2*(d + 2)/9
Let q(k) be the second derivative of 14*k + 0 + 4/9*k**2 - 1/27*k**4 + 2/27*k**3. Factor q(x).
-4*(x - 2)*(x +