h + 5*g + 79 = 0. Let v be -3 - (0 - 2) - h. Factor 8*c**4 - v*c**3 + 16*c**4 - 6*c**5 - c - 2*c**3 - 3*c**5 + 8*c**2.
-c*(c - 1)**2*(3*c - 1)**2
Let y(u) be the first derivative of 3*u**5/10 - 75*u**4/8 - u**3/2 + 75*u**2/4 + 204. Solve y(z) = 0.
-1, 0, 1, 25
Let 1 - 5*o**2 + 9 + 38159*o - 38154*o = 0. What is o?
-1, 2
Let s = -43 + 39. Let g be (16/20)/(s/(-10)). Factor -2/3*w**3 - 1/3*w**g - 1/3*w**4 + 0 + 0*w.
-w**2*(w + 1)**2/3
Let x(h) be the third derivative of 0 + 0*h + 28*h**2 + 2/105*h**7 - 1/15*h**6 + 2/3*h**4 + 8/3*h**3 - 1/5*h**5. Factor x(t).
4*(t - 2)**2*(t + 1)**2
Let b = -68 + 70. Let r(p) be the third derivative of 0 - 2/105*p**7 - 2/3*p**3 + 4*p**b + 0*p**6 + 0*p**4 + 0*p + 2/15*p**5. Find n, given that r(n) = 0.
-1, 1
Suppose -5*v - 8*v + 39 = 0. Let a = -15/4 - -29/4. Find l such that -7/2*l**2 + 0 + a*l**4 - 3/2*l**v + 5/2*l**5 - l = 0.
-1, -2/5, 0, 1
Suppose -o + 5*o = 16. Let q be ((-90)/(-24) - 3)*o. Solve -17/3*w**4 + 8/3*w - 22/3*w**2 - 1/3 + 28/3*w**q + 4/3*w**5 = 0 for w.
1/4, 1
Let d(u) be the first derivative of -4*u**3/3 - 12*u**2 + 64*u - 111. Find p, given that d(p) = 0.
-8, 2
Let j = -145/133 + 37/19. Factor 0 + 3/7*n - j*n**2 + 3/7*n**3.
3*n*(n - 1)**2/7
Let k = -1384 + 1386. Factor 6*r - 3/4*r**k - 12.
-3*(r - 4)**2/4
Let s(i) be the first derivative of i**3/2 - 3*i**2/2 - 9*i/2 - 83. Solve s(q) = 0.
-1, 3
Let x(a) be the third derivative of -1/45*a**5 + 0 + 1/9*a**4 + 1/126*a**7 - 1/1008*a**8 + 0*a**3 - 1/60*a**6 + 0*a + 12*a**2. Let x(b) = 0. What is b?
-1, 0, 2
Suppose 5*o + 0*o - 3*c + 5 = 0, 5*o + 3*c - 25 = 0. Factor 70*y**o + 10*y + 12*y**3 - 26*y**2 - 7*y + 21*y.
4*y*(y + 3)*(3*y + 2)
Let v = 3 - -2. Factor -8*h**4 + 4*h**5 + 3*h**3 + h**3 + 0*h**v.
4*h**3*(h - 1)**2
Let u(n) be the second derivative of n**9/5040 - n**7/700 + n**5/200 + 5*n**3/2 + 13*n. Let y(v) be the second derivative of u(v). Factor y(w).
3*w*(w - 1)**2*(w + 1)**2/5
Suppose 13*i + 20 = 18*i. Factor 18*w**3 - 12*w**i - 6*w**2 + 4*w - 4*w - 3*w**3 + 3*w**5.
3*w**2*(w - 2)*(w - 1)**2
Let d = 18/5 - 49/15. Let z = 1408 + -1405. Find n such that -1/3*n**z + 1/3*n + d*n**4 + 0 - 1/3*n**2 = 0.
-1, 0, 1
Let l(j) = 3*j**3 + 75*j**2 - 348*j - 438. Let d(g) = -g**3 - g**2 - 2*g + 1. Let m(r) = 6*d(r) + l(r). Let m(x) = 0. Calculate x.
-1, 12
Suppose -1/5*w**5 + 0 + 4/5*w**3 - 3/5*w - 2/5*w**4 + 2/5*w**2 = 0. Calculate w.
-3, -1, 0, 1
Let i(x) be the first derivative of x**4/12 + 5*x**3/18 - x**2/3 - 54*x + 10. Let a(o) be the first derivative of i(o). Find z, given that a(z) = 0.
-2, 1/3
Let u(g) be the first derivative of g**6/15 - 14*g**5/25 + 11*g**4/10 + 14*g**3/15 - 12*g**2/5 - 225. What is q in u(q) = 0?
-1, 0, 1, 3, 4
Suppose 93*d**2 + 22*d**4 - 4 + 179/2*d**3 + 2*d = 0. What is d?
-2, -1/4, 2/11
Let d = 34/35 + -673/700. Let z(j) be the third derivative of 1/100*j**5 + 0*j**4 + d*j**6 + 0*j + 0*j**3 + 0 + 5*j**2. Solve z(v) = 0.
-1/2, 0
Let z(v) be the second derivative of -v**4/28 + 32*v**3/7 - 1536*v**2/7 - 2*v - 1. Determine n, given that z(n) = 0.
32
Let x = -396 + 5942/15. Let r(o) be the second derivative of -1/25*o**5 + x*o**3 + 0 + 1/15*o**4 - 2/5*o**2 + 6*o. Find v, given that r(v) = 0.
-1, 1
Let a(y) be the second derivative of -25*y**7/42 + 278*y**6/3 + 559*y**5/5 + 112*y**4/3 + 742*y. Factor a(l).
-l**2*(l - 112)*(5*l + 2)**2
Let k(r) be the third derivative of -r**6/420 - 4*r**5/105 + 19*r**4/84 - 10*r**3/21 + 2*r**2 - 52*r. Suppose k(l) = 0. What is l?
-10, 1
Let f(q) be the third derivative of -1/72*q**5 + 23*q**2 + 0*q**4 + 5/4*q**3 + 0*q + 0. Factor f(y).
-5*(y - 3)*(y + 3)/6
Let r(v) = -v**3 - 23*v**2 + 7. Let u be r(-23). Factor 3*y**4 - u*y**2 + 16 - 16*y - 4*y + 11*y**3 - y**5 - y**2 - y**4.
-(y - 4)*(y - 1)**2*(y + 2)**2
Solve 0 + 57/8*g - 3/8*g**2 = 0.
0, 19
Let m(u) be the first derivative of -2*u - 1/3*u**2 + 4 - 1/18*u**4 + 10/27*u**3. Factor m(n).
-2*(n - 3)**2*(n + 1)/9
Let f = -720 + 728. Let h(k) be the second derivative of 9/2*k**2 - 4*k**3 + 0 - 3/4*k**4 - f*k. Factor h(r).
-3*(r + 3)*(3*r - 1)
Let a(t) be the second derivative of -5*t**7/42 + t**6 - 7*t**5/2 + 20*t**4/3 - 15*t**3/2 + 5*t**2 - 6*t - 8. Suppose a(k) = 0. What is k?
1, 2
Let u(m) be the third derivative of m**8/84 - 2*m**7/45 - m**6/10 + 7*m**5/45 + m**4/3 - 21*m**2. Determine z so that u(z) = 0.
-1, -2/3, 0, 1, 3
Suppose 9 = -j + 4*j, 5*j - 25 = -5*q. Suppose -v + q*h - 45 = -6*v, 0 = -5*v + h + 45. Factor v*t - 4*t**3 - 2*t**3 - t + 4*t**3.
-2*t*(t - 2)*(t + 2)
Let y(p) be the third derivative of -7*p**6/360 + p**5/10 + p**4/6 - 11*p**3/6 + 3*p**2. Let i(a) be the first derivative of y(a). Factor i(m).
-(m - 2)*(7*m + 2)
Let a(o) be the second derivative of -o**6/120 - o**3 + 10*o. Let p(j) be the second derivative of a(j). Factor p(x).
-3*x**2
Let w(p) be the first derivative of -p**8/5040 - p**7/5040 + p**6/2160 - 5*p**3 + 16. Let d(f) be the third derivative of w(f). Factor d(b).
-b**2*(b + 1)*(2*b - 1)/6
Let c be (-83)/21 + (-3 - -7). Let g(w) be the second derivative of 1/70*w**5 + 0 + c*w**3 - 7*w - 1/21*w**4 + 0*w**2. Find a, given that g(a) = 0.
0, 1
Let h(j) = 8*j + 4. Let t be h(0). Let u(z) be the third derivative of 1/60*z**t + 0*z**3 + 0*z - 4*z**2 + 0 + 1/300*z**5. Find l such that u(l) = 0.
-2, 0
Let k(i) be the second derivative of -i**4/6 - 8*i**3/3 - 93*i. What is r in k(r) = 0?
-8, 0
Let h(q) be the second derivative of -2*q**7/525 - q**6/75 - q**5/75 + 3*q**2 + 9*q. Let a(z) be the first derivative of h(z). Factor a(j).
-4*j**2*(j + 1)**2/5
Let i(n) be the third derivative of n**5/90 + 55*n**4/36 - 56*n**3/9 - n**2 - 332. Factor i(y).
2*(y - 1)*(y + 56)/3
Let l be (-5 + 4)/(2/(-4)). Let j = 31 - 29. Factor m**2 + 3*m**2 - j*m - 2*m**l.
2*m*(m - 1)
Let c = 2 + 2. Suppose -c*i - 4*b + 20 = 0, -7*i + 2*i = 4*b - 23. Find f such that i*f**3 - 4*f**2 + 3*f**2 + 4*f - 5*f**2 - f = 0.
0, 1
Let y(n) = -795*n**3 - 835*n**2 + 5*n + 75. Let t(i) = 199*i**3 + 209*i**2 - 2*i - 20. Let a(w) = -15*t(w) - 4*y(w). Factor a(p).
5*p*(p + 1)*(39*p + 2)
Let c(n) = n**2 - 11*n + 12. Let z be c(10). Let h be (-548)/685 + 16/10. Suppose 2/5*b**z + 0 + h*b = 0. What is b?
-2, 0
Let b(j) = 70*j**3 + 55*j**2 - 1135*j - 2435. Let h(z) = 5*z**3 + 4*z**2 - 81*z - 174. Let g(f) = 6*b(f) - 85*h(f). Factor g(w).
-5*(w - 4)*(w + 3)**2
Let i = -2064616/1095 - -28292/15. Let w = i - -2/73. Find p such that -w*p**4 + 0 + 8/3*p**3 - 8/3*p**2 + 0*p = 0.
0, 2
Let l(y) be the first derivative of y**6/1080 - y**5/135 - 9*y**2/2 + 25. Let s(m) be the second derivative of l(m). Suppose s(q) = 0. What is q?
0, 4
Let v(q) be the first derivative of q**6/120 + 5*q**2/2 - 11. Let o(s) be the second derivative of v(s). Determine c so that o(c) = 0.
0
Suppose -15*d = 120*d - 270. Determine a so that 1/2*a + 1/2*a**d - 1 = 0.
-2, 1
Let l = 63 - 43. Let b be l/15 + -2 - (-152)/84. Factor 2/7*t**3 + 0 - 8/7*t**2 + b*t.
2*t*(t - 2)**2/7
Let y be (1/2 - -1)*(-16)/(-12). Let a be 8/y + 46/(-12). Suppose 1/6*b**5 - 1/3*b**2 + a*b**4 + 1/6 - 1/3*b**3 + 1/6*b = 0. What is b?
-1, 1
Suppose 5*x - 205 = -v, 5*x + 0*v = 3*v + 185. Let c be x/12*20/75. Solve -2*s + 4*s**3 + 4/9*s**4 - 2*s**5 - c*s**2 + 4/9 = 0.
-1, 2/9, 1
Solve -434*a**2 - 578 - 282*a**2 - 20*a**3 + 25*a**3 - 2*a**4 - 1224*a - 77*a**3 = 0 for a.
-17, -1
Let k = -24 - -28. Determine y, given that -3*y**5 + 4*y**4 + 6*y**3 - 5*y**4 + 0*y**k - 2*y**4 = 0.
-2, 0, 1
Let p(m) be the second derivative of -m**7/42 - m**6/15 + m**5/10 + m**4/3 - m**3/6 - m**2 + 12*m + 5. Factor p(g).
-(g - 1)**2*(g + 1)**2*(g + 2)
Let q(r) be the second derivative of 0 + 5/6*r**3 + 27*r - 1/12*r**5 + 0*r**4 - 5/3*r**2. Factor q(m).
-5*(m - 1)**2*(m + 2)/3
Let l(k) = -8*k**2 - 98*k - 21. Let n be l(-12). Suppose 0*v**n - 2/5*v**2 + 0*v + 2/5*v**4 + 0 = 0. Calculate v.
-1, 0, 1
Let p(g) = 16*g**2 + 2*g - 32. Let b(v) = -2*v - 1 - 4*v**2 + 5*v**2 + v + 2*v. Let y(a) = 36*b(a) - 2*p(a). What is x in y(x) = 0?
-7, -1
Let t(u) be the first derivative of 3*u**4/32 - 7*u**3/4 + 45*u**2/4 - 27*u - 89. Find d such that t(d) = 0.
2, 6
Let z = 57/5 - 683/60. Let s(n) be the third derivative of -z*n**5 - 6*n**2 + 0*n**3 + 0 + 0*n + 1/12*n**4. Factor s(g).
-g*(g - 2)
Let o = 693 + -4849/7. Find r such that -6/7*r + 10/7*r**2 - o*r**3 - 18/7 = 0.