*3.
2*p**2*(2*p + 1)/3
Let k(t) be the second derivative of 0 - 1/10*t**5 + 1/3*t**4 + 1/3*t**3 - 6*t - 2*t**2. Suppose k(d) = 0. Calculate d.
-1, 1, 2
Let r(m) = m**3 + 6*m - 4*m**2 - 2*m**3 - 5 - 2*m. Let t be r(-5). Factor -2/7*l**4 + 2/7*l**3 + 0*l + t + 0*l**2.
-2*l**3*(l - 1)/7
Let h = -121 + 487/4. Factor -3/4*c**2 + 3/4*c - h*c**3 + 3/4*c**4 + 0.
3*c*(c - 1)**2*(c + 1)/4
Let i be (-36)/(-10) + (-9)/15. Suppose -4*r = -5*r + i. Solve -18/5*z - 2/5*z**5 - 12/5*z**4 - 32/5*z**2 - 4/5 - 28/5*z**r = 0.
-2, -1
Let m(x) be the second derivative of 9*x**5/40 + x**4 + 3*x**3/4 - 3*x**2/2 - x. Suppose m(c) = 0. Calculate c.
-2, -1, 1/3
Let q(c) be the first derivative of 0*c**3 - 1/3*c**2 + 1/6*c**4 - 1/15*c**5 + 1/3*c - 5. What is y in q(y) = 0?
-1, 1
Let k(p) be the second derivative of -p**4/60 - 2*p**3/15 - 3*p**2/10 + 11*p. Let k(s) = 0. What is s?
-3, -1
Let s(d) be the first derivative of d**5/20 - d**4/16 - d**3/12 + d**2/8 - 9. Suppose s(x) = 0. Calculate x.
-1, 0, 1
Let x = 1 + 1. Let -2*h**3 + h**x + 3*h**3 - 6*h + 6*h = 0. Calculate h.
-1, 0
Let t be (2 + (-36)/15)*-5. Suppose -s - 2 = 2*m, m - 9 = -s - t*s. Factor 2/7*h**3 - 4/7*h**s + 0 + 2/7*h**5 + 0*h**2 + 0*h.
2*h**3*(h - 1)**2/7
Let m(f) be the third derivative of f**5/80 - 5*f**4/16 + 25*f**3/8 - 6*f**2. Let m(q) = 0. What is q?
5
Suppose -1/3*v**4 + 1/3*v - 2/3*v**3 - 1/3 + 2/3*v**2 + 1/3*v**5 = 0. What is v?
-1, 1
Let r(t) = t**2 - 4*t + 5. Let j(z) = -1. Let u(s) = 10*j(s) + 2*r(s). Factor u(c).
2*c*(c - 4)
Let k(u) = 3*u**4 - 9*u**3 - 25*u**2 + 4*u + 17. Let w(t) = -t**4 - t**3 - t**2 + 1. Let g(p) = -k(p) + 5*w(p). Determine x so that g(x) = 0.
-1, 1, 3/2
Let d(c) be the second derivative of -8*c - 19/3*c**4 + 0 + 8*c**2 - 8/3*c**3 - 14/5*c**5 - 2/5*c**6. What is n in d(n) = 0?
-2, -1, 1/3
Let m(w) be the third derivative of w**9/2268 + w**8/5040 - w**3/6 + 3*w**2. Let u(v) be the first derivative of m(v). Solve u(r) = 0 for r.
-1/4, 0
Let d(m) be the first derivative of -1/2*m**2 + 1/9*m**3 - 3 + 1/4*m**4 - 1/3*m. Suppose d(s) = 0. What is s?
-1, -1/3, 1
Let t = -5 + 7. Suppose -t*z**2 + 132*z + 147*z**5 - 84*z**4 - 7*z**3 - 40*z**2 - 422*z**3 - 24 = 0. What is z?
-1, 2/7, 2
Let t(u) be the first derivative of 2/3*u**2 - 4/9*u**4 - u - 2 - 1/9*u**3 - 1/6*u**5. Let c(g) be the first derivative of t(g). Find v, given that c(v) = 0.
-1, 2/5
Let m(s) = s**4 - s**3 - s**2 - s - 1. Let h(t) = -73*t**4 - 392*t**3 - 29*t**2 + 226*t - 62. Let l(p) = -h(p) + 2*m(p). Solve l(f) = 0.
-5, -1, 2/5
Let j be (0 - 0)*1/(-1). Find b, given that -2 + j*b**3 + 2*b**3 - 3*b**4 + 2 + b**2 = 0.
-1/3, 0, 1
Let s(n) = n**2 - 2*n - 5. Let x be ((-24)/9)/(4/(-6)). Let f be s(x). Factor 5*z**3 + 5*z - z**f - 1 - 6*z**2 - z - z**4.
-(z - 1)**4
Let q(l) = 2*l - 6. Let y be q(10). Let x be 1 + (-6)/y*1. Solve 0*o**2 - 4/7*o**3 - 2/7 + x*o + 2/7*o**4 = 0.
-1, 1
Let g = 4 + -7/2. Let r(f) be the first derivative of 6/5*f**5 + 0*f + 1 + f**2 - g*f**4 - 2*f**3. Factor r(s).
2*s*(s - 1)*(s + 1)*(3*s - 1)
Suppose h = -3*h - 5*t + 15, 4*h = 2*t + 22. Suppose h*c - 12 = c. Solve -4/9*z**2 - 2/9*z**c + 4/9 + 2/9*z = 0.
-2, -1, 1
Let r be (2 - (-35)/(-18))/(2/4). Let f(p) be the second derivative of -4*p + 0 - r*p**3 + 0*p**2 + 1/36*p**4. Factor f(k).
k*(k - 2)/3
Let y be (-46)/(-9) + (-3)/27. Let o(c) be the third derivative of 0*c**y + 3/8*c**4 - 1/40*c**6 - 5*c**2 + 0 + 0*c + c**3. Factor o(i).
-3*(i - 2)*(i + 1)**2
What is q in -20*q**3 + 0*q**2 - 16*q - 32*q**2 - 5*q**4 + 4*q**4 - 3*q**4 = 0?
-2, -1, 0
Let n(t) be the second derivative of t**8/2520 - t**7/420 + t**6/270 + t**3/3 - 5*t. Let a(f) be the second derivative of n(f). Factor a(u).
2*u**2*(u - 2)*(u - 1)/3
Let g be 31/3 + 2/3. Suppose 0 = -2*c + g + 1. Solve a**3 + 0 - 2*a**3 - 6*a + c*a**2 - a**3 + 2 = 0 for a.
1
Let g(b) be the first derivative of -21*b**5/25 - 69*b**4/20 - 27*b**3/5 - 39*b**2/10 - 6*b/5 - 12. Find k, given that g(k) = 0.
-1, -2/7
Let w be 119/70 + (-1)/(-2). Let i = w - 17/10. Let -3/2*g**3 - 1/2*g**5 + 0*g + 0 + i*g**2 + 3/2*g**4 = 0. What is g?
0, 1
Let z(t) be the first derivative of -t**6/12 - t**5/5 - t**4/8 - 3. Factor z(u).
-u**3*(u + 1)**2/2
Suppose 2*v - d + 19 - 24 = 0, 0 = -3*v + d + 8. Factor -1/6*j - 4/3*j**v - 7/6*j**2 + 8/3*j**4 + 0.
j*(j - 1)*(4*j + 1)**2/6
Let l(j) be the first derivative of j**7/210 + j**6/50 + j**5/50 - j**4/30 - j**3/10 - j**2/10 + 4*j - 2. Let g(d) be the first derivative of l(d). Factor g(f).
(f - 1)*(f + 1)**4/5
Let a(k) = -k**2 - k. Suppose m = -4*v + 2, -3*m - v + 0 = -6. Let r(u) = u**2. Let g(n) = m*r(n) + a(n). Factor g(d).
d*(d - 1)
Determine p so that -3*p**2 - 1/2*p**3 - 7/2*p - 5/4 + 1/4*p**4 = 0.
-1, 5
Suppose -8/9*f - 2/3 - 2/9*f**2 = 0. What is f?
-3, -1
Suppose -5*p + 17 = -x, x - 3*x + 14 = 2*p. Solve -w**x + w**4 + 0*w**4 + 2*w**3 = 0.
-1, 0
Suppose -5*f = -12*f + 14. Determine d, given that -2/3*d**4 + 0 - 2/3*d**3 + 2/3*d + 2/3*d**f = 0.
-1, 0, 1
Let j(k) be the third derivative of k**6/160 + k**5/80 - k**4/32 - k**3/8 + 7*k**2. Solve j(q) = 0 for q.
-1, 1
Let u(n) = -25*n**4 - 5*n**3 + 35*n**2 + 10*n + 5. Let x(c) = -13*c**4 - 3*c**3 + 17*c**2 + 5*c + 2. Let m(r) = 2*u(r) - 5*x(r). Factor m(t).
5*t*(t - 1)*(t + 1)*(3*t + 1)
Suppose -3*i + 4*h = -6*i + 14, 2*h - 12 = -4*i. Let b(q) = 2*q + 1. Let s be b(1). Factor -4/3*c**4 - 2/3*c**2 + 0 + 0*c - i*c**s.
-2*c**2*(c + 1)*(2*c + 1)/3
Let j be (64 + 2)/(-3 + 5). Suppose 3*k + 21 = 5*k + 3*m, -5*k - m = -j. Factor 0*y**2 - 3*y**2 - k + 0 + 9*y.
-3*(y - 2)*(y - 1)
Let l(k) = -k**3 + k**2 - k + 4. Let w be l(0). Let f be 2/8 + 7/w. Determine a so that -2*a**2 + 2*a**f - 2*a**4 + 0*a**3 + 4*a**3 = 0.
0, 2
Let m be 6/((10/(-8))/5). Let h be 6/m + (-37)/(-4). Determine p so that p**5 + 0*p**5 + h*p**3 - 10*p**3 = 0.
-1, 0, 1
Let d(k) = 6*k**4 - 8*k**3 + 2*k. Let n(y) = 7*y**4 - 9*y**3 - y**2 + 3*y. Let a(u) = -3*d(u) + 2*n(u). Factor a(z).
-2*z**2*(z - 1)*(2*z - 1)
Let x(k) = 3*k**4 - 11*k**3 + 14*k**2 - 4*k + 4. Let t(p) = 21*p**4 - 78*p**3 + 99*p**2 - 27*p + 27. Let a(y) = 4*t(y) - 27*x(y). Factor a(j).
3*j**2*(j - 3)*(j - 2)
Let p(i) be the first derivative of -2 + 0*i**3 - 1/8*i**4 + 0*i + 0*i**2 + 1/10*i**5. Let p(z) = 0. What is z?
0, 1
Suppose 4*d + 2*c - 18 = 0, 2*c + 8 + 37 = 5*d. Let h = d + -5. Find f such that -h*f + f**2 - f**2 + 2*f**2 = 0.
0, 1
Factor -27*i**2 - 486*i**3 - 3 - 8 - 1 + 84*i.
-3*(2*i + 1)*(9*i - 2)**2
Let d(f) be the first derivative of 0*f**2 + 1 + 0*f - 1/15*f**3. What is t in d(t) = 0?
0
Let r = 1 + -3. Let t be 5/((-20)/(-9)) + r. Factor 0*i**2 + 0 - 1/4*i**5 + 0*i + t*i**4 + 0*i**3.
-i**4*(i - 1)/4
Let z(h) = h + 2. Let p be z(-5). Let t be 0*(1 - p/(-6)). Factor -2/5*k**2 + 0 + 2/5*k**3 + t*k.
2*k**2*(k - 1)/5
Factor 0 - 4/5*h**4 + 8/5*h**3 + 4/5*h**2 - 8/5*h.
-4*h*(h - 2)*(h - 1)*(h + 1)/5
Let s(m) be the first derivative of 6 + 2*m**2 + 0*m**3 + 8/3*m - 1/3*m**4. Factor s(z).
-4*(z - 2)*(z + 1)**2/3
Let k(q) be the first derivative of -1/10*q**4 + 4 - 4/9*q**3 + 16/15*q - 4/15*q**2. Find y, given that k(y) = 0.
-2, 2/3
Suppose 10 = 4*q - 2*c, -1 = -q - 3*c - 2. Let 6*k**3 - 4*k**4 + q*k - 4*k**2 + 0*k**2 + 2*k**4 - 2*k**2 = 0. Calculate k.
0, 1
Suppose 0 = 4*m + 2*w - 5 - 1, -4*m = w - 9. Let -1/2*i + 0*i**2 + 0 + i**m + 0*i**4 - 1/2*i**5 = 0. Calculate i.
-1, 0, 1
Let d(z) be the first derivative of 3*z**5/5 + 3*z**4/2 + z**3 + 3. Factor d(f).
3*f**2*(f + 1)**2
Let z be 6*(1 + 6/(-18)). Determine b so that 10/3*b - 4/3*b**2 - 2/3*b**5 + 8/3*b**z - 8/3*b**3 - 4/3 = 0.
-1, 1, 2
Find i such that 6/5 - 9/5*i + 0*i**2 + 3/5*i**3 = 0.
-2, 1
Let x(q) be the second derivative of -q**7/70 - 3*q**6/25 - 9*q**5/50 + 4*q**4/5 + 3*q**3/2 - 27*q**2/5 + q + 1. Find y such that x(y) = 0.
-3, -2, 1
Let k(t) be the first derivative of -t**4/20 + 2*t**3/15 - t**2/10 - 4. Suppose k(z) = 0. What is z?
0, 1
Let j(m) = -7*m + 10. Let u be j(4). Let w be ((-9)/u)/((-10)/(-8)). Factor -4/5*p**2 + w*p + 2/5*p**4 - 4/5*p**3 + 2/5 + 2/5*p**5.
2*(p - 1)**2*(p + 1)**3/5
Let a(r) be the first derivative of 1/3*r**6 + 9*r**4 + 0*r**3 - 27*r**2 + 0*r - 16/5*r**5 - 1. Factor a(q).
2*q*(q - 3)**3*(q + 1)
Let t(b) be the second derivative of -b**4/4 + 5*b**3/2 - 6*b**2 - 14*b. Determine v, given that t(v) = 0.
1, 4
Let d(c