5 + 0*p**4 - x*p**6 - 9*p**2. Solve c(z) = 0.
-1, 0
Let z(t) be the third derivative of 5*t**7/42 - 19*t**6/15 + 79*t**5/20 - 59*t**4/12 + 4*t**3/3 + 28*t**2 + 4. Factor z(j).
(j - 4)*(j - 1)**2*(25*j - 2)
Let b(q) = q**2 - q + 2. Let u(a) = 4*a**2 + 16*a - 4. Let d(s) = -8*b(s) + u(s). Factor d(m).
-4*(m - 5)*(m - 1)
Let k(u) be the first derivative of -1/10*u**2 - 3/20*u**4 + 0*u - 1 + 1/25*u**5 + 1/5*u**3. Factor k(h).
h*(h - 1)**3/5
Let c(o) be the second derivative of -o**5/140 - o**4/7 - 8*o**3/7 - 3*o**2 - 8*o. Let j(b) be the first derivative of c(b). Solve j(l) = 0.
-4
Let y(i) = i**3 - 14*i**2 - 15*i - 4. Let b be y(15). Let o be -1 - b - (286/(-10))/(-11). What is m in 0 - 4/5*m**4 + 0*m + 4/5*m**2 + o*m**5 - 2/5*m**3 = 0?
-1, 0, 1, 2
Suppose -4*x + 3*d = 0, -2*x - 5*d + 10 + 16 = 0. Suppose 0*p - x*p = 3*p. Factor 4/11*i + 2/11*i**2 + p.
2*i*(i + 2)/11
Let j(q) be the first derivative of -147/5*q - 1/5*q**3 + 21/5*q**2 - 25. Suppose j(r) = 0. What is r?
7
Let q(k) = -k**3 - 2*k**2 + 2*k + 3. Let x be q(-3). Factor 5*f + 4*f**2 + 3*f + x*f + 6*f.
4*f*(f + 5)
Let x be (-1056)/7560 + (-2)/(-14). Let y(t) be the third derivative of 0*t + 1/18*t**3 + 0 - 3*t**2 - 1/360*t**6 + x*t**7 - 1/60*t**5 + 1/72*t**4. Factor y(d).
(d - 1)**2*(d + 1)*(2*d + 1)/3
Let j be (-3)/(-1) - (-2 - -5)/(-1). Let u be 20/j - (3 + 8/(-3)). Factor 0*g**u + 0*g + 2/5*g**4 - 2/5*g**2 + 0.
2*g**2*(g - 1)*(g + 1)/5
Factor 15*f + 49/4*f**4 - 61/2*f**2 - 2 + 21/4*f**3.
(f - 1)*(f + 2)*(7*f - 2)**2/4
Suppose -5*o = -76 - 414. Suppose o - 93 = k. Find d, given that 0*d + 1/4*d**k - 1/2*d**3 + 0 + 1/4*d**4 + 0*d**2 = 0.
-2, 0, 1
Suppose -22*k - 47 = 14 - 105. Factor 15/2*j + 3/4*j**k + 75/4.
3*(j + 5)**2/4
Let m(o) be the third derivative of -o**6/100 + o**5/15 - o**4/15 - 8*o**3/15 - 3*o**2 + 21. What is t in m(t) = 0?
-2/3, 2
Suppose 4*g + 5*g = 4*g, 0 = -4*d - 3*g. Determine s so that 4/5*s + 4/5*s**2 + d = 0.
-1, 0
Let x be (21/(-35))/(-6*(-3)/(-12)). Let -x*u - 7/5*u**4 - 1/5 - 2/5*u**3 + 8/5*u**2 + 4/5*u**5 = 0. What is u?
-1, -1/4, 1
Solve -32/13*l**4 + 0*l**2 - 32/13*l + 6/13*l**5 + 0 + 48/13*l**3 = 0 for l.
-2/3, 0, 2
Let q(v) be the second derivative of v**5/45 + 212*v**4/27 + 7630*v**3/9 + 4900*v**2 + 2*v + 7. Determine x, given that q(x) = 0.
-105, -2
Let y(x) be the third derivative of x**9/36960 + x**8/36960 - x**7/5544 + x**6/3960 - x**5/30 + 13*x**2. Let c(d) be the third derivative of y(d). Factor c(u).
2*(u + 1)*(3*u - 1)**2/11
Let g be (-8)/8 + 4 + 0. Determine v, given that 30*v**2 - 588*v**4 - 5*v + 5*v**2 - 3*v + 65*v**2 - 224*v**g = 0.
-2/3, 0, 1/7
Let y(p) be the second derivative of p**5/240 - p**4/24 + p**3/8 + 11*p**2/2 + 13*p. Let g(d) be the first derivative of y(d). Let g(m) = 0. Calculate m.
1, 3
Let r(k) be the second derivative of k**4/72 + 7*k**3/36 + 5*k**2/6 + 77*k. What is v in r(v) = 0?
-5, -2
Let g = -61301/8 - -7663. Factor 9/8*m**4 + 0*m + 3/8*m**2 + 0 + g*m**5 + 9/8*m**3.
3*m**2*(m + 1)**3/8
Suppose 30*s - 12*s = 11*s. Suppose -7 = -t + b, 5*t - 3*b - 9 = 16. Find q, given that 2/9*q**t - 2/9 + s*q = 0.
-1, 1
Let a(r) be the third derivative of 1/48*r**4 + 0*r + 0 - 1/1260*r**7 - 1/240*r**6 + 0*r**3 + 1/360*r**5 + r**2. Factor a(d).
-d*(d - 1)*(d + 1)*(d + 3)/6
Suppose -34*w + 37*w = 0. Let o(k) be the first derivative of w*k - 1 - 3/5*k**5 - 3/2*k**2 + k**3 + 3/4*k**4. Suppose o(f) = 0. What is f?
-1, 0, 1
Let w = -116 - -118. Let h = 3 + -1. Factor -3*v**2 - v**4 + v**h + 4*v**4 - v**w.
3*v**2*(v - 1)*(v + 1)
Let b = -245 + 245. Let c(p) be the second derivative of 1/3*p**4 + 1/21*p**7 + 0*p**2 + b*p**6 + 0 + 0*p**3 - 5*p - 3/10*p**5. Factor c(f).
2*f**2*(f - 1)**2*(f + 2)
Let y = -19511/2 + 9758. Factor -10*x - y*x**2 + 5/2*x**3 + 10.
5*(x - 2)*(x - 1)*(x + 2)/2
Let c(h) be the second derivative of -h**5/12 + 55*h**4/24 - 25*h**3/3 - 39*h**2/2 - 12*h. Let v(z) be the first derivative of c(z). What is p in v(p) = 0?
1, 10
Let r(l) = -5*l**2 - 55*l - 85. Let m(i) = -i**3 - i**2 + i - 1. Let x(w) = -5*m(w) + r(w). Find f such that x(f) = 0.
-2, 4
Let g(a) be the second derivative of 0 - 3/2*a**3 - a**2 - 8*a - 1/10*a**6 - 11/20*a**5 - 5/4*a**4. Suppose g(j) = 0. Calculate j.
-1, -2/3
Factor 0*j + 3/7*j**5 - 3/7*j**2 + 3/7*j**4 - 3/7*j**3 + 0.
3*j**2*(j - 1)*(j + 1)**2/7
Suppose 8*p + 13 - 5 = 0. Let g be (p + -1 + -1)*2/(-24). Factor -3/4*z**2 + 3/4*z**3 + 0 - g*z**4 + 1/4*z.
-z*(z - 1)**3/4
Solve 0 + 0*b + 2*b**2 + 1/3*b**4 + 7/3*b**3 = 0.
-6, -1, 0
Let a be 2*1/(-12) - (-5146)/(-12). Let t be (a/(-135) - 3)*20. Determine i so that -16/9*i - 2/9 - t*i**2 = 0.
-1/4
Let h(p) = p**2 - p + 1. Let x(j) = 3*j**2 - 5*j + 7. Let k be (-4)/(-6)*(-225)/(-10). Let q = k - 14. Let o(l) = q*x(l) - 5*h(l). Factor o(z).
-2*(z - 1)*(z + 1)
Let l(u) be the first derivative of -5*u**4/4 - 65*u**3/3 - 255*u**2/2 - 315*u - 55. Suppose l(k) = 0. What is k?
-7, -3
Let t be -2 + 14 + 1066/(-91). Suppose -2/7*s**2 + 0 + t*s**3 + 2/7*s**4 - 2/7*s = 0. What is s?
-1, 0, 1
Let x(q) = -4*q**5 - q**4 + q**3. Let u(v) = 15*v**5 + 7*v**4 - 7*v**3 + v**2. Let a(m) = -u(m) - 4*x(m). Let a(w) = 0. Calculate w.
0, 1
Let b(a) be the second derivative of -a**4/30 + 71*a**3/15 + 72*a**2/5 + 48*a. Factor b(y).
-2*(y - 72)*(y + 1)/5
Let x(v) be the second derivative of -v**6/180 - v**5/15 - v**4/3 - v**3/2 - 19*v. Let d(o) be the second derivative of x(o). Factor d(j).
-2*(j + 2)**2
Let o(b) be the second derivative of -b**4/24 + b**3 + 13*b**2/4 + 48*b - 2. Factor o(d).
-(d - 13)*(d + 1)/2
Let q be 3 + (-12 - -4) - -1940. Factor -q*z**2 + 0*z**3 + 4*z**3 + 1937*z**2 + 2*z**4.
2*z**2*(z + 1)**2
Let c(o) be the second derivative of o**6/20 + 9*o**5/4 + 193*o**4/8 - 120*o**3 + 192*o**2 - 180*o. Find w, given that c(w) = 0.
-16, 1
Let d = 302 + -302. Let w be (4 - (-24)/(-22)) + d. Solve -w - 2/11*k**2 - 16/11*k = 0 for k.
-4
Determine o so that 2 - 30*o + 4*o**2 + o**2 + 23 = 0.
1, 5
Let u be 39/6 + (-3)/6. Suppose -j**3 + j**3 - u*j**2 - 3*j**3 = 0. What is j?
-2, 0
Let -184*b**2 - 66*b - 263*b + 100*b**4 - 173*b + 180 + 118*b + 480*b**3 = 0. What is b?
-5, -1, 3/5
Let f(g) be the second derivative of g**6/6 - g**5/4 - 5*g**4/4 + 5*g**3/6 + 5*g**2 + 7*g. Factor f(s).
5*(s - 2)*(s - 1)*(s + 1)**2
Let v(q) be the first derivative of 8/3*q**3 - 15 + 0*q**2 + 3*q**4 + 4/5*q**5 + 0*q. Factor v(x).
4*x**2*(x + 1)*(x + 2)
Suppose 0 = 18*z + 2*z - 100. Let v(w) be the second derivative of -z*w - 1/6*w**4 - 2/3*w**3 - w**2 + 0. Find d, given that v(d) = 0.
-1
Suppose 27/2*p - 27/4*p**2 - 1/8*p**4 - 15/8*p**3 + 81 = 0. Calculate p.
-6, 3
Let c(t) = t**2 + t + 1. Let n be 50/(-15)*45/(-2). Let q(j) = -42 + n*j**2 + 15*j - 15 - 87*j**2. Let x(i) = 9*c(i) + q(i). Solve x(h) = 0.
4
Suppose -d + 2*f = -2*f - 32, 3*f = 2*d - 54. Let g = -22 + d. Factor 2*t**g + 0 - 2*t - 1/2*t**3.
-t*(t - 2)**2/2
Let x be (3/(-5))/(152/10). Let s = x - -11/38. Find r, given that -1/4*r**2 + 0 - 1/2*r**3 + 0*r - s*r**4 = 0.
-1, 0
Let x(f) be the third derivative of f**5/120 + 5*f**4/8 - 16*f**3/3 + 125*f**2. Factor x(k).
(k - 2)*(k + 32)/2
Let i be 108/35*190/57. Find r such that -2/7*r**3 + i - 22/7*r**2 - 48/7*r = 0.
-6, 1
Let j(i) be the third derivative of 0 - 8*i**2 + 0*i + 1/8*i**4 + 1/25*i**5 + 1/10*i**3. Factor j(g).
3*(g + 1)*(4*g + 1)/5
Let -79/3*b**2 + 4/3 - 35/3*b**3 - 16/3*b = 0. Calculate b.
-2, -2/5, 1/7
Let j be (1/(-2))/((-2)/84). Suppose 0 = j*w + 5*w - 130. Find s such that 0*s + 25/4*s**w - 5/4*s**4 + 0 - s**2 - 4*s**3 = 0.
-2/5, 0, 1
Let y(u) be the third derivative of -u**6/40 + u**5/4 - 11*u**2. Let o(h) = 2*h**3 - 14*h**2 - h. Let t(v) = -6*o(v) - 5*y(v). Let t(q) = 0. What is q?
-2, -1, 0
Let w = -35941 + 35944. What is x in 2/5*x**4 - 8/5*x + 16/5 - 12/5*x**2 + 2/5*x**w = 0?
-2, 1, 2
Let s be (3/(-2))/((-1)/(-96)*-9). Suppose 6*d = 2*d + s. Suppose 0 + 1/5*q**d + 0*q**2 - 3/5*q**3 + 0*q = 0. Calculate q.
0, 3
Suppose -21*u - 19 - 9 = -70. Factor 2/3*h**u + 16/3*h + 32/3.
2*(h + 4)**2/3
Let s(b) be the second derivative of -b**6/180 - 7*b**5/120 - 11*b**4/72 - 5*b**3/36 + 2*b - 54. Solve s(h) = 0 for h.
-5, -1, 0
Factor 2/9*y + 2/9*y**2 + 0.
2*y*(y + 1)/9
Let t(a) = -a + 10. Let o be t(8). Solve 43*c + 19*c**3 + 17*c - 24 + 4 - 5*c**4 + 11*c**3 - 65*c**o = 0 for c.
1, 2
S