u(k) = -35*w(k) - 5*z(k). Factor u(x).
-5*(x - 1)*(x + 1)*(x + 21)
Let d(r) be the second derivative of -r**5/80 + r**4/3 + 17*r**3/24 + 2*r + 107. Factor d(y).
-y*(y - 17)*(y + 1)/4
Let -33*h + 140 + 0*h**2 - 2*h**2 + 19*h - h - 51*h = 0. What is h?
-35, 2
Factor -20402/5 - 2/5*x**2 - 404/5*x.
-2*(x + 101)**2/5
Let q(b) be the third derivative of -b**7/70 + 3*b**6/20 + 3*b**5/20 - 5*b**4/2 + 6*b**3 + 44*b**2 - b. Factor q(h).
-3*(h - 6)*(h - 1)**2*(h + 2)
Let r = 50849 - 4576361/90. Let n = -2/45 + r. Let 3/2*q - n*q**2 + 0 = 0. What is q?
0, 3
Let l(i) be the second derivative of 1/2*i**4 + 14*i + 2/3*i**3 + 0 + 1/3*i**2. Factor l(j).
2*(3*j + 1)**2/3
Let q(h) be the second derivative of 0 + 5/32*h**4 + 1/4*h**3 + 8*h + 0*h**2 + 3/160*h**5. Solve q(s) = 0 for s.
-4, -1, 0
Let h = -2 + 10. Let v be 15 + 5 - h/(-2). Suppose 0*f - 4*f**2 + 12*f - v*f - 3*f**3 - 8*f**2 = 0. Calculate f.
-2, 0
Factor -52*r + 2/11*r**2 + 3718.
2*(r - 143)**2/11
Let h(p) = -3*p**2 - 13*p + 53. Let y(d) = -3*d**2 - 12*d + 54. Let b(f) = 6*h(f) - 5*y(f). Determine w, given that b(w) = 0.
-8, 2
Let m = -264/41 + 6328/779. Factor -46/19*q**2 - 80/19*q + m - 6/19*q**3.
-2*(q + 4)**2*(3*q - 1)/19
Let g(u) be the third derivative of 2*u**7/735 - u**6/70 - u**5/7 - 17*u**4/42 - 4*u**3/7 - 16*u**2. Suppose g(p) = 0. What is p?
-1, 6
Let -9*n + 4*n + 5601*n**3 + 58*n**2 - 664*n**2 + 4600*n**3 + 14*n = 0. What is n?
0, 3/101
Let l(q) be the second derivative of -q**4/6 - 7*q**3/3 + 8*q**2 + 5*q + 2. Factor l(s).
-2*(s - 1)*(s + 8)
Let v(k) be the third derivative of k**7/1890 + k**6/1080 - k**5/90 - k**4/54 + 4*k**3/27 + 242*k**2. Suppose v(u) = 0. What is u?
-2, 1, 2
Let -16/3 + 130/3*n + 32/3*n**3 - 272/3*n**2 = 0. Calculate n.
1/4, 8
Let t(v) be the second derivative of -1/8*v**2 - 31*v + 0 + 1/12*v**3 - 1/48*v**4. Suppose t(j) = 0. What is j?
1
Let n(r) = 8*r**3 - 14*r + 6. Let w be 179/5 + 1/5. Let p be 1/(-3)*w/(-2). Let h(j) = 9*j**3 - 15*j + 6. Let o(i) = p*n(i) - 5*h(i). Factor o(q).
3*(q - 1)**2*(q + 2)
Let k(m) be the second derivative of m**9/3780 - m**8/420 + m**4/2 + 3*m. Let u(t) be the third derivative of k(t). Factor u(d).
4*d**3*(d - 4)
Factor 9*l - 19/2 + 1/2*l**2.
(l - 1)*(l + 19)/2
Let d(b) = 4*b**2 - b - 3. Suppose 0 = -5*l + 3*q + 15, 3*q - 9 = -3*l - 0*q. Let t(z) = 7*z**2 - z - 6. Let v(o) = l*t(o) - 5*d(o). Solve v(c) = 0.
-3, 1
Let a(n) be the first derivative of -16*n**2 + n**4 - 16/3*n**3 + 1/6*n**6 - 16*n - 25 + n**5. Suppose a(t) = 0. Calculate t.
-2, -1, 2
Let k(z) = z**3 + 11*z**2 + 17*z - 7. Let a be k(-9). Let w(h) be the first derivative of -2/3*h**3 + 0*h + 1/2*h**4 - 5 + 0*h**a. Factor w(s).
2*s**2*(s - 1)
Solve -9*o**5 - 4284*o + 4278*o + 15*o**2 + 33*o**4 + 12*o**2 - 45*o**3 = 0.
0, 2/3, 1
Let j(r) be the second derivative of r**7/56 + r**6/40 - 3*r**5/16 - r**4/16 + r**3 - 3*r**2/2 + 56*r - 2. Factor j(k).
3*(k - 1)**3*(k + 2)**2/4
Let d(q) be the first derivative of q**4/16 - 7*q**3/3 - 31*q**2/8 + 29*q/2 - 346. Factor d(j).
(j - 29)*(j - 1)*(j + 2)/4
Let q(z) be the second derivative of z**6/40 + 3*z**5/16 - 33*z**4/16 + 27*z**3/8 - 846*z. Factor q(d).
3*d*(d - 3)*(d - 1)*(d + 9)/4
Let q(a) be the first derivative of -a**5/20 + a**4/8 - a**2/4 - 7*a - 12. Let z(g) be the first derivative of q(g). Suppose z(j) = 0. Calculate j.
-1/2, 1
Let l(r) = -r**5 - r**4 - r**3 - r**2 - r. Let b(f) = -20*f**5 - 30*f**4 - 5*f**3 + 5*f**2 + 5*f. Let y(d) = b(d) + 5*l(d). Solve y(q) = 0.
-1, -2/5, 0
Let s(b) be the third derivative of b**8/110880 - b**6/3960 - b**5/20 + 9*b**2. Let r(w) be the third derivative of s(w). Suppose r(z) = 0. Calculate z.
-1, 1
Let k(n) = n**3 + 2*n**2 - 2*n + 2. Let a be k(-4). Let z = a - -45/2. Factor -f - z*f**2 - 1/2.
-(f + 1)**2/2
Suppose 5*q + 3*v - 23 = q, 2*q - 11 = -v. Let u be (-4)/(-16)*4 + -1. Find a, given that 3*a**4 - a**q + u*a**2 - 4*a**2 + 0*a**2 = 0.
-1, 0, 2
Let n = -137/4 - -35. Let y = -16403 + 65987/4. Factor -225/4*f - y - 45/4*f**2 - n*f**3.
-3*(f + 5)**3/4
Let b(c) be the second derivative of c**6/90 + 7*c**5/30 + 11*c**4/12 - 2*c**3/9 - 22*c**2/3 + 11*c + 9. Factor b(t).
(t - 1)*(t + 2)**2*(t + 11)/3
Let s = 20 - 18. Factor -5*a**s - 4*a**4 + 3*a**3 - 15*a**3 - 4*a**2 + a**2.
-4*a**2*(a + 1)*(a + 2)
Factor -30*i**3 + 176*i**2 - 6*i - 143*i**2 + 3*i**3.
-3*i*(i - 1)*(9*i - 2)
Let y = 12 + -12. Let r be y + 0 + 0 - -3. Let -3*t - 2*t**4 - r*t**5 + 5*t**4 + 56 - 6*t**2 - 53 + 6*t**3 = 0. Calculate t.
-1, 1
Let y = 3530 + -3527. Let v = 35/114 + 1/38. Suppose 3*u**y - v - u**2 - 5/3*u = 0. What is u?
-1/3, 1
Let d(c) = 2*c**2 + 18*c - 15. Let x be d(-10). Factor 93*v - 28*v**4 - 122*v**3 - 84*v - 168*v**2 - 2*v**x - 81*v.
-2*v*(v + 1)**2*(v + 6)**2
Let v(w) = w**3 - 6*w**2 - 431*w - 22. Let z be v(24). Solve 3/2*q**z - 3/2*q + 0 = 0.
0, 1
Suppose -3*t + 5*s + 215 = 0, 4*s = 3*s - 1. Suppose -4*i - 6 = -t. Suppose -6*l + 3 + 4 - 4 + 19*l**2 - i*l**2 = 0. Calculate l.
1
Let l(z) = 2*z**3 - 9*z**2 + 7*z + 5. Let h(m) = m**3 - 4*m**2 + 3*m + 3. Let p(k) = -5*h(k) + 3*l(k). Find o, given that p(o) = 0.
0, 1, 6
Let b be (180/330)/(4/11). Suppose -3*n**2 + 0*n - b*n**3 + 0 = 0. What is n?
-2, 0
Let g(b) be the first derivative of -16*b - 1/5*b**5 + 2*b**4 + 16*b**2 - 8*b**3 - 6. Factor g(z).
-(z - 2)**4
Let d = 15 + -15. Suppose -4*u - 9 = w - 7*u, -4*w + 15 = 5*u. Factor 2*a**3 + d*a**3 + w*a**3 + 2*a**4 + 2*a - 6*a**2 - 4 - 12*a.
2*(a - 2)*(a + 1)**3
Let w(u) be the second derivative of -3/4*u**7 + 3*u**2 - 9*u - 9/40*u**5 + 0 + 6*u**3 - 41/20*u**6 + 37/8*u**4. Solve w(x) = 0 for x.
-1, -2/3, -2/7, 1
Suppose -38*a = -33*a. Let d(j) be the third derivative of 0*j**4 + a*j**3 + 0*j - 1/1050*j**7 + 1/100*j**5 + 0 + 1/300*j**6 - 10*j**2. Factor d(t).
-t**2*(t - 3)*(t + 1)/5
Let q(h) be the first derivative of -h**6/8 - 3*h**5/10 + 9*h**4/8 + 2*h**3 - 15*h**2/8 - 9*h/2 - 767. Suppose q(g) = 0. What is g?
-3, -1, 1, 2
Let t = 968 + -4722/5. Let f = t + -116/5. What is r in -4/5*r - f*r**2 + 0 = 0?
-2, 0
Suppose 0 = -16*d + 19*d - 9. Suppose 191*j**4 - d*j - 3*j + 14*j**2 - 10*j**3 - 189*j**4 = 0. Calculate j.
0, 1, 3
Let v(p) be the second derivative of 1/21*p**3 + 0*p**2 + 1/84*p**4 + 10*p + 0. Factor v(h).
h*(h + 2)/7
Let v(m) = 5*m + m + 14 - 5*m - 2*m. Let u be v(10). Let u*i**5 + 3*i**4 - 4*i**5 + i**4 - 4*i**5 = 0. What is i?
0, 1
Let i(x) be the first derivative of -5*x**4/4 + 3*x**3/8 + 3*x**2/4 + 20*x + 27. Let q(j) be the first derivative of i(j). Find p, given that q(p) = 0.
-1/4, 2/5
Suppose 2*q - 4 = 3*x - 7, 0 = 3*x - 3*q. Suppose -o - 3*g = x, -4*o + 9 = -5*g - 13. Factor 0 + 12/5*j**o - 8/5*j**2 - 8/5*j**4 + 2/5*j**5 + 2/5*j.
2*j*(j - 1)**4/5
Factor 34/13*o**4 + 0*o**2 + 0*o - 2/13*o**5 + 36/13*o**3 + 0.
-2*o**3*(o - 18)*(o + 1)/13
Suppose -3*u - 2*u = b - 12, -3*b - u = -8. Suppose p + 18 = -0*p + 5*w, -8 = -b*w. Solve p*n**3 + 0*n**3 + 3*n + 0*n**3 - 5*n = 0 for n.
-1, 0, 1
Let i(n) be the first derivative of 69*n**2 + 1029/10*n**5 + 12*n + 1911/8*n**4 + 28 + 189*n**3. Find l, given that i(l) = 0.
-1, -2/7
Find j such that -j + 1/5*j**2 + 4/5 = 0.
1, 4
Let 4/13*q**2 + 0 + 2/13*q**4 - 6/13*q**3 + 0*q = 0. Calculate q.
0, 1, 2
Let u(c) = -18*c**4 + 8*c**3 + 5*c**2 + 5. Let s(g) = 116*g**4 - 52*g**3 - 32*g**2 - 32. Let x(i) = -5*s(i) - 32*u(i). Solve x(b) = 0.
0, 1
Let q = 27 - 0. Suppose -q = 3*f - 6*f. Determine j, given that -3*j + 2 - 3*j**2 - 3*j**3 + f*j**2 - 2 = 0.
0, 1
Let a be ((-346236)/(-360))/43 + 18/135. Factor -27/4*z**2 - 75/4 - a*z.
-3*(3*z + 5)**2/4
Let a = 2695 - 18861/7. Factor 2/21*o - a + 4/7*o**2 - 2/21*o**3.
-2*(o - 6)*(o - 1)*(o + 1)/21
Find z such that -32*z**5 + 128/7 - 5224/7*z**3 + 1884/7*z**4 - 1632/7*z + 784*z**2 = 0.
1/8, 2/7, 2, 4
Suppose 110 = 3*x + 7*x. Let w = x + -9. Factor -2/13*k**3 + 0 + 2/13*k + 0*k**w.
-2*k*(k - 1)*(k + 1)/13
Let j be (1 + 366/(-132))*-8. Let s = -14 + j. Factor 8/11 + s*c**4 + 24/11*c + 12/11*c**3 + 26/11*c**2.
2*(c + 1)**2*(c + 2)**2/11
Suppose l - 14 = -4*k, 3*l + 3*k - 24 + 9 = 0. Suppose -2*i + 2*a = l, -4*i + a + 3 + 8 = 0. Factor -7*w - 4*w**2 + i*w + 0*w**2 + 2*w.
-w*(4*w + 1)
Let m(z) be the second derivative of 2*z**6/75 - 13*z**5/100 + 11*z**4/60 - z**3/15 + 133*z. What is k in m(k) = 0?
0, 1/4, 1, 2
Find b such that -6*b