t is k?
-2, -2/7, -1/4, 0
Let q(r) be the first derivative of r**6/16 - 3*r**5/20 - 34. Let q(j) = 0. What is j?
0, 2
Find i such that -1/3*i**4 + 0*i - 3*i**2 + 10/3*i**3 + 0 = 0.
0, 1, 9
Let m be (-1116)/(-63) + 4/14. Factor -9*c**4 + c**2 - 2*c - 10*c**4 + 2*c**3 + m*c**4.
-c*(c - 2)*(c - 1)*(c + 1)
Let k(m) = -90*m - 10 - 3*m**2 - 2 - m**3 + 91*m. Let d be k(-4). Factor -1/2*f**2 + d - 1/4*f**3 - 1/4*f.
-f*(f + 1)**2/4
Let q(l) = -l**2 + 429*l - 8178. Let g be q(20). Factor -2/7*p**3 - 10/7*p**g + 0 + 0*p.
-2*p**2*(p + 5)/7
Solve 5*u - 6*u**4 - 30*u**5 - 9*u**3 - 31*u**5 + 64*u**5 + 24*u**2 - 17*u + 0*u = 0 for u.
-2, 0, 1, 2
Let q(u) be the second derivative of -u**7/630 + u**6/15 - 6*u**5/5 + 2*u**4/3 + 10*u. Let p(z) be the third derivative of q(z). Factor p(b).
-4*(b - 6)**2
Find l, given that -32/9*l**3 + 16*l**2 + 26/3*l - 676/9 = 0.
-2, 13/4
Let w(f) be the second derivative of -f**5/20 - 7*f**4/18 - 7*f**3/18 + 2*f**2/3 - 4*f. Factor w(l).
-(l + 1)*(l + 4)*(3*l - 1)/3
Let c(p) be the first derivative of 5*p**3/12 - 13*p**2/8 + 2*p + 32. Find a such that c(a) = 0.
1, 8/5
Let z(v) = v**2 - 14*v - 21. Let r be z(12). Let q be (10/r)/(-1) + 50/18. Find p such that 2/7*p - 2/7*p**q + 8/7*p**2 - 8/7*p**4 + 0 = 0.
-1, -1/4, 0, 1
Let t(p) be the third derivative of -p**6/720 + p**5/120 + 25*p**4/144 + 7*p**3/12 - 166*p**2 - 2*p. Factor t(m).
-(m - 7)*(m + 1)*(m + 3)/6
Let z(g) be the third derivative of g**7/105 - g**6/15 - 11*g**5/30 - g**4/2 - 229*g**2. Suppose z(n) = 0. Calculate n.
-1, 0, 6
Let z = 13 + -9. Let d be ((-6)/z)/((-30)/40). Factor d*i**4 + 4*i**4 + i**5 - 5*i**4.
i**4*(i + 1)
Let i(v) = v + 4. Let h be i(-2). Find n, given that 18*n - n**h + 8 - 2*n**2 - 23 = 0.
1, 5
Let v(l) = -l**5 + l**4 + l**3 - l**2 + 1. Let g(x) = -9*x**5 + 6*x**3 + 3*x + 6. Let a = 6 + -12. Let r(b) = a*v(b) + g(b). Factor r(u).
-3*u*(u - 1)*(u + 1)**3
Let x be 0 - 13/(143/(-22)). Let t(u) be the first derivative of -2 - 3/2*u**3 - u - 11/4*u**x. Factor t(d).
-(d + 1)*(9*d + 2)/2
Let r = 283 + -2829/10. Let s(y) be the first derivative of 1/15*y**3 + 0*y + 1/20*y**4 - 1/25*y**5 - 4 - r*y**2. Factor s(j).
-j*(j - 1)**2*(j + 1)/5
Let h(y) be the third derivative of -y**8/84 + y**7/56 + y**6/72 - 3*y**3/2 + 6*y**2. Let q(b) be the first derivative of h(b). What is s in q(s) = 0?
-1/4, 0, 1
Let y(m) be the second derivative of -m**4/30 + m**3 + 76*m**2/5 + 326*m. Solve y(a) = 0 for a.
-4, 19
Factor 4*q**3 + 1231*q + q**5 - 3*q**5 - 1233*q.
-2*q*(q - 1)**2*(q + 1)**2
Let h(a) be the second derivative of -a**4/48 - a**3/2 + 11*a. Factor h(r).
-r*(r + 12)/4
Let i(b) = -62*b**3 + 52*b**2 + 6*b - 4. Let q(p) = p**3 + p + 2. Let z(m) = -i(m) - 2*q(m). Factor z(a).
4*a*(a - 1)*(15*a + 2)
Factor i**2 - 8*i**3 + 2*i**3 + 2*i**2 - 12 + 24*i.
-3*(i - 2)*(i + 2)*(2*i - 1)
Let d = 7922 - 15843/2. Determine t, given that -d*t + 1/2*t**3 + 1/2*t**2 - 1/2 = 0.
-1, 1
Let k(m) be the first derivative of 17*m - 108*m**3 + 38*m**2 - 33*m + 34*m**2 + 13. Determine d, given that k(d) = 0.
2/9
Let l = 1 + 2. Factor 3*f**4 + 25*f**3 - 25*f**l - 5*f**4 + 6*f**2 - 4*f.
-2*f*(f - 1)**2*(f + 2)
Let j(v) be the second derivative of v**6/60 + v**5/100 - v**4/8 + v**3/15 + v**2/5 + 3*v + 51. Let j(a) = 0. What is a?
-2, -2/5, 1
Factor 1/7*j**4 + 0 + 8/7*j**3 + 12/7*j + 19/7*j**2.
j*(j + 1)*(j + 3)*(j + 4)/7
Let v(n) be the second derivative of 729*n**2 + 9/2*n**4 + 81*n**3 + 12*n + 1/10*n**5 + 0. Solve v(b) = 0 for b.
-9
Let z(g) = 190*g**4 - 540*g**3 - 2160*g**2 + 2160*g + 6535. Let j(b) = 7*b**4 - 20*b**3 - 80*b**2 + 80*b + 242. Let k(q) = 55*j(q) - 2*z(q). Factor k(y).
5*(y - 6)*(y - 2)*(y + 2)**2
Let x(a) be the third derivative of 9/2*a**3 + 7/20*a**5 + 15/8*a**4 + 0 + 4*a**2 + 1/40*a**6 + 0*a. Determine i, given that x(i) = 0.
-3, -1
Let g(m) be the second derivative of 25*m**4 - 2*m - 36*m**5 + 0*m**2 + 2*m**2 - 6*m - 10*m**3 + 11*m**5. Factor g(w).
-4*(5*w - 1)**3
Let p(r) be the third derivative of 0*r + 1/80*r**5 - 1/64*r**4 + 0*r**3 - 15*r**2 - 1/320*r**6 + 0. Find g, given that p(g) = 0.
0, 1
Let w(j) = 4*j + 3. Let m be w(0). Factor m*u + 7*u**2 - 4*u**2 - 15*u**4 + 12*u**4 + 0*u**3 - 3*u**3.
-3*u*(u - 1)*(u + 1)**2
Let n(y) be the first derivative of -y**7/840 + y**6/96 - y**5/40 - y**4/24 + y**3/3 - y**2 + 14. Let m(z) be the second derivative of n(z). Factor m(w).
-(w - 2)**3*(w + 1)/4
Let y be (-3)/(3339/5353) + -1*5/(-1). Factor -y*w**2 - 4/21 + 10/21*w.
-2*(w - 2)*(2*w - 1)/21
Let w = 182 - 102. Suppose -n + 2*x + 9 = 0, -4*n - n + 3*x + w = 0. Determine j so that 0*j**2 - 17*j + 1 + n*j + j**2 = 0.
-1
Let k(s) = -s**3 + 6*s**2 + 6. Let n be 4*((-27)/(-6) + -3). Let d be k(n). Factor 9*h**2 + 0*h**3 + 5*h + d*h - 5*h + 3*h**3.
3*h*(h + 1)*(h + 2)
Let d(i) be the first derivative of 0*i**3 + 3/2*i**4 + 3/5*i**5 + 0*i**2 - 11 + 0*i. Factor d(p).
3*p**3*(p + 2)
Let v = -1680 + 1684. Let j(i) be the second derivative of -1/18*i**3 + 0 + 1/3*i**2 - 11*i - 1/36*i**v. Factor j(k).
-(k - 1)*(k + 2)/3
Let t = -955 + 6689/7. Let v be 2/(-3) + 8/3. Factor t*b**v + 6/7*b + 2/7.
2*(b + 1)*(2*b + 1)/7
Let j be 58/5 + (-12)/20. Suppose -l + 3 + 0 = 0. Suppose -d**2 - 16*d + l - 3*d**2 - j - 8 = 0. Calculate d.
-2
Let t(j) be the first derivative of 11*j**6/69 + 38*j**5/115 - 3*j**4/23 + 162. Factor t(s).
2*s**3*(s + 2)*(11*s - 3)/23
Let c be (-10)/(-5 + 15) - (-82)/10. Let -96/5*t + 4/5*t**4 - 32/5*t**3 + c + 88/5*t**2 = 0. Calculate t.
1, 3
Find n, given that -28/5*n - 2/5*n**2 - 98/5 = 0.
-7
Let s(n) be the first derivative of -n**9/15120 - n**8/8400 + n**7/2100 - n**3/3 - 24. Let z(x) be the third derivative of s(x). Suppose z(k) = 0. What is k?
-2, 0, 1
Let b(f) be the third derivative of -f**6/30 + f**5/5 + f**4/6 - 2*f**3 + 121*f**2. Solve b(d) = 0.
-1, 1, 3
Let r be 200/(-420)*-21 - (-86)/(-9). Solve 1/9*f**4 + 2/9*f**2 - 1/3 + r*f**3 - 4/9*f = 0.
-3, -1, 1
Factor -6*r**2 + 88*r**4 + 8*r + 4*r**3 + 2*r**5 - 82*r**4 - 14*r**3.
2*r*(r - 1)**2*(r + 1)*(r + 4)
Let v(i) be the first derivative of i**4/4 + 2*i**3 - i**2/2 - 6*i - 115. Factor v(f).
(f - 1)*(f + 1)*(f + 6)
Let o(i) = -i**2 + 12*i + 3. Let a(j) = -12*j - 9. Let n(l) = 60*l + 44. Let v(d) = -24*a(d) - 5*n(d). Let m(h) = -4*o(h) - 3*v(h). Factor m(c).
4*c*(c - 3)
Factor 2/19*x + 2/19*x**2 - 2/19 - 2/19*x**3.
-2*(x - 1)**2*(x + 1)/19
Factor -29469*c**2 - 692*c - 5500*c**2 - 5 - 1 + 2 - 56*c.
-(187*c + 2)**2
Suppose w + 464 = 5*w - 3*s, -4*s + 97 = w. Let d = -788/7 + w. Factor 0 - 3/7*y**2 + 3/7*y**4 + 3/7*y - d*y**3.
3*y*(y - 1)**2*(y + 1)/7
Let j(k) be the second derivative of 11*k**5/25 - 7*k**4/15 - 38*k**3/15 + 6*k**2 + 253*k. Factor j(w).
4*(w - 1)**2*(11*w + 15)/5
Let q(h) be the second derivative of 6*h + 1/18*h**3 + 1/36*h**4 - 1/3*h**2 + 0. Factor q(v).
(v - 1)*(v + 2)/3
Let q(v) be the first derivative of 3*v**4/4 - 6*v**3 + 33*v**2/2 - 18*v - 7. Factor q(l).
3*(l - 3)*(l - 2)*(l - 1)
Let d(g) be the third derivative of g**7/2520 + g**6/720 - g**5/60 - 7*g**4/24 - 12*g**2. Let v(f) be the second derivative of d(f). Factor v(u).
(u - 1)*(u + 2)
Let g = 5 - 5. Determine c, given that 2 + g*c**2 + c**2 + 2*c - c - 2*c**2 = 0.
-1, 2
Let g(l) be the second derivative of -l**7/147 - 2*l**6/35 - 6*l**5/35 - 4*l**4/21 + 47*l. Find i such that g(i) = 0.
-2, 0
Let t(g) be the second derivative of g**6/10 + g**5/2 - 2*g**4 + g**3 + 5*g**2/2 + g - 22. Suppose t(m) = 0. Calculate m.
-5, -1/3, 1
Let f be (-1)/(464/(-87) + 5*1). Solve 3/2*t**f + 0*t + 0 - 3*t**2 = 0.
0, 2
Let g = -38 + 42. Let a(h) be the third derivative of 0*h + g*h**2 - 1/150*h**5 - 1/30*h**4 + 0 - 1/15*h**3. Factor a(z).
-2*(z + 1)**2/5
Factor -5*k - 21*k + 5*k - 4*k - 8 - 3*k**2.
-(k + 8)*(3*k + 1)
Let d(l) be the second derivative of -1/15*l**4 + 9/5*l**2 + 1/75*l**6 + 4/5*l**3 + 0 - 2/25*l**5 - 7*l. Determine n, given that d(n) = 0.
-1, 3
Suppose c + c + 10 = 3*b, -20 = -4*b + 4*c. Let k be (3 + -4 + b)*-2. Find p such that -8*p**2 + 23*p**5 - 5*p**4 - 3*p**4 - 25*p**5 - k*p - 12*p**3 = 0.
-1, 0
Let w(m) be the second derivative of m**4/96 - 9*m**3/16 + 30*m + 9. Find j, given that w(j) = 0.
0, 27
Factor 110 - 135*n - 14*n**2 + 48 - 18 + 9*n**2.
-5*(n - 1)*(n + 28)
Suppose 12 = -3*m, 3*m = -4*i - 2*m + 16. Suppose 19*h = i*h + 20. Factor 8/7*l