lculate x.
2
Let b(r) be the first derivative of -3*r**2 - 1/30*r**5 + 0*r - 2/3*r**3 - 5 + 1/4*r**4. Let g(h) be the second derivative of b(h). Factor g(i).
-2*(i - 2)*(i - 1)
Let y(w) = -2*w**2 + 45*w + 290. Let m(l) = -3*l**2 + 42*l + 288. Let c(h) = -5*m(h) + 6*y(h). Determine k, given that c(k) = 0.
-10
Suppose 2*l = l + 18. Suppose m = -m + l. Let m*j**2 - 9*j**3 + 4*j**4 + 7*j**2 - 8*j**2 - 3*j**3 = 0. Calculate j.
0, 1, 2
Let l = -1 - -7. Suppose -w = 5*d - 12, 3*w = -2*w - 5*d + 20. Solve -3*x - 8*x**2 + 15*x**2 - 2*x**w - l*x**2 = 0 for x.
-3, 0
Suppose -33 = -2*v - 5*z, -5*v - 5*z + 28 = -17. Factor -4*k**2 + 10*k**4 - 4*k**3 - 22*k**v - 4*k**5 - 8*k**3.
-4*k**2*(k + 1)**3
Let p be (-16)/((-1)/(1/(-2))). Let b(y) = y + 12. Let l be b(p). Solve -l*g**2 - 20/3*g**4 + 4/3*g**5 + 0*g + 0 + 28/3*g**3 = 0.
0, 1, 3
Let z(x) be the third derivative of -x**7/840 + x**6/32 - 9*x**5/80 + 13*x**4/96 - 9*x**2 - 2. Factor z(r).
-r*(r - 13)*(r - 1)**2/4
Let p(c) be the second derivative of c**7/13860 + c**6/1980 - 5*c**4/6 + c**3/6 - 47*c. Let j(k) be the third derivative of p(k). Factor j(g).
2*g*(g + 2)/11
Let h = 56/3 + -109/6. Let f(t) be the first derivative of h*t**2 + 2 - 3/4*t - 1/12*t**3. Factor f(c).
-(c - 3)*(c - 1)/4
Let b be ((-24890)/4)/((-238)/68). Let z = -1775 + b. Let -z*v - 50/7 - 2/7*v**2 = 0. What is v?
-5
Suppose -35 = -5*n - 15. Let w(d) be the second derivative of -1/21*d**n + 1/140*d**5 + 5/42*d**3 - 5*d + 0 - 1/7*d**2. Solve w(u) = 0 for u.
1, 2
Let t(i) be the second derivative of 0 - 2/7*i**2 + 1/42*i**4 - 1/21*i**3 + 25*i. Solve t(c) = 0.
-1, 2
Suppose -z + 42 = 5*g, 0 = -2*z + 3*g - 19 - 1. Factor 72*x - 10 + 49/2*x**3 - 273/2*x**z.
(x - 5)*(7*x - 2)**2/2
Let s = 300498/21229 - 2/1633. Factor 1058/13*v**2 + 8/13 - s*v.
2*(23*v - 2)**2/13
Let t(l) be the first derivative of l**4/30 + 44*l**3/45 + 7*l**2/5 - 41. Suppose t(s) = 0. Calculate s.
-21, -1, 0
Let k(v) = -v**3 + 17*v**2 + 43*v - 92. Let i be k(19). Factor 2/11*j**i + 0 + 0*j - 6/11*j**2.
2*j**2*(j - 3)/11
Let c(b) be the first derivative of -15 - 5/9*b**3 + 0*b**2 + 20/3*b. Factor c(a).
-5*(a - 2)*(a + 2)/3
Let l be (-167)/(-11) + (-6)/33. Let 31 + 2*y**2 - l - 6*y - 12 = 0. Calculate y.
1, 2
Find r such that -82/7*r - 18/7*r**2 + 18/7*r**3 + 12 - 2/7*r**4 = 0.
-2, 1, 3, 7
Let k = -1058 - -1061. Let q(w) be the second derivative of -1/4*w**4 - 6*w**2 + 2*w**k + 0 + 3*w. Factor q(p).
-3*(p - 2)**2
Let y(g) = -15*g**3 + 23*g**2 + 15*g - 23. Let h(z) = -7*z**3 + 11*z**2 + 7*z - 11. Let d(b) = 7*h(b) - 3*y(b). Find p such that d(p) = 0.
-1, 1, 2
Let a(k) be the second derivative of -3*k**5/40 + 19*k**4/8 - 20*k**3 - 75*k**2 - 115*k. Factor a(w).
-3*(w - 10)**2*(w + 1)/2
Suppose -2*v + 7*v - 5*z = -405, 0 = v + 2*z + 66. Let m = -74 - v. What is u in -1/4*u**3 + 1/2*u**m + 1/4*u - 1/2 = 0?
-1, 1, 2
Let a(c) be the first derivative of -c**5 + 35*c**4/4 + 205*c**3/3 + 165*c**2/2 - 302. Factor a(h).
-5*h*(h - 11)*(h + 1)*(h + 3)
Let q = 1364/21 - 194/3. Factor 0 + 1/7*c**3 - 1/7*c**4 + q*c**2 + 0*c.
-c**2*(c - 2)*(c + 1)/7
Let m = 28/61 - 13/427. Let 15/7*k - m*k**2 - 12/7 = 0. What is k?
1, 4
Suppose 5*q - n - 23 = 0, 0*n + n - 12 = -2*q. Suppose -5*w = 5*d, 9 = -2*w - q*d - 0*d. Factor -84*z**2 - 16/9 + 184/9*z + 1274/9*z**w - 686/9*z**4.
-2*(z - 1)*(7*z - 2)**3/9
Let q be (-1)/(2/((-18)/15)). Let o(x) be the first derivative of 23/3*x**3 + 8*x**2 - 2 + 7/2*x**4 + q*x**5 + 4*x. Factor o(w).
(w + 1)**2*(w + 2)*(3*w + 2)
Let u(n) be the first derivative of -4*n**3/27 + 44*n**2/9 + 73. Factor u(t).
-4*t*(t - 22)/9
Let l(m) = -2*m**2 + 9*m + 31. Let f be l(7). Let z = 6 + f. Determine q, given that 0 - 2/9*q**z - 2/9*q = 0.
-1, 0
Suppose -21 = -4*c - 5*f - 28, c + 5*f = -13. Let v(i) be the second derivative of 0*i**3 + 0*i**c - 1/30*i**5 - 1/9*i**4 + 2*i + 0. Factor v(w).
-2*w**2*(w + 2)/3
Determine p so that 175*p - 13*p**2 + 630 - 480*p + 8*p**2 = 0.
-63, 2
Let j(u) be the first derivative of u**5/40 + u**4/8 + 11*u**2/2 + 8. Let n(k) be the second derivative of j(k). Suppose n(l) = 0. Calculate l.
-2, 0
Let t be (8*(-9)/(-288))/(-23 + 24). Find f such that t*f**4 + 9/2*f**2 - 2*f**3 + 0*f - 27/4 = 0.
-1, 3
Let w(x) be the first derivative of -429/4*x**4 + 6*x**2 - 4*x**3 + 0*x + 216/5*x**5 + 8 + 648*x**6. Solve w(d) = 0.
-1/4, 0, 2/9
Let c = -23/47 - -599/1128. Let p(y) be the third derivative of 0 - 1/180*y**5 - 1/9*y**3 + 0*y - c*y**4 + 2*y**2. What is x in p(x) = 0?
-2, -1
Let g(k) be the first derivative of -k**6/180 - k**5/10 - 2*k**4/3 + k**3 - 1. Let v(a) be the third derivative of g(a). Determine h so that v(h) = 0.
-4, -2
Let d(o) be the third derivative of -o**5/360 + o**4/24 + 4*o**3/9 - 4*o**2 + 8*o. Determine k, given that d(k) = 0.
-2, 8
Find o such that 22/15*o**3 - 4/3*o - 2/15*o**5 + 2/5*o**4 + 0 - 2/5*o**2 = 0.
-2, -1, 0, 1, 5
Let f = -5751/4 - -1438. Let c(r) be the first derivative of -4*r**2 - 4*r + 8 - 5/3*r**3 - f*r**4. Determine x so that c(x) = 0.
-2, -1
Let i(x) be the first derivative of -2*x**3/15 - 18*x**2/5 - 162*x/5 - 41. Factor i(k).
-2*(k + 9)**2/5
Let u be (-3 + 3)*(9 - 8). Find h, given that 4/21*h**2 + u*h**4 + 2/21*h**5 + 0*h - 2/7*h**3 + 0 = 0.
-2, 0, 1
Solve -86*b**3 + 6*b**4 + 65*b**2 - 17*b**2 + 24*b**2 - 61*b**3 = 0 for b.
0, 1/2, 24
Let z(w) be the first derivative of -5/24*w**3 + 1/80*w**5 + 6*w - 9 - 1/120*w**6 + 1/16*w**4 + 1/4*w**2. Let n(b) be the first derivative of z(b). Factor n(s).
-(s - 1)**3*(s + 2)/4
Let l(t) be the third derivative of -1/10*t**5 + 0*t + 1/36*t**6 - 2/9*t**3 + 20*t**2 + 7/36*t**4 - 1/315*t**7 + 0. Factor l(o).
-2*(o - 2)*(o - 1)**3/3
Let p(s) = s**2 + 21*s + 2. Let u be p(-21). Factor -k**3 - u*k**3 + 5*k - 3 - 2*k**3 + 10*k**2 - 7.
-5*(k - 2)*(k - 1)*(k + 1)
Factor 0*k**2 + 1/6*k**4 - 18*k + 3/2*k**3 + 0.
k*(k - 3)*(k + 6)**2/6
Let t(i) be the first derivative of 9*i**4 + 376*i**3 - 382*i**2 + 128*i - 659. Factor t(s).
4*(s + 32)*(3*s - 1)**2
Let h = -347 + 349. Factor 1/5*t**h + 8/5*t + 16/5.
(t + 4)**2/5
Let j(t) = t**2 + 9*t + 5. Let m be j(-8). Let w be (-4)/(-6) - 4/m. Factor -1/4*k + 0 - 1/4*k**w.
-k*(k + 1)/4
Let x(m) = m**3 - 14*m**2 + 35*m - 16. Let c(f) = 4*f**3 - 68*f**2 + 176*f - 79. Let o(l) = -2*c(l) + 11*x(l). Let o(r) = 0. What is r?
1, 2, 3
Let h(s) = -13*s + 8. Let m be h(0). Suppose m - 32 = -8*k. Factor 6/7*x + 2/7*x**k + 0 + 8/7*x**2.
2*x*(x + 1)*(x + 3)/7
Let g(p) = 13*p**2 - 517*p + 16900. Let d(i) = 120*i**2 - 4652*i + 152100. Let k(m) = -3*d(m) + 28*g(m). Determine q so that k(q) = 0.
65
Let q be 1 - (353/(-33))/1. Let w = q + -4/11. Factor w*y**3 + 8/3*y**4 + 0 + 40/3*y**2 + 8/3*y.
2*y*(y + 2)**2*(4*y + 1)/3
Let y = -912 + 912. Determine w so that -2/3*w**5 - 4/3*w**2 + 0*w**4 + 2*w**3 + y + 0*w = 0.
-2, 0, 1
Let u be -4*(2/12)/((-9)/27). Let 6*v - 8/3*v**3 - 4/3 - 2*v**u = 0. What is v?
-2, 1/4, 1
Let 0 - 3/2*f**2 - 33/2*f = 0. Calculate f.
-11, 0
Let b = -119703/76 + 1575. Let a = 131/532 - b. Solve -a - 2/7*t**5 - 2/7*t**4 + 4/7*t**3 - 2/7*t + 4/7*t**2 = 0.
-1, 1
Suppose m + 34 = -5*d - 0*m, 2*m + 32 = -4*d. Let r be (16/(-14))/(d/21). Determine f, given that 3*f**2 + f - r*f + 1 + 5*f - 2*f**2 = 0.
-1
Let m(f) be the first derivative of f**6/6 + 11*f**5/5 + 12*f**4 + 104*f**3/3 + 56*f**2 + 48*f - 84. Factor m(t).
(t + 2)**4*(t + 3)
Let m(u) be the second derivative of u**7/189 - 31*u**6/135 + 19*u**5/9 + 383*u**4/27 + 833*u**3/27 + 289*u**2/9 + 38*u. Solve m(v) = 0 for v.
-1, 17
Let q(r) be the second derivative of 0*r**2 - 1/8*r**3 + 3/16*r**4 + 0 + 4*r + 1/40*r**6 - 9/80*r**5. Find j, given that q(j) = 0.
0, 1
Factor 10/3*r + 2/3*r**2 - 28/3.
2*(r - 2)*(r + 7)/3
Let u(w) be the first derivative of 2*w**3/33 - 9*w**2/11 + 28*w/11 + 92. Factor u(m).
2*(m - 7)*(m - 2)/11
Suppose 0 = -3*g + g + 4*h - 4, g + h - 4 = 0. Let n(l) be the third derivative of -1/9*l**4 + 0 - 1/90*l**5 - 4/9*l**3 + 0*l - l**g. Factor n(v).
-2*(v + 2)**2/3
Let a(b) be the second derivative of -b**9/60480 + b**7/3360 - b**6/1440 - 7*b**4/4 - 21*b. Let y(z) be the third derivative of a(z). Factor y(h).
-h*(h - 1)**2*(h + 2)/4
Let b(t) be the third derivative of t**8/108 - 46*t**7/945 - 11*t**6/135 + 8*t**5/135 + 3*t**2 + 69. Determine x, given that b(x) = 0.
-1, 0, 2/7, 4
Let t be 105/42*