*m = 5*m + 77. Let b be 54/10 - (m + -6). Factor b*p - 1/5*p**4 + 1/5*p**2 - 2/5*p**3 + 0.
-p*(p - 1)*(p + 1)*(p + 2)/5
Let n(w) be the second derivative of 1/8*w**3 + 0*w**6 - 10*w + 1/24*w**4 - 1/4*w**2 + 1/168*w**7 + 0 - 1/20*w**5. Determine r, given that n(r) = 0.
-2, -1, 1
Let y be 105/(-140) - 6/(-8). Let t(b) be the second derivative of -1/105*b**7 + 1/75*b**6 + 0*b**2 + y + 0*b**5 + b + 0*b**3 + 0*b**4. Solve t(m) = 0.
0, 1
Let n = 7 - 5. Let p = -189 - -195. Factor -6*y - n*y**3 + 2 - p*y**2 - 7 + 3.
-2*(y + 1)**3
Let g(w) be the first derivative of 3*w**5/5 - 3*w**4/4 - w**3 + 3*w**2/2 - 47. Factor g(d).
3*d*(d - 1)**2*(d + 1)
Let a(x) be the second derivative of -x**5/4 - 25*x**4/4 - 125*x**3/2 - 625*x**2/2 - 394*x. Factor a(o).
-5*(o + 5)**3
Let y(d) = -5*d**2 - 33*d + 36. Let f(x) = -15*x**2 - 98*x + 106. Let t(v) = -2*f(v) + 7*y(v). Determine m so that t(m) = 0.
-8, 1
Let o(m) be the first derivative of 3/4*m**3 - 3/4*m**4 + 0*m**2 + 3/20*m**5 + 5 + 0*m. Factor o(d).
3*d**2*(d - 3)*(d - 1)/4
Suppose 5*t = 10*t + 2*c - 6, -3*c - 2 = 2*t. Let q be (-1 + (-1)/t)*12/(-9). Factor -3/2*b - 9/4 - 1/4*b**q.
-(b + 3)**2/4
Let g be (1 - 5)*(-14)/(-4). Let h = 17 + g. Suppose -4*x**2 + 3*x**h - 5*x + 5 - 3 - 4*x**3 - 4 = 0. What is x?
-2, -1
Let h(i) be the first derivative of 3*i**5/2 + 15*i**4/8 - 25*i**3/6 - 4*i**2 - 2. Let c(x) be the second derivative of h(x). Factor c(p).
5*(3*p - 1)*(6*p + 5)
Let l(a) be the first derivative of -10*a**3/9 - 3*a**2 + 4*a/3 - 52. Factor l(k).
-2*(k + 2)*(5*k - 1)/3
Suppose 0 = 6*f - 5*f - 5. Let t be -2*(f/20)/((-21)/12). Let t*b**2 + 0 - 2/7*b**3 - 2/7*b**4 + 2/7*b = 0. What is b?
-1, 0, 1
Let t(c) be the third derivative of c**8/1512 - 4*c**7/189 - 11*c**6/90 - 34*c**5/135 - 23*c**4/108 + 140*c**2. Factor t(b).
2*b*(b - 23)*(b + 1)**3/9
Let 14*r**5 - 5*r**3 + 85*r**4 - 53*r**4 + 3*r + 24*r**2 + 5*r - 17*r**3 - 56*r**4 = 0. What is r?
-1, -2/7, 0, 1, 2
Let m(g) be the first derivative of 5/4*g**4 - 2 - 10/3*g**3 + 40*g - 10*g**2. Let m(r) = 0. Calculate r.
-2, 2
Let i(u) be the first derivative of -u**6/15 - u**5/5 - u**4/6 - 24*u - 23. Let n(j) be the first derivative of i(j). Factor n(p).
-2*p**2*(p + 1)**2
Let h(t) be the first derivative of t**3 + 0*t - 14 + 3/5*t**5 - 3/2*t**4 + 0*t**2. Let h(k) = 0. Calculate k.
0, 1
Let k(m) be the third derivative of m**5/30 + m**4/12 + m**2 + 16*m. Factor k(r).
2*r*(r + 1)
Suppose 3*f - 3*q - 12 = 0, -3*q = 3*f + q + 9. Let t be f*(-2 - -2 - -3). Let -3*o**2 - 10 - 10 - 5*o**t + 18*o**2 = 0. What is o?
-1, 2
Let d(h) be the third derivative of -5*h**2 - 5/336*h**8 + 0*h**3 + 0 + 0*h**4 + 0*h + 1/6*h**6 + 0*h**5 + 0*h**7. Solve d(y) = 0.
-2, 0, 2
Let a(h) be the second derivative of h**4/3 - 46*h**3/3 + 204*h**2 - h - 112. Determine c, given that a(c) = 0.
6, 17
Let p(u) = -3*u - 10. Let k be p(-4). Factor 7*o**2 - o**4 + o - o**4 + 0*o**2 - 5*o**k - o**5.
-o*(o - 1)*(o + 1)**3
Let -1/2*k**2 - 1/2*k + 0 = 0. Calculate k.
-1, 0
Let f(z) be the third derivative of -24*z**2 - 4/5*z**3 + 0*z + 0 - 1/20*z**4 + 1/100*z**5. Factor f(c).
3*(c - 4)*(c + 2)/5
Let h(m) be the first derivative of -m**3/12 + 9*m**2/4 - 8*m - 192. Let h(p) = 0. What is p?
2, 16
Let w(k) be the first derivative of -k**4/2 - 50*k**3/3 - 24*k**2 - 621. Factor w(u).
-2*u*(u + 1)*(u + 24)
Factor 9*q**3 - q - 13*q**3 + 0*q**3 + 5*q**3.
q*(q - 1)*(q + 1)
Solve 0*z - 3/2*z**2 + 0 - 1/4*z**5 + 3/2*z**4 + 1/4*z**3 = 0.
-1, 0, 1, 6
Let s(t) be the third derivative of t**10/45360 + t**9/22680 - t**4/4 + 34*t**2. Let d(b) be the second derivative of s(b). Factor d(f).
2*f**4*(f + 1)/3
Solve 0*h**2 + 0*h - 1/5*h**4 - 2/5*h**3 + 0 + 1/5*h**5 = 0.
-1, 0, 2
Suppose 2*w = u - 4, 0 = -3*u - w - 4*w + 1. Factor 38*f**2 - f**3 - 42*f**u - 5*f**3 - 2*f**4.
-2*f**2*(f + 1)*(f + 2)
Factor 3*n**3 + 5 - 3*n + 10 + 1 - 16.
3*n*(n - 1)*(n + 1)
Let b(q) = -22*q**3 + 40*q**2 - 15*q - 5. Let r(p) = 7*p**2 - 1. Let u be r(2). Let x = u + -28. Let w(l) = -l - 1. Let s(k) = x*w(k) + b(k). Factor s(t).
-2*(t - 1)**2*(11*t + 2)
Suppose 0 = 10*w + 2*w - 552. Suppose -w*q**4 - 12*q**3 - 492*q**2 - 18*q**4 - 16*q + 28*q**5 + 556*q**2 = 0. Calculate q.
-1, 0, 2/7, 1, 2
Let u(c) = -9*c**2 - 6*c - 36. Let i(w) = 2*w**2 - 2*w. Let p(z) = 15*i(z) + 3*u(z). Factor p(j).
3*(j - 18)*(j + 2)
Find z, given that 3*z - 3162*z**2 + 22 + z**3 + 3176*z**2 + 32*z = 0.
-11, -2, -1
Suppose -10*m + 2*k - 2 = -3*m, 0 = m + 4*k - 34. Determine s so that 3/7*s**m + 0 - 3/7*s = 0.
0, 1
Find q, given that 20*q + 5/4*q**2 - 20*q**3 + 0 - 5/4*q**4 = 0.
-16, -1, 0, 1
Let w(f) = 2*f**2 - 19*f + 30. Let b be w(12). Let t = b + -88. Suppose -1/3 + 1/3*y**t + 0*y = 0. Calculate y.
-1, 1
Let p(t) be the third derivative of t**6/300 - t**5/30 + t**4/20 + 3*t**3/5 - 39*t**2. Factor p(l).
2*(l - 3)**2*(l + 1)/5
Let g(h) be the first derivative of -h**6/70 + h**5/105 - h**3/3 - 10. Let s(i) be the third derivative of g(i). What is a in s(a) = 0?
0, 2/9
Let n be (-20)/(-110) + 4353/(-5247). Let a = 1/53 - n. Factor -2/3*y**2 + 8/3 + 8/3*y - a*y**3.
-2*(y - 2)*(y + 1)*(y + 2)/3
Let s(o) = o**3 + 10*o**2 + 5*o - 2. Let q be s(-9). Let a = -32 + q. Determine t, given that -4*t**2 + 4*t**3 + t**2 + 7*t**a = 0.
-1, 0
Let x = 248 + -2234/9. Let r = 17/36 + x. Let 0 + 1/4*f**2 + r*f = 0. What is f?
-1, 0
Let n = 434/9 - 2152/45. Let h = 91 + -453/5. Let 4/5*t**2 + n*t - h = 0. What is t?
-1, 1/2
Let v(n) be the first derivative of n**4/30 - 4*n**3/15 + 4*n**2/5 - 4*n + 5. Let j(k) be the first derivative of v(k). Factor j(w).
2*(w - 2)**2/5
Let c(o) be the third derivative of -o**6/40 - o**5/4 + 3*o**4/4 + 48*o**2 + 6. Factor c(p).
-3*p*(p - 1)*(p + 6)
Let j(o) be the third derivative of o**6/90 + o**5/5 - 5*o**4/9 - 7*o**2 + 4. What is w in j(w) = 0?
-10, 0, 1
Let d(f) be the first derivative of 2*f**4 + 0*f + 31 + 6/5*f**5 + 1/2*f**2 - 2*f**3 - 3/2*f**6. What is q in d(q) = 0?
-1, 0, 1/3, 1
Let w be (-9)/6 + 208/96. Let h(t) be the second derivative of w*t**3 - 1/3*t**4 + 0*t**2 + 7*t + 0. Let h(m) = 0. Calculate m.
0, 1
Suppose 0*h - 24 = -3*h + 3*x, -h + 3*x + 16 = 0. Find o such that -4*o**3 - o**4 - 3*o**2 + 7*o**3 + h*o**3 + o - 4*o**3 = 0.
0, 1
Let p(o) be the second derivative of -2/9*o**3 + 1/60*o**5 - 14 + 2*o + 2/3*o**2 - 1/36*o**4. Factor p(f).
(f - 2)*(f - 1)*(f + 2)/3
Let a(n) be the second derivative of -2*n**7/105 + 4*n**5/15 - 10*n**2 + 9*n. Let r(t) be the first derivative of a(t). Factor r(b).
-4*b**2*(b - 2)*(b + 2)
Let y be 16/6*(-45)/(-30). Determine l so that -3*l**5 - 2*l**3 + l**5 - 19*l**y - 14*l**4 + 37*l**4 = 0.
0, 1
Suppose 4*d + 14 = 5*j, -5*d = j - 2*j + 7. Factor 7*i**j + 2*i**3 + 8*i**2 - 17*i**2 + 6*i**2.
2*i**2*(i + 2)
Let j(r) be the second derivative of 2*r**6/75 - 3*r**5/5 + 58*r**4/15 - 56*r**3/5 + 16*r**2 - 137*r. What is x in j(x) = 0?
1, 2, 10
Let c(p) be the first derivative of -p**8/420 + p**7/105 - p**6/90 + p**3/3 - 1. Let s(t) be the third derivative of c(t). Factor s(i).
-4*i**2*(i - 1)**2
Factor -50*s**4 + 46*s**4 - 26*s**2 - 26*s**2 - 56*s**3.
-4*s**2*(s + 1)*(s + 13)
Let u = 4322999/2040 - 35990/17. Let a = u + 13/24. Determine z so that 1/5*z**4 - 6/5*z**3 - 12/5*z + a*z**2 + 4/5 = 0.
1, 2
Let k(x) = x**2 - 104*x + 500. Let u be k(5). Let l = 93/2 - 27. Solve 93/2*p**2 - l*p**3 - 30*p - 21/2*p**4 + 15/2*p**u + 6 = 0 for p.
-2, 2/5, 1
Determine z, given that -27*z**3 - 12*z + 0 - 21/2*z**4 - 30*z**2 - 3/2*z**5 = 0.
-2, -1, 0
Let u(l) = -752*l + 1508. Let k be u(2). Determine a so that 4/7*a**k + 0 + 24/7*a + 52/7*a**2 + 32/7*a**3 = 0.
-6, -1, 0
Let 1/4*s**2 + 1/4*s + 0 = 0. What is s?
-1, 0
Let f(s) be the first derivative of s**5/24 - 35*s**4/24 + 245*s**3/12 - 3*s**2 + 6. Let a(p) be the second derivative of f(p). Solve a(h) = 0.
7
Let d = 528 + -522. Let c(s) be the second derivative of -1/18*s**4 + 0 + 1/90*s**5 + 1/9*s**3 + d*s - 1/9*s**2. Factor c(m).
2*(m - 1)**3/9
Let r(w) be the second derivative of 4*w + 1/2*w**4 + 0 - 23/3*w**3 - 8*w**2. Find u, given that r(u) = 0.
-1/3, 8
Let d = -40465/7 + 5781. Factor 8/7*g + 0 + d*g**2.
2*g*(g + 4)/7
Let f be 63/24*1/2*(-4)/(-3). Factor -1/2 + j**3 - f*j + 5/4*j**2.
(j - 1)*(j + 2)*(4*j + 1)/4
Let x(f) be the second derivative of -147*f**5/20 + 161*f**4/4 - 88*f**3 +