 l(q) be the first derivative of q**3/2 - 9*q**2/2 + 27*q/2 + 29. Suppose l(z) = 0. Calculate z.
3
Let c(a) be the first derivative of -2*a**5/15 + a**4 + 2*a**3/9 - 2*a**2 - 43. Factor c(t).
-2*t*(t - 6)*(t - 1)*(t + 1)/3
Let p be (534/351)/2 - 0. Let j = p - 7/13. Solve 2/3*i**3 - j*i**2 + 0 - 4/9*i**5 - 2/9*i + 2/9*i**4 = 0.
-1, -1/2, 0, 1
Let w(v) be the second derivative of 0*v**4 + 1/30*v**6 + 0*v**5 + 0*v**3 - 4*v + 0*v**2 - 1/84*v**7 + 0. Factor w(k).
-k**4*(k - 2)/2
Let x be 0 - -1 - (-20 + 21). Let q(i) be the first derivative of -1 - 4/15*i**3 + 2/5*i + 0*i**2 + 2/25*i**5 + x*i**4. Factor q(k).
2*(k - 1)**2*(k + 1)**2/5
Let q(w) = -15*w**4 - 142*w**3 - 414*w**2 - 383*w - 96. Let t(k) = k**3 - k. Let c(f) = -q(f) - t(f). Factor c(b).
3*(b + 1)*(b + 4)**2*(5*b + 2)
Let r = 24 - 32. Let v be (r/10)/((-36)/20). Factor v*q + 2/3*q**2 + 0 - 10/9*q**3.
-2*q*(q - 1)*(5*q + 2)/9
Suppose -5 = -i + 2*u + 2, -2*i - u + 4 = 0. Suppose a + 0*a - a**3 + 0*a + 0*a**i = 0. Calculate a.
-1, 0, 1
Let s(b) = -25*b**3 + 53*b**2 - 16*b + 5. Let j(m) = m**3 - m**2 - 1. Let t(c) = -5*j(c) - s(c). Factor t(f).
4*f*(f - 2)*(5*f - 2)
Factor 2/7*f**2 - 2/7 + 0*f.
2*(f - 1)*(f + 1)/7
Let x(m) be the first derivative of m**4/10 - 2*m**3/5 + 2*m**2/5 + 5. Factor x(o).
2*o*(o - 2)*(o - 1)/5
Let j = 91 + -181/2. Let l be (-1)/(0/2 - 2). Factor l*p**2 - j + 0*p.
(p - 1)*(p + 1)/2
Factor 21*k + k**3 - 19*k**2 + 33*k**2 + 28*k.
k*(k + 7)**2
Let l(z) be the third derivative of 2/39*z**3 - 11*z**2 + 0*z + 0 + 1/52*z**4 + 1/390*z**5. Suppose l(p) = 0. What is p?
-2, -1
Let l(k) be the first derivative of -k**4/10 - 2*k**3/3 + 13*k**2/5 - 14*k/5 + 26. Factor l(t).
-2*(t - 1)**2*(t + 7)/5
Suppose 0 = 2*s - 2*r - 14, -4*s + 5*r - 1 = -3*s. Let g be 15/(-5) + 29/s. Factor -2/9*j**2 - 4/9*j - g.
-2*(j + 1)**2/9
Let z be (-63)/(-84) + (-42)/(-8). Let d(p) be the second derivative of 0*p**3 + 0*p**2 + 0*p**z + p + 1/63*p**7 + 0 + 0*p**4 - 1/30*p**5. Factor d(a).
2*a**3*(a - 1)*(a + 1)/3
Determine n, given that -3*n + 5/2*n**2 + 1/2 = 0.
1/5, 1
Suppose -6*c = -2*c - 12. Determine h so that -h**2 + c*h - h - h + 0*h = 0.
0, 1
Let p(l) be the second derivative of -l**5/4 + 5*l**3/2 - 5*l**2 - 11*l. Factor p(j).
-5*(j - 1)**2*(j + 2)
Let v = -298/3 - -100. Factor 0*q - v*q**4 + 0*q**3 + 4/3*q**2 - 2/3.
-2*(q - 1)**2*(q + 1)**2/3
Suppose -u - 4*h = 6, 3*h - 6 = -2*u + 4*h. Suppose o - u = 1. Factor 0*f + 2/9*f**o + 0 + 0*f**2.
2*f**3/9
Find w, given that 177/2*w**3 + 45/2*w**4 - 10*w + 61*w**2 - 12 = 0.
-3, -2/3, 2/5
Let x(s) be the third derivative of -s**7/21 + 11*s**6/120 + s**5/60 - s**4/12 + 46*s**2. Factor x(c).
-c*(c - 1)*(2*c - 1)*(5*c + 2)
Suppose -3*q + 3 = -2*t, 4 = 5*t - 4*q + 8. Factor 0*f + t + 2/9*f**2 + 2/9*f**3.
2*f**2*(f + 1)/9
Let p be (-1)/(-3) + 53/3. Let t = p + -13. Factor -3*k**t + 6*k**3 + 2*k**3 - 3*k - 2*k**3.
-3*k*(k - 1)**2*(k + 1)**2
Let s(q) be the second derivative of -q**6/50 + q**4/20 + q. Determine h so that s(h) = 0.
-1, 0, 1
Let v(i) = 2*i**3 + 3*i**2 - 6*i - 7. Let t be v(-1). Solve t + 1/4*x + 1/4*x**2 = 0 for x.
-1, 0
Let l(q) be the first derivative of -q**6/14 + 6*q**5/35 - 3*q**4/28 + 4. Factor l(w).
-3*w**3*(w - 1)**2/7
Let d(x) = 3*x**4 - x**3 - 4*x**2 - 4*x + 4. Let b(c) = -5*c**4 + 2*c**3 + 7*c**2 + 7*c - 7. Let i(p) = -4*b(p) - 7*d(p). Solve i(s) = 0.
-1, 0
Let n(p) be the second derivative of -p**4/54 - 2*p**3/27 - p**2/9 - 9*p + 1. Factor n(j).
-2*(j + 1)**2/9
Let a be (-32)/12*3/(-2). Factor -2*z**3 - 12*z + 10*z + 0*z**3 + a*z**2.
-2*z*(z - 1)**2
Let n(m) = -m + 7*m**5 - m**4 + 6*m**3 - 4*m**2 + 0*m - m**4. Let b(d) = d**5 + d**3 - d**2. Let s(y) = 6*b(y) - n(y). Determine t, given that s(t) = 0.
-1, 0, 1
Determine y so that -2*y**4 - 575*y**2 + 573*y**2 + 6 - 2 - 6*y + 6*y**3 = 0.
-1, 1, 2
Let r(n) = 4*n**3. Let u be r(1). Let a(p) = 5*p**2 + 8*p. Suppose -5 = 3*i - 4*i. Let m(g) = -6*g**2 - 9*g + 1. Let s(b) = i*a(b) + u*m(b). Factor s(k).
(k + 2)**2
Let f(z) = 49*z**2 - 32*z. Let h(t) = -49*t**2 + 31*t - 1. Let s(m) = -3*f(m) - 4*h(m). Factor s(d).
(7*d - 2)**2
Let o(d) = 12*d**5 + 4*d**4 + 10*d**3. Let m = -13 - -7. Let h(y) = y**5 - y**4 + y**3. Let v(u) = m*h(u) + o(u). Find r such that v(r) = 0.
-1, -2/3, 0
Let l = -21 + 68/3. Find f, given that -2/3 - 3*f**2 + l*f**3 - 1/3*f**4 + 7/3*f = 0.
1, 2
Let -k**2 + 0*k**4 + 0*k**2 - k**4 + k**3 + 2*k**2 - k**5 = 0. Calculate k.
-1, 0, 1
Let b(m) be the second derivative of m**4/66 + 8*m**3/33 + 16*m**2/11 + 8*m. Suppose b(l) = 0. What is l?
-4
Suppose -28 = -0*b - 4*b. Factor -x**2 - x - 2*x**2 + 6*x**2 + b*x.
3*x*(x + 2)
Factor 2*s - 3 - 1/3*s**2.
-(s - 3)**2/3
Factor -4/9*z + 0 + 10/9*z**2 + 2/9*z**4 - 8/9*z**3.
2*z*(z - 2)*(z - 1)**2/9
Let f(q) be the second derivative of q**5/18 + 7*q**4/36 + 2*q**3/9 + 4*q**2 - 8*q. Let a(d) be the first derivative of f(d). Let a(m) = 0. Calculate m.
-1, -2/5
Find r such that 4*r**3 - 2*r**5 - 28*r + 0*r**3 + 12*r + 14*r = 0.
-1, 0, 1
Suppose 4*x - 3*y - 23 + 3 = 0, -5*x + 5*y + 30 = 0. Suppose 3*k + k - k**x + k**4 - 2*k**3 - 2*k = 0. What is k?
-1, 0, 1, 2
What is z in -2/17*z**2 - 4*z - 34 = 0?
-17
Let i = -95 + 62. Let s = i - -33. Factor s*q + 1/3 - 1/3*q**2.
-(q - 1)*(q + 1)/3
Let v(x) be the second derivative of -3*x**6/5 - 24*x**5/5 - 79*x**4/6 - 52*x**3/3 - 12*x**2 - 2*x + 41. Suppose v(t) = 0. Calculate t.
-3, -1, -2/3
Let u(f) be the first derivative of 2*f**2 + 0*f - 14/3*f**3 + 6. Factor u(z).
-2*z*(7*z - 2)
Let t = 3 + 0. Let r be ((-25)/3)/((-2)/t). Factor -r*s**2 - 1/2 + 5*s.
-(5*s - 1)**2/2
Factor -1/8*w**3 + 3/8*w + 1/4 + 0*w**2.
-(w - 2)*(w + 1)**2/8
Factor -1/3*p**3 + 5/3*p - 2/3 - p**2 + 1/3*p**4.
(p - 1)**3*(p + 2)/3
Suppose -3 + 5 = m. Let w be ((-2)/(-1))/(2/m). Let -w*q**2 + 0*q**2 - 4*q**4 + 4*q**3 + 2*q**4 = 0. Calculate q.
0, 1
Factor 0 + 2/7*z**2 + 0*z.
2*z**2/7
Let q(l) be the third derivative of l**6/1080 + l**5/360 - l**3/6 - l**2. Let g(a) be the first derivative of q(a). Factor g(b).
b*(b + 1)/3
Let y(o) be the second derivative of 3/20*o**4 + 8/5*o**2 + 1/100*o**5 + 4/5*o**3 + 0 + 6*o. Factor y(k).
(k + 1)*(k + 4)**2/5
Let w(u) = -u**2 + 5*u + 26. Let q be w(8). Solve -1/3*m**3 + 0*m**q + 1/3*m**4 + 0*m + 0 = 0.
0, 1
Let b(l) be the second derivative of l**4/66 - l**3/11 + 2*l**2/11 + l. Factor b(w).
2*(w - 2)*(w - 1)/11
Find y such that -4/5*y - 2/5*y**2 - 2/5 = 0.
-1
Suppose 5*h + s = 10*h - 11, 5*h = -2*s + 23. Factor 0*m + 2/5*m**2 + 1/5*m**4 + 3/5*m**h + 0.
m**2*(m + 1)*(m + 2)/5
Factor -3*v + 7*v - 2 - 5*v + v**2.
(v - 2)*(v + 1)
Determine w so that -290 - 21*w**2 + 0*w**4 - 45*w + 9*w**3 + 3*w**4 + 344 = 0.
-3, 1, 2
Let n(j) = -5*j**4 + 5*j**2 - 6. Suppose d - 4*d = r + 1, -3*r = 4*d - 12. Let i = -2 + r. Let h(z) = -z**4 + z**2 - 1. Let v(y) = i*h(y) - n(y). Factor v(m).
-m**2*(m - 1)*(m + 1)
Let z(y) be the first derivative of -y**2 - 1/6*y**3 + 5 - 3/2*y. Factor z(t).
-(t + 1)*(t + 3)/2
Let m(d) be the third derivative of -d**6/360 + 7*d**5/180 - 7*d**4/36 + 4*d**3/9 + 2*d**2 - d. Factor m(f).
-(f - 4)*(f - 2)*(f - 1)/3
Let f(q) be the second derivative of 2*q**7/105 + q**6/15 + q**5/50 - q**4/15 - 24*q + 2. Find t such that f(t) = 0.
-2, -1, 0, 1/2
Let q(o) be the third derivative of -9*o**8/1120 + o**7/70 - o**6/90 - o**5/60 - 9*o**2. Let u(c) be the third derivative of q(c). Factor u(h).
-2*(9*h - 2)**2
Let f(l) = 3*l**3 - l**2. Let t be f(2). Let s be 3/(-4) - (-45)/t. Factor -3/2*z**2 - 9/4*z + 3/4*z**5 - 3/4 + 9/4*z**4 + s*z**3.
3*(z - 1)*(z + 1)**4/4
Let q(j) be the third derivative of 9*j**2 + 0*j + 0 - 1/24*j**4 + 0*j**7 + 0*j**3 + 0*j**5 - 1/336*j**8 + 1/60*j**6. Factor q(d).
-d*(d - 1)**2*(d + 1)**2
Let f = -12 - -17. Solve 12*j**5 + 6*j - 18*j**3 + 13*j**2 - 21*j**4 - 3*j**2 - f*j**2 + 16*j**2 = 0 for j.
-1, -1/4, 0, 1, 2
Let b be 5 + 1 - (1 - 2*-1). Let n(f) be the second derivative of 2/165*f**6 - 1/11*f**2 + 1/33*f**3 - 1/22*f**5 - b*f + 1/22*f**4 + 0. Factor n(m).
2*(m - 1)**3*(2*m + 1)/11
Suppose 5*q = 3*n + 12, -2*n = 2*n - 4. Factor 3 + 1 - 1 - 2 + s - s**2 - s**q.
-(s - 1)*(s + 1)**2
Let c(f) be the third derivative of -f**8/1512 + 2*f**7/945 - f**5/135 + f**4/108 - 6*f**2. Factor c(q).
-2*q*(q - 1)**3*(q + 1)/9
Let v = 3 + -3. Let y = -12 - -16. Factor v*r**3 + 1/4*r**5 - 1