05 + t**6/60 + t**5/6 + t**4/6 - 60*t**2. What is s in u(s) = 0?
-1, -1/2, 0, 2
Let v(q) = 215*q**4 - 635*q**3 + 325*q**2 + 95*q. Let i(u) = -18*u**4 + 53*u**3 - 27*u**2 - 8*u. Let x(d) = -25*i(d) - 2*v(d). Let x(z) = 0. What is z?
-1/4, 0, 1, 2
Let x = -1064 + 10641/10. Let p(y) be the second derivative of 1/60*y**4 - x*y**2 + 0 + 0*y**3 - 7*y. Factor p(i).
(i - 1)*(i + 1)/5
Let o be ((-560)/(-168))/(5/3 - 1). Let c(l) be the third derivative of 5*l**2 - 1/8*l**4 + 0*l + 1/3*l**3 + 0 + 1/60*l**o. Let c(f) = 0. Calculate f.
1, 2
Let m = -8 + 19. Let a = m - 11. Suppose a - 14/11*v**2 + 4/11*v = 0. Calculate v.
0, 2/7
Let g be -3 - (7 - 135/9) - (-68)/(-20). Suppose -2/5*h**4 + 8/5*h + 0 + 2/5*h**2 - g*h**3 = 0. What is h?
-4, -1, 0, 1
Let o(k) = 2*k - 2*k + k + 11. Let x be o(-8). What is c in -x*c**4 - 12*c + 14*c - 2*c**3 + 2*c**2 + c**4 = 0?
-1, 0, 1
Suppose -226*p = 4*a - 225*p - 13, a = -2*p + 12. Factor -1/2*s**a - 1 - 3/2*s.
-(s + 1)*(s + 2)/2
Let r = 18548 - 18545. Suppose 3/5*t**r - t**4 + t**2 - 4/5*t**5 + 0 + 1/5*t = 0. Calculate t.
-1, -1/4, 0, 1
Let h(g) be the first derivative of -3*g**5/190 + g**4/57 + g**3/57 + 5*g - 11. Let k(x) be the first derivative of h(x). Factor k(d).
-2*d*(d - 1)*(3*d + 1)/19
Let q be (-175)/(-14)*(-4)/(-10). Factor 4*i + 16*i**4 - q*i**4 + 4*i + 7*i**4 + 32*i**2 + 42*i**3.
2*i*(i + 1)*(3*i + 2)**2
Let t(q) = 6*q**4 - 6*q**3 + 4*q**2 + 4. Let y(a) be the first derivative of -a**5 + 3*a**4/2 - 4*a**3/3 - 3*a - 5. Let d(v) = 3*t(v) + 4*y(v). Factor d(l).
-2*l**2*(l - 2)*(l - 1)
Suppose -68*k**2 - 66*k**2 + k**3 + 138*k**2 + 3*k = 0. What is k?
-3, -1, 0
Let s(v) be the first derivative of -v**3/3 + 28*v**2 - 784*v - 302. Solve s(z) = 0.
28
Let i(s) be the first derivative of s**6/6 - 2*s**5/5 - 7*s**4/4 + 20*s**3/3 - 6*s**2 - 293. Factor i(p).
p*(p - 2)**2*(p - 1)*(p + 3)
Let d(v) = 53*v - 53. Let k be d(1). Let t(l) be the second derivative of 1/48*l**4 - 3/8*l**2 + k + 6*l + 1/12*l**3. Suppose t(g) = 0. Calculate g.
-3, 1
Let p = 9145/7 + -1306. Factor -6/7*n**2 + 3/7*n**5 - 6/7*n**3 + 3/7*n + p*n**4 + 3/7.
3*(n - 1)**2*(n + 1)**3/7
Suppose 21/2*w - 3/2*w**2 + 27 = 0. Calculate w.
-2, 9
Let p(k) be the first derivative of -k**4/27 - 10*k**3/27 + 4*k**2/3 + 24*k - 29. Let i(x) be the first derivative of p(x). Factor i(j).
-4*(j - 1)*(j + 6)/9
Let v(x) = -9*x**4 + x**3 + x**2 - 5*x. Suppose 0 = -6*f + 2*f - 3*l - 4, -l + 4 = -4*f. Let a(q) = q**4 + q**3 + q**2. Let r(c) = f*v(c) - 4*a(c). Factor r(o).
5*o*(o - 1)**2*(o + 1)
Let y(g) be the third derivative of g**6/120 + g**5/3 + 3*g**4/2 - 94*g**2. Factor y(s).
s*(s + 2)*(s + 18)
Let p(f) be the second derivative of -f**5/20 - f**4/2 - 11*f**3/6 - 3*f**2 + 97*f. Factor p(r).
-(r + 1)*(r + 2)*(r + 3)
Let q be 14/10 + (-28)/21. Let x(v) be the third derivative of 0*v**3 + 0*v - q*v**7 + 0 - 1/3*v**4 - 4/15*v**5 - v**2 + 19/60*v**6. Factor x(f).
-2*f*(f - 2)*(f - 1)*(7*f + 2)
Let v(a) = -2*a**2 - 1. Let c(m) = 11*m**2 + 36*m - 318. Let y(b) = -5*c(b) - 30*v(b). Factor y(l).
5*(l - 18)**2
Let u = 2/311 + 299/1866. Let b(z) be the second derivative of 1/4*z**5 - 4*z - 2/15*z**6 + 1/42*z**7 + 0*z**2 + 0*z**3 - u*z**4 + 0. Factor b(h).
h**2*(h - 2)*(h - 1)**2
Factor 11/2*w + 1/2*w**2 - 6.
(w - 1)*(w + 12)/2
Let v(c) be the second derivative of c**6/6 + 7*c**5/4 + 85*c**4/12 + 85*c**3/6 + 15*c**2 - 4*c - 9. Find x such that v(x) = 0.
-3, -2, -1
Let t(a) be the first derivative of 0*a + 1/6*a**4 + 18 - 4/3*a**2 + 2/3*a**3. Suppose t(r) = 0. What is r?
-4, 0, 1
Suppose 0*l = 3*l - 4*n + 4, -3*n = 2*l - 3. Suppose -601*k + 27 = -592*k. Factor 18*w**k + 8/7*w + 64/7*w**2 + l.
2*w*(7*w + 2)*(9*w + 2)/7
Let z be 3*((-4)/(-3) + -1). Let s be 3/(-12)*(z + -2 - 11). Factor -2/5*r**5 + 2/5*r**2 - 2/5*r**4 + 0*r + 2/5*r**s + 0.
-2*r**2*(r - 1)*(r + 1)**2/5
Let r(c) = 20*c**2 + 31*c + 5. Let f(u) = 82*u + 63*u**2 - 3*u**2 + 9 + 6 + 10*u. Let t(n) = 6*f(n) - 17*r(n). Find b, given that t(b) = 0.
-1, -1/4
Let c(w) be the first derivative of -w**5/30 + 2*w**4 - 48*w**3 - 43*w**2/2 - 2*w - 47. Let j(i) be the second derivative of c(i). Factor j(n).
-2*(n - 12)**2
Suppose 0 = p + 4*s - 31, -2*p - 3*s + 75 = -8*s. Factor 16*g**3 + 35*g + 10*g**2 - p*g**3 + 20 + 14*g**3.
-5*(g - 4)*(g + 1)**2
Let j(w) be the third derivative of w**6/210 + 92*w**5/105 + 1058*w**4/21 - 68*w**2 - 2. Let j(o) = 0. What is o?
-46, 0
Let y(g) = 304*g + 8818. Let t be y(-29). Let h be ((-8)/(-18))/(2/12). Find w such that -h + 8/3*w - 2/3*w**t = 0.
2
Solve -3/4*u**2 + 27/4 + 6*u = 0.
-1, 9
Let n be (-606)/(-10) + 12/(-20). Let t = n + -58. Factor -18/7*a - 2*a**t - 4/7.
-2*(a + 1)*(7*a + 2)/7
Find y such that 254/5*y**3 + 0 - 544/5*y**5 - 48*y**4 - 48/5*y**2 + 2/5*y = 0.
-1, 0, 1/17, 1/4
Let c(l) be the second derivative of 0 + 1/33*l**3 - 5*l - 1/66*l**4 + 0*l**2 + 1/165*l**6 - 1/110*l**5. Determine s, given that c(s) = 0.
-1, 0, 1
Let z = 29 + -34. Let c(a) = -30*a**2 - 20*a + 1. Let o(r) = r**2 - 1. Let u(w) = z*o(w) - c(w). Suppose u(p) = 0. Calculate p.
-2/5
Suppose -5*d + 8*j = 3*j, -2*d + 12 = 4*j. Let h(i) = i**3 + 2*i**2 + 2. Let u be h(-2). Factor -4*g**4 - 4*g**3 + u*g**3 + 3*g**3 + g**5 + d*g**4.
g**3*(g - 1)**2
Suppose 35 = 7*q, -2*h - 4*q - 8 = -32. Let n(b) be the third derivative of 0 + 0*b - 1/420*b**6 + 1/105*b**5 - 1/84*b**4 - 6*b**h + 0*b**3. Factor n(j).
-2*j*(j - 1)**2/7
Let n(q) = 3*q + 1. Let c be n(1). Suppose -c = -2*z - 0*z. Solve 2*m**4 + 2 - z + m - 2*m**2 - m**3 + 0*m**3 = 0 for m.
-1, 0, 1/2, 1
Let y(u) be the second derivative of -28*u - 1/54*u**4 - 2/27*u**3 - 1/9*u**2 + 0. Factor y(m).
-2*(m + 1)**2/9
Let l(j) be the third derivative of -5/12*j**4 + 2*j**2 - 1/168*j**8 + 0*j + 0 - 1/3*j**3 - 1/6*j**6 - 1/21*j**7 - 1/3*j**5. Solve l(v) = 0 for v.
-1
Determine n, given that 8*n**2 - 21 + 40 + 21 + 2*n**2 + 28*n - 6*n**2 = 0.
-5, -2
Let x(m) be the first derivative of -m**5/20 - 11*m**4/8 - 3. Solve x(b) = 0.
-22, 0
Let t(h) be the third derivative of 0*h - 1/6*h**4 + 1/15*h**5 + 0 + 0*h**3 + h**2. Find s such that t(s) = 0.
0, 1
Let k be (-100)/(-400) - 21/(-60). Factor k - 9/5*v + 9/5*v**2 - 3/5*v**3.
-3*(v - 1)**3/5
Let a(f) = 36*f - 142. Let k be a(4). Determine d so that 3/5 + 3/5*d**5 - 14/5*d**3 + 2/5*d**k + 11/5*d - d**4 = 0.
-1, -1/3, 1, 3
Factor 62*q**3 + 34*q**2 - 560*q + 10*q**4 + 320 - 5*q**4 + 131*q**2 + 8*q**3.
5*(q - 1)**2*(q + 8)**2
Suppose -15 = -4*n - 3. What is t in -10*t**4 + 2*t**n + 0*t**4 + 11*t**4 - 2*t - 1 = 0?
-1, 1
Let t(v) be the third derivative of v**8/672 - 2*v**7/105 + 3*v**6/80 + 3*v**5/20 - 2*v**2 - 22. Find a, given that t(a) = 0.
-1, 0, 3, 6
Suppose 22*y - 70 + 9*y + 37*y - 7*y**2 - 7*y**2 + 16*y**2 = 0. Calculate y.
-35, 1
Suppose 0 = -4*g - 2*k + 14, -2*g + 22 = 2*k + 2*k. Let y be (56/(-32) - g/(-1))*-2. Find q, given that 12*q - 24 - y*q**2 = 0.
4
Let z(a) be the second derivative of a**5/90 - a**3/9 - 2*a**2/9 + 51*a. Factor z(n).
2*(n - 2)*(n + 1)**2/9
Let d(y) = -13*y**2 - 36*y - 61. Let r(u) = -18*u - 31 + 20*u**2 - 55*u**2 + 28*u**2. Suppose -b + 4*b = -21. Let p(g) = b*r(g) + 4*d(g). Factor p(o).
-3*(o + 3)**2
Suppose -4*r + 20 = -4*a, 4*r + 4*a = r + 15. Let u(x) = 3*x**2 - 10*x + 7. Let y(n) = 5*n**2 - 20*n + 15. Let o(b) = r*u(b) - 2*y(b). Factor o(q).
5*(q - 1)**2
Let c(i) be the first derivative of -i**6/6 - 2*i**5 - 13*i**4/2 + 16*i**3/3 + 123*i**2/2 + 90*i + 451. Solve c(l) = 0 for l.
-5, -3, -1, 2
Let y be -16*-6*3/24. Factor -20*f + 4*f**2 + 2*f**2 - 5*f**3 - 2*f**2 + 9*f**3 + y.
4*(f - 1)**2*(f + 3)
Factor -2469*y - y**2 + 2457*y - y**2.
-2*y*(y + 6)
Let y = -231 + 463/2. Let q(c) be the first derivative of -c**2 + 1/2*c + c**3 + 1/10*c**5 + 1 - y*c**4. Factor q(l).
(l - 1)**4/2
Find f, given that 66/7*f**2 + 12*f + 24/7 + 15/7*f**3 = 0.
-2, -2/5
Let u(m) be the first derivative of -m**7/70 + m**6/10 - m**5/4 + m**4/4 - 7*m**2 - 10. Let y(s) be the second derivative of u(s). Let y(i) = 0. Calculate i.
0, 1, 2
Let -36/5*h - 8/5 - 51/5*h**3 - 62/5*h**2 - 4*h**4 - 3/5*h**5 = 0. Calculate h.
-2, -1, -2/3
Factor 62*f**2 + 30 + 63*f + 3*f**3 + 0*f**3 - 26*f**2.
3*(f + 1)**2*(f + 10)
Factor 6/5*m**3 - 3/5*m**4 + 0*m + 0*m**2 + 0.
-3*m**3*(m - 2)/5
Let b(a) be the first derivative of -5*a**3/21 - 29*a**2/7 + 24*a/7 + 391.