)**2/3
Suppose 0 = -8*q + 4*q - 16. Let v(k) = -4*k - 16. Let h be v(q). Find j such that 0 + h*j - 1/2*j**3 + 1/2*j**2 = 0.
0, 1
Let x(g) be the third derivative of -g**8/3360 - g**7/420 + g**6/200 - 78*g**2 - 2. Find i such that x(i) = 0.
-6, 0, 1
Factor 2/7*a**2 - 52/7 + 22/7*a.
2*(a - 2)*(a + 13)/7
Let l be ((-360)/72)/(-1 + 2/(-3)). Factor 0 + 7/4*i**4 - 1/2*i - 7/4*i**2 + 1/2*i**l.
i*(i - 1)*(i + 1)*(7*i + 2)/4
Let m be (3/(-6))/(4/(-96)). Let h = m - 8. Determine o, given that 21*o**3 + 2*o**2 + h*o**2 - 4*o + 4*o + 15*o**4 = 0.
-1, -2/5, 0
Suppose -230*o + 226*o = 0. Let i(k) be the third derivative of -1/30*k**6 + 0*k**3 + 0 - 4*k**2 + 0*k**7 + 1/12*k**4 + o*k**5 + 1/168*k**8 + 0*k. Factor i(z).
2*z*(z - 1)**2*(z + 1)**2
Let i(v) be the first derivative of 5*v**3/3 + 155*v**2/2 - 160*v + 82. Suppose i(t) = 0. What is t?
-32, 1
Let m(t) be the first derivative of 6/25*t**5 + 0*t + 0*t**3 + 0*t**2 - 3/20*t**4 + 26 - 1/10*t**6. Solve m(w) = 0.
0, 1
Let m(h) be the first derivative of h**6/90 - h**5/20 + h**4/36 + h**3/6 - h**2/3 + 10*h + 18. Let l(g) be the first derivative of m(g). Factor l(n).
(n - 2)*(n - 1)**2*(n + 1)/3
Let l be 0 + 3 - -1*(-649)/220. Let m(g) be the second derivative of 0 - 1/6*g**4 - 6*g - 1/6*g**3 + 0*g**2 - l*g**5. Suppose m(i) = 0. What is i?
-1, 0
Determine c, given that 20/13*c**2 + 22/13*c - 14/13*c**3 - 12/13 = 0.
-1, 3/7, 2
Let m(q) be the third derivative of q**5/120 + 5*q**4/16 - 21*q**3/2 - 281*q**2. Factor m(i).
(i - 6)*(i + 21)/2
Let z(j) be the third derivative of 12*j**2 + 0*j + 1/156*j**4 + 1/390*j**5 - 2/39*j**3 + 0. Let z(t) = 0. Calculate t.
-2, 1
Let i be (12/(-10))/(6/(-15)). Suppose 0 = -4*w - 4*r + 32, 3*w + 0*r = -4*r + 21. Factor w*z - 26*z + 13*z + 2*z**i.
2*z*(z - 1)*(z + 1)
Let w(q) be the second derivative of -q**4/24 - 5*q**3/12 + 7*q**2/2 + 19*q. Solve w(k) = 0 for k.
-7, 2
Let w(v) be the second derivative of -v**6/75 + 2*v**5/5 - 59*v**4/15 + 12*v**3 - 81*v**2/5 - v - 10. Suppose w(z) = 0. What is z?
1, 9
Let s be 6/9 - (-256)/(-480). Find u, given that 0 - 16/15*u**4 + 0*u - s*u**2 - 2/3*u**3 - 8/15*u**5 = 0.
-1, -1/2, 0
Let b(z) = 4*z**3 + 459*z**2 + 72075*z + 3723872. Let g(h) = 5*h**3 + 457*h**2 + 72075*h + 3723871. Let d(w) = -4*b(w) + 3*g(w). Solve d(u) = 0 for u.
-155
Let s be (5 - (-15 + 20))/(2/2 - 5). What is n in n**5 + 0*n + 0*n**2 + 0*n**3 + s + 1/4*n**4 = 0?
-1/4, 0
Suppose 0 = 6*g - 2*g + 12, 5*l - 2*g - 116 = 0. Factor -4*b**3 + l*b**4 + 5*b**3 + 8*b**3 - 19*b**4.
3*b**3*(b + 3)
Suppose 4 = -3*x - 2. Let q(y) = 4*y**2 + 2*y + 1. Let f be q(x). Factor n**3 + 0*n**2 - f*n**3 - 8*n**2 + 7*n**4 + n**4.
4*n**2*(n - 2)*(2*n + 1)
Let a(n) be the third derivative of n**6/210 + 88*n**5/105 + 29*n**4/14 - 406*n**2. Factor a(w).
4*w*(w + 1)*(w + 87)/7
Let f(m) be the first derivative of -m**4/5 + 8*m**3/15 - 2*m**2/5 - 121. Determine c so that f(c) = 0.
0, 1
Let a be 4 - (-5 - (-5 - -18) - -1). Let f be 3/(-8 + 5) + a/13. Factor 6/13*t**3 - 14/13*t**2 + 0*t + f.
2*(t - 2)*(t - 1)*(3*t + 2)/13
Let c(k) be the third derivative of 0*k**4 + 0*k + 1/30*k**6 + 2/105*k**7 - 2/15*k**5 + 0*k**3 + 0 + 11*k**2. Factor c(j).
4*j**2*(j - 1)*(j + 2)
Let n be (((-12)/10)/3)/((-24)/(-120)). Let y be 0/(((-6)/12)/(1/n)). Factor -w**2 + y*w + 2*w**3 + 1/4*w**5 - 5/4*w**4 + 0.
w**2*(w - 2)**2*(w - 1)/4
Let n(i) be the first derivative of i**8/2240 - i**7/3360 - i**6/480 + i**5/480 + i**3/3 + 18. Let d(r) be the third derivative of n(r). Solve d(w) = 0.
-1, 0, 1/3, 1
Let m = -212/3 - -1697/24. Let t(k) be the second derivative of 1/4*k**2 + 4*k + 1/24*k**3 - m*k**4 - 1/80*k**5 + 0. Factor t(g).
-(g - 1)*(g + 1)*(g + 2)/4
Suppose 0 = -2*t - 10 + 226. Solve 15*r - r + t*r**2 + 20*r + 3 + 2*r = 0 for r.
-1/6
Let t(y) = 3*y**2 + 27*y. Let v be t(-9). Let g(z) be the third derivative of -1/150*z**5 + 1/300*z**6 + 5*z**2 + 0 + v*z**3 + 0*z**4 + 0*z. Factor g(m).
2*m**2*(m - 1)/5
Let s(z) be the second derivative of -2*z**6/15 + 17*z**5/5 - 30*z**4 + 72*z**3 + 432*z**2 - 27*z + 1. Factor s(n).
-4*(n - 6)**3*(n + 1)
Let h(u) = -u + 10. Let k be h(3). Find m such that 5*m - m**2 + 4*m - 5*m - k*m**2 = 0.
0, 1/2
Let g(w) be the third derivative of -w**8/3360 - w**7/1120 + 9*w**5/20 - 26*w**2. Let h(v) be the third derivative of g(v). Solve h(m) = 0.
-3/4, 0
Let d be (-24)/(-14) - (-34)/119. Factor -24*k**d - 6*k**3 - 2*k**3 - 20*k + 4*k**3 + 0*k**3.
-4*k*(k + 1)*(k + 5)
Let o(y) be the first derivative of -10 + 10*y + 5/4*y**4 - 15/2*y**2 + 0*y**3. Let o(q) = 0. Calculate q.
-2, 1
Let b = -30 - -60. Let n be b/(-6)*(-4)/10. Suppose -l**2 + 0*l - n*l + 4 - l**2 = 0. What is l?
-2, 1
Let w = -15 - -10. Let r(g) = g**3 + 5*g**2 - g. Let p be r(w). Determine x so that -x**2 - 3*x**4 + 2*x**2 + 3*x - 2*x**3 - 7*x**p + 6*x**5 + x**2 + 1 = 0.
-1, 1
Let n(k) = -k**3 + 7*k**2 - 4*k - 6. Let a be n(5). Let b be -3 - (-4 + a)/(-4). Factor -4*q**3 - 4 - 11 - q + 3 + 12*q**b + 5*q.
-4*(q - 3)*(q - 1)*(q + 1)
Suppose -13 - 27*i + 144*i**2 - 53*i + 397 - 148*i**2 = 0. Calculate i.
-24, 4
Suppose 8*v - 10*v = -4*b - 218, b = 5*v - 590. Let l = v + -117. Solve -1/2*i**3 + 0 + 3/2*i - i**l = 0 for i.
-3, 0, 1
Factor -2/13*o**2 + 18/13*o - 16/13.
-2*(o - 8)*(o - 1)/13
Let y(o) be the first derivative of -o**3/3 - o**2/2 + 6*o + 312. Suppose y(k) = 0. What is k?
-3, 2
Let m(o) = 52*o**2 - 3*o - 2. Let g(t) be the third derivative of -53*t**5/60 + t**4/12 + t**3/2 + 27*t**2. Let y(p) = -2*g(p) - 3*m(p). Factor y(l).
-5*l*(10*l - 1)
Let g(w) be the first derivative of -2*w**5/15 + 77*w**4/6 - 174. Find c, given that g(c) = 0.
0, 77
Let t(a) be the third derivative of -19*a**6/240 + 173*a**5/120 - 3*a**4/8 + a**2 + 7*a. Factor t(f).
-f*(f - 9)*(19*f - 2)/2
Let p(m) = -m**5 + m**4 + 3*m**3 - m**2 + m. Let f(b) = 12*b**5 - 14*b**4 - 38*b**3 + 14*b**2 - 7*b. Let n(g) = 4*f(g) + 44*p(g). Find l such that n(l) = 0.
-1, 0, 1, 4
Let k be (150/(-100))/(6/(-22)) + (-5)/1. Factor 1/3*c + 1/6*c**2 - k.
(c - 1)*(c + 3)/6
Let m(d) be the third derivative of -d**6/660 - d**5/33 + 17*d**4/132 + 2*d**3 - 3*d**2 + 4*d. Solve m(f) = 0.
-11, -2, 3
Suppose 645*t - 1857 = 78. Suppose -6/11*r**t + 18/11*r**4 + 8/11*r + 0 - 16/11*r**2 = 0. Calculate r.
-1, 0, 2/3
Factor -147*u + u**2 - 7*u**2 + 3*u**3 - 224 + u**3 - 34*u**2 - 61*u.
4*(u - 14)*(u + 2)**2
Factor 1/3*y**5 + 5/3*y**3 + 0 + 2*y**4 - 12*y - 8*y**2.
y*(y - 2)*(y + 2)*(y + 3)**2/3
Let z = -46 - -50. Solve 2382 - 2382 + 2*o + 6*o**2 + 2*o**z + 6*o**3 = 0 for o.
-1, 0
Factor -47*l + 27/4 + 317/4*l**2 + 3*l**3.
(l + 27)*(3*l - 1)*(4*l - 1)/4
Suppose 0 = j, 4*j = -3*u - j. Let b(w) be the third derivative of -1/96*w**4 + u*w - 1/80*w**5 + 0*w**3 - 1/240*w**6 + 0 - 2*w**2. Find v, given that b(v) = 0.
-1, -1/2, 0
Let w(d) be the third derivative of -d**7/210 + 2*d**5/15 - 8*d**3/3 + 135*d**2. Factor w(c).
-(c - 2)**2*(c + 2)**2
Suppose 3*p - 13 + 1 = -2*b, 0 = b - p - 6. Let l(h) be the second derivative of 3*h + 0*h**2 + 0 + 3/40*h**b + 0*h**3 + 3/20*h**5 + 1/16*h**4. Factor l(k).
3*k**2*(k + 1)*(3*k + 1)/4
Factor -4/3*c**2 - 2*c**3 + 0*c**4 + 0 + 0*c + 2/3*c**5.
2*c**2*(c - 2)*(c + 1)**2/3
Suppose -3*a = -f + 114, 3*f + 4*a + 236 - 604 = 0. Solve -f*u**4 + 23*u**3 + u**2 + 52*u**3 - 2*u**2 - 9*u**2 - 80*u**5 = 0 for u.
-2, 0, 1/4
Let g(f) be the third derivative of f**8/1344 - f**7/120 + 7*f**6/480 + 19*f**5/240 - f**4/6 - 5*f**3/6 - 117*f**2. Suppose g(t) = 0. Calculate t.
-1, 2, 5
Suppose 76*l - 75*l = 6. Let z(q) be the third derivative of -q**2 + 1/8*q**4 - 1/20*q**5 + 0*q + 1/120*q**l - 1/6*q**3 + 0. Factor z(y).
(y - 1)**3
Let a(n) be the first derivative of -4*n**5/45 - 2*n**4/9 + 20*n**3/27 + 4*n**2/3 - 66. Factor a(l).
-4*l*(l - 2)*(l + 1)*(l + 3)/9
Factor 10/3*w**2 - 32/9*w**3 + 4*w + 0 + 2/3*w**4.
2*w*(w - 3)**2*(3*w + 2)/9
Let x(a) be the second derivative of 0*a**2 - 1/6*a**4 + 12*a + 0 + 1/40*a**5 + 1/15*a**6 - 1/12*a**3. Find i, given that x(i) = 0.
-1, -1/4, 0, 1
Let b(z) be the first derivative of 9*z**4/7 - 128*z**3/7 + 122*z**2/7 - 40*z/7 - 204. Factor b(i).
4*(i - 10)*(3*i - 1)**2/7
Let y = 41/18 + -1/36. Let j(b) be the first derivative of -y*b**4 + 6*b**2 - 27/5*b**5 + 8 + 8*b**3 + 0*b. Let j(s) = 0. What is s?
-2/3, 0, 1
Suppose -65 = -15*s + 10. Let r(i) be the third 