1. Let i = a + 186. Suppose -2/3*t**2 - 2 + i*t = 0. Calculate t.
1, 3
Let y be (4/(-4) - -2)/6. Let j(a) be the first derivative of y*a**4 + 0*a + 1/27*a**6 + 0*a**2 - 2/27*a**3 - 2/15*a**5 - 6. Factor j(k).
2*k**2*(k - 1)**3/9
Determine q, given that -25*q**4 + 11*q**3 - 6*q**3 + 5*q**5 - 37*q**5 + 12*q**5 + 15*q**2 + 5*q**3 = 0.
-1, 0, 3/4
Let a(d) be the first derivative of d**3/2 - 87*d**2/2 + 2523*d/2 - 30. Factor a(p).
3*(p - 29)**2/2
Let t(f) be the first derivative of -f**3/15 + 18*f**2/5 + 37*f/5 + 59. Factor t(n).
-(n - 37)*(n + 1)/5
Suppose -3*q = -0 - 15. Suppose 2 = -4*y + q*y. Determine w so that -15*w**3 + 5 - 9*w + 1 - 6*w**3 - 36*w**y = 0.
-1, 2/7
Find w such that 21/5*w**2 - 6*w + 0 + 12/5*w**3 - 3/5*w**4 = 0.
-2, 0, 1, 5
Let g = 124 - 113. Let x = 11 - g. Factor -2/5*z + 1/5*z**3 + x - 1/5*z**2.
z*(z - 2)*(z + 1)/5
Let n(u) be the first derivative of 0*u**4 - 4/5*u**3 + 0*u + 9/25*u**5 + 22 - 1/10*u**6 + 0*u**2. Factor n(j).
-3*j**2*(j - 2)**2*(j + 1)/5
Let m = -3 - -11. Suppose -2*b = 2*b - m. Determine h so that -3 + b*h - 18*h**2 + 21*h**2 + h - 3*h**3 = 0.
-1, 1
Let h(r) = 15*r**3 + 53*r**2 - 56*r - 6. Let x(g) = -135*g**3 - 475*g**2 + 505*g + 55. Let f(c) = -55*h(c) - 6*x(c). Find k such that f(k) = 0.
-5, 0, 2/3
Suppose 3*y + 7 + 26 = 4*o, 3*o - 3*y - 27 = 0. Suppose -2 = -4*f + o. Determine t so that 2*t**4 + 9*t**f - 6*t**3 - 2*t + 0*t**4 - 3*t**2 = 0.
0, 1
Suppose -4*y + 11 = 4*u + 3, 2*y - u - 10 = 0. Suppose 54 = y*l + 6. Factor 9 + 15 - 8 + 4*p**3 - l*p**2.
4*(p - 2)**2*(p + 1)
Let o be 6*3/9*(-33)/(-22). Let q(s) be the first derivative of 0*s + 6 + 2*s**2 + 2/3*s**o. Determine l so that q(l) = 0.
-2, 0
Suppose 2/9*c**3 - 8/9*c - 352/9 + 88/9*c**2 = 0. What is c?
-44, -2, 2
Let m(j) = -j**5 + 19*j**4 - 49*j**3 + 53*j**2 - 16*j - 2. Let f(i) = -i**5 + i**4 - i**3 - i**2 - i + 1. Let h(g) = -2*f(g) - m(g). Factor h(z).
3*z*(z - 3)*(z - 2)*(z - 1)**2
Factor 0 - g + 1/8*g**3 - 7/8*g**2.
g*(g - 8)*(g + 1)/8
Let m(c) = -c**4 - c**3 + 5*c**2 - 7*c. Let p(f) = -f**4 - f**3 + 6*f**2 - 8*f + 1. Let u(r) = 3*m(r) - 4*p(r). Let u(j) = 0. Calculate j.
-4, 1
Let m = 157/4 + -2353/60. Let i(y) be the third derivative of 1/3*y**3 + 1/4*y**4 - 1/168*y**8 + 1/15*y**5 + 0*y + 0 - m*y**6 - 1/35*y**7 - 7*y**2. Factor i(n).
-2*(n - 1)*(n + 1)**4
Let w = -1791 + 5375/3. Suppose w*i - 4/3 + 2/3*i**2 = 0. What is i?
-2, 1
Let k = -6905/4 + 20731/12. Suppose -1/3*c**2 - 4/3 - k*c = 0. What is c?
-2
Let k(x) = -3*x**2 + 66*x + 957. Let t(m) = -m**2 + m - 1. Let d(r) = k(r) - 4*t(r). Solve d(z) = 0 for z.
-31
Let w(y) be the third derivative of y**9/52920 - y**8/5880 + y**7/2205 + 7*y**4/24 + 10*y**2. Let r(n) be the second derivative of w(n). Factor r(p).
2*p**2*(p - 2)**2/7
Factor 25*x**3 - 20*x**3 + 22*x**3 + 6*x**2 + 21*x**4.
3*x**2*(x + 1)*(7*x + 2)
Let i(c) be the third derivative of c**5/120 + 2*c**4/3 + 64*c**3/3 + 43*c**2. Factor i(w).
(w + 16)**2/2
Let r(u) = -6*u**2 + 8*u + 3. Suppose -4*z + 27 = -z. Let n(w) = -z*w**2 + 10*w + 4 + 0 - w + 2*w**2. Let k(i) = 5*n(i) - 6*r(i). Factor k(s).
(s - 2)*(s - 1)
Suppose 70*c = 71 + 139. Solve 2/7*f**c - 4/7 - 2/7*f**4 - 2/7*f + 6/7*f**2 = 0.
-1, 1, 2
Suppose -19*a - 2 = 4*y - 17*a, y + 2*a = -8. Let 2/7*z**5 + 4/7*z + 2/7*z**y + 0 - 6/7*z**3 - 2/7*z**4 = 0. What is z?
-1, 0, 1, 2
Let q(d) be the third derivative of d**5/150 + 3*d**4/20 - 12*d**3/5 + 314*d**2. Find v, given that q(v) = 0.
-12, 3
Let y = 18487/2 + -9243. Factor 1 + 3/2*c - y*c**3 + 0*c**2.
-(c - 2)*(c + 1)**2/2
Suppose 0*o - 3*k = -4*o + 24, -5*o = 4*k + 1. Let v be 4 + o + -3 - 0/(-2). Factor 1/4*r**3 + 0 - 1/4*r**v + 1/4*r**2 - 1/4*r.
-r*(r - 1)**2*(r + 1)/4
Suppose -26*j**2 + 84*j**3 + 92*j**2 + 59*j**2 - 120*j - 89*j**3 = 0. What is j?
0, 1, 24
Let i be (-20)/(-4) + 42/(-6). Let f be (i/16*-1)/((-3)/(-8)). Solve -f*u**3 - 1/3*u + 2/3*u**2 + 0 = 0.
0, 1
Let m = -213 - -221. Suppose m*d - 26 = -5*d. Factor -7/3*r - 5/3*r**d - 1 - 1/3*r**3.
-(r + 1)**2*(r + 3)/3
Let q(k) = -k**2 + 449*k - 6926. Let n be q(16). Factor -65/2 - 5/2*j**n - 35*j.
-5*(j + 1)*(j + 13)/2
Let c be 50/6 + (-2)/6. Factor -15*x**3 + 3*x - c*x - 68*x**2 - 5*x**4 + 53*x**2.
-5*x*(x + 1)**3
Factor -9/4*q**2 + 0 - 3/2*q - 3/4*q**3.
-3*q*(q + 1)*(q + 2)/4
Suppose 4*d - 155*s - 24 = -151*s, -3 = 5*d + 6*s. Factor -1/5*b**d - 1/5*b**2 + 0 + 2/5*b.
-b*(b - 1)*(b + 2)/5
Let l(c) be the first derivative of -1/12*c**2 - 14 + 0*c - 2/9*c**3. Let l(y) = 0. Calculate y.
-1/4, 0
Let a(i) = -i**3 + 6*i**2 + 55*i. Let q be a(11). Solve q + 2/3*b**3 + 4/3*b + 2*b**2 = 0 for b.
-2, -1, 0
Let b(y) be the third derivative of y**9/12096 + y**8/4032 - y**7/504 + y**5/60 + 16*y**2. Let d(i) be the third derivative of b(i). Find f such that d(f) = 0.
-2, 0, 1
Let y(p) = -7*p**2 + 91*p - 102. Let a(z) = -2*z**2 + z - 2. Let c(w) = -6*a(w) + y(w). Determine f so that c(f) = 0.
-18, 1
Let d(r) = 61*r**3 + 80*r**2 - 7*r - 11. Let q(l) = -60*l**3 - 76*l**2 + 8*l + 12. Let n(z) = 4*d(z) + 5*q(z). Find b such that n(b) = 0.
-1, -4/7, 1/2
Let t(u) be the third derivative of -5*u**8/84 + 34*u**7/105 - 8*u**6/15 + 4*u**5/15 - 277*u**2. Solve t(a) = 0.
0, 2/5, 1, 2
Let x(a) = 8*a**3 - a**2 - 15*a + 1. Let u = 30 - 24. Let i(b) = 3*b**3 - 5*b. Let h(g) = u*x(g) - 21*i(g). Let h(w) = 0. What is w?
-1, -2/5, 1
Let j = 3219 - 16083/5. Factor 4/5*z**2 - 16/5*z + j.
4*(z - 3)*(z - 1)/5
Let u = 14047/28102 - -2/14051. Find g, given that 0 - 1/4*g - 1/4*g**3 + u*g**2 = 0.
0, 1
Let c = 579 + -1184. Let t = c + 1843/3. Suppose -25/3*y**3 + 38/3*y**2 - t*y + 8/3 - 1/3*y**5 + 8/3*y**4 = 0. Calculate y.
1, 2
Let k be (-789)/154 - 3*5/(-30). Let q = k - -54/11. Solve -q*n - 3/7*n**2 + 0 - 1/7*n**3 = 0 for n.
-2, -1, 0
Factor 0*w + 1/3*w**3 + 0 + 1/3*w**4 - 1/3*w**2 - 1/3*w**5.
-w**2*(w - 1)**2*(w + 1)/3
Let g(c) be the second derivative of 5*c**8/672 - c**7/35 + 3*c**6/80 - c**5/60 + 4*c**2 + 16*c. Let o(r) be the first derivative of g(r). Factor o(k).
k**2*(k - 1)**2*(5*k - 2)/2
Let y(n) = -n**3 + n - 2. Let p(c) = -3*c**3 + 87*c**2 + 6*c - 12. Let r(w) = p(w) - 6*y(w). Factor r(x).
3*x**2*(x + 29)
Suppose -61/2*q**4 + 7/2*q**5 + 0*q + 0 + 8*q**2 + 19*q**3 = 0. What is q?
-2/7, 0, 1, 8
Let w(y) be the second derivative of 2*y**7/21 - 2*y**6/3 + 7*y**5/5 - y**4 + 15*y + 4. Determine c so that w(c) = 0.
0, 1, 3
Factor 83*y + 27*y - 45*y**2 + 50*y**2.
5*y*(y + 22)
Suppose 72 = -o + 4*o. Let r = o - 13. Let 2*c**3 + r*c**2 - 4*c**3 - 9*c**2 = 0. Calculate c.
0, 1
Let x(f) = -3*f + 5. Let j be x(1). Factor 2*z**3 - 13*z + 12*z**2 + 54 + 45*z + 6*z**j + 22*z.
2*(z + 3)**3
Factor -15/4*u**3 + 0*u**2 + 0 - 3/4*u**4 + 0*u.
-3*u**3*(u + 5)/4
Let h(p) be the third derivative of -p**8/896 + 3*p**7/560 + 3*p**6/64 + 17*p**5/160 + 3*p**4/32 + 3*p**2 - 28. Determine d, given that h(d) = 0.
-1, 0, 6
Let s(i) be the third derivative of 0 + 0*i + 1/540*i**6 - 41*i**2 + 0*i**3 + 0*i**4 + 1/270*i**5. Find b, given that s(b) = 0.
-1, 0
Let k(s) = -4*s**3 - 268*s**2 + 272. Let t(a) = a**2 - a. Let x(z) = -k(z) + 4*t(z). Factor x(y).
4*(y - 1)*(y + 1)*(y + 68)
Factor -75/4 - 192*w**2 - 120*w.
-3*(16*w + 5)**2/4
Let n(z) be the first derivative of -12*z**5/5 - z**4 + 4*z**3 + 2*z**2 + 24. What is a in n(a) = 0?
-1, -1/3, 0, 1
Suppose -v + 19*q + 2 = 17*q, 0 = v + q + 1. Solve 1/3*w**4 + 0*w**2 + 1/3*w**5 - 2/3*w**3 + 0 + v*w = 0 for w.
-2, 0, 1
Suppose -18*t + 3/8*t**2 + 141/8 = 0. What is t?
1, 47
Let x(t) be the second derivative of 1/90*t**5 + 0 - 1/27*t**3 + 1/54*t**4 - 23*t - 1/9*t**2. Factor x(d).
2*(d - 1)*(d + 1)**2/9
Let n = -85 - -114. Factor 7*s**3 - 10*s**3 + n*s**2 + 2*s**4 - 15*s**3 - 54*s + 25*s**2.
2*s*(s - 3)**3
Let b(p) = 2*p**2 - p + 2. Let f be b(-2). Factor 4*o**5 - 3*o**4 + o**5 - o**5 - f*o**3 + 11*o**4.
4*o**3*(o - 1)*(o + 3)
Suppose 0 = -34*k + 28*k + 18. Let w = 4 - -1. Solve 2*d**4 + d**4 - 9*d**k + 9*d**w - 3*d**2 + 0*d**4 = 0 for d.
-1, -1/3, 0, 1
Let i(w) = 12*w**2 + 113*w + 1458. Let o(p) = 10*p**2 + 112*p + 1458. Let r(t) = 4*i(t) - 5*o(t). Determine k so that r(k) = 0.
-27
Let a(y) be the second derivative of 5*y**4/12 + 5*y**3/2 - 135*y**2 - 939*y. Find z such that a(z) = 0.
-9, 6
Suppose 2*k = -j - 4, 0*j = -4*j - 16. Factor 1/6*t**2 + k + 1/3*t.
t*(t + 2)/6
Let b(q) be the third d