- y**4/44 + 28*y**2. Determine f, given that r(f) = 0.
-3, -1, 0
Let 0*r**2 + 0 + 2/3*r**3 - 1/3*r**4 + 0*r = 0. Calculate r.
0, 2
Let w be (-3 - 0)/(((-54)/(-4))/(-3)). Determine f so that w*f**3 + 2/3*f**2 + 0 + 0*f = 0.
-1, 0
Let p(h) be the second derivative of -h**7/7560 - h**6/2160 - 2*h**4/3 - 4*h. Let z(y) be the third derivative of p(y). Factor z(s).
-s*(s + 1)/3
Let m be (-35)/(-46) + (-1)/2. Let w = m + 28/69. Factor 0*q + w*q**3 + 2/3*q**2 + 0.
2*q**2*(q + 1)/3
Let y(n) be the second derivative of n**5/140 - n**3/42 + 3*n. Find d such that y(d) = 0.
-1, 0, 1
Suppose 0 = -2*u + 3*b + 19, -2*b + 5 = -u + 17. Let q be (u/24)/((-6)/(-18)). Factor -q*n + 1/2 - 1/4*n**2.
-(n - 1)*(n + 2)/4
Let v(j) be the third derivative of j**8/141120 - j**7/11760 + j**6/2520 + j**5/15 - 3*j**2. Let y(n) be the third derivative of v(n). Factor y(a).
(a - 2)*(a - 1)/7
Suppose -4*n - 18 = v + n, 4*n = 5*v - 26. Determine y, given that 0*y**v + 0 + 8/9*y**4 + 2/9*y**5 + 0*y + 8/9*y**3 = 0.
-2, 0
Let p = -3 + 3. Let l be (-9 + 10)*(0 - -1)/2. Determine n so that 1/2*n**2 + p*n - l = 0.
-1, 1
Let o(b) = 4*b**3 + b**2 - b - 1. Suppose 5*h + 2*a = h - 68, 2*h = 3*a - 26. Let d(m) = 20*m**3 + 4*m**2 - 4*m - 4. Let c(z) = h*o(z) + 3*d(z). Factor c(y).
-4*(y - 1)*(y + 1)**2
Let z(r) = r**3 - 6*r**2 + 5*r + 7. Let x be z(5). Factor x - 7 - b**2.
-b**2
Factor -10*z + 2*z**3 + 7*z + 2*z**3 - z.
4*z*(z - 1)*(z + 1)
Let t(c) = -5*c**3 + 4*c**2 - 6*c - 6. Let i(k) = 9*k**2 - 7*k**2 - 5*k - 4*k**3 + k**2 - 1 - 4. Let p(u) = 6*i(u) - 5*t(u). Suppose p(j) = 0. What is j?
0, 2
Suppose 5*g = 5*k + 55, 0*g - 2*k = 5*g - 34. Suppose -4*d = m - 2*m - 16, -2*d + g = 0. Factor m - 2/7*y**2 + 0*y.
-2*y**2/7
Suppose 4 = -4*a - 0. Let w = 1 - a. What is t in t**2 + 0*t**3 - w*t**3 - 3*t**2 = 0?
-1, 0
Let m(f) be the first derivative of 2*f**5/55 - f**4/11 + 5. Suppose m(c) = 0. Calculate c.
0, 2
Let u(g) = -g + 1. Let b(p) = p**2 - p + 1. Let t(w) = -9*w**2 + 9*w - 18. Let d(v) = 6*b(v) + t(v). Let m(s) = -d(s) - 9*u(s). Factor m(y).
3*(y + 1)**2
Let c = -178/9 + 20. Let 2/9 - 2/9*z**3 + 2/9*z - c*z**2 = 0. Calculate z.
-1, 1
Let l = -4 + 6. Suppose p - h = -6*h - 2, -3*p + 7 = 2*h. Determine y, given that 0*y**2 - 2*y**3 - 2*y**l + 0*y**p = 0.
-1, 0
Let b(a) = a**3 - 3*a**2 - 7*a. Let g(w) = 4*w**3 - 8*w**2 - 22*w. Let i(f) = 10*b(f) - 3*g(f). Factor i(l).
-2*l*(l + 1)*(l + 2)
Let v(t) be the second derivative of t**6/10 - 9*t**5/20 - t**4/4 + 3*t**3/2 + 3*t. Factor v(l).
3*l*(l - 3)*(l - 1)*(l + 1)
Let k(g) be the second derivative of g**8/2240 - g**7/420 + g**6/240 - g**4/12 + 6*g. Let m(i) be the third derivative of k(i). Factor m(r).
3*r*(r - 1)**2
Let g(b) be the second derivative of -b**4/6 + b**3 - 2*b**2 + b. Solve g(l) = 0 for l.
1, 2
Let m(y) be the second derivative of -y**7/42 + y**6/10 - y**5/10 - y**4/6 + y**3/2 - y**2/2 + 10*y. Factor m(z).
-(z - 1)**4*(z + 1)
Let y be 2/4 - (-62)/(-4). Let q = -11 - y. Factor 13*v**2 + 0*v**3 - 5*v**3 - q*v + 0 - 4.
-(v - 2)*(v - 1)*(5*v + 2)
Suppose -3*g + 2*t = -7*g + 18, 2*t = g + 8. Let b(c) be the third derivative of 0 - 1/30*c**5 + g*c**2 + 1/4*c**4 + 0*c - 2/3*c**3. Factor b(m).
-2*(m - 2)*(m - 1)
Let k(x) = -x - 1. Let g be k(-7). Let b = 4 - 1. Factor 2*s**2 - 1 - b + 0 + g*s + 8.
2*(s + 1)*(s + 2)
Let y(m) = -5*m**5 - 5*m**4 - m**3 + 5*m**2. Let p(d) = 5*d**5 + 5*d**4 + 2*d**3 - 5*d**2. Let i(n) = -6*p(n) - 7*y(n). Factor i(w).
5*w**2*(w - 1)*(w + 1)**2
Suppose 5*i + 9 = -4*l + l, -3*l + 3*i = -15. Determine s so that 0*s**l - 2/5*s**3 + 0*s**4 + 0*s + 2/5*s**5 + 0 = 0.
-1, 0, 1
Let h = 76 + -39. Let 12*t - h*t**3 + 22*t**3 - 42*t**2 + 80*t**4 + 4 - 2*t - 37*t**3 = 0. What is t?
-1/2, -1/4, 2/5, 1
Let z = -1295/12 + 108. Let n(k) be the first derivative of 0*k + 0*k**5 - z*k**4 - 1 + 0*k**3 + 0*k**2 + 1/18*k**6. Factor n(j).
j**3*(j - 1)*(j + 1)/3
Let f = -39 + 41. Determine b so that 8/5 - 16/5*b + f*b**2 - 2/5*b**3 = 0.
1, 2
Let f(b) be the first derivative of b**7/1680 - b**6/360 + b**5/240 - 2*b**3/3 + 3. Let z(d) be the third derivative of f(d). Find p, given that z(p) = 0.
0, 1
Factor 1/2*w**4 - 1/2*w**3 + 0 + 0*w + 0*w**2.
w**3*(w - 1)/2
Suppose 15 = 5*z - 10*z + 5*f, 5*z + f = 3. Let q(r) be the third derivative of -2*r**2 + 1/156*r**4 + z*r**3 + 1/390*r**5 + 0 + 0*r. Find p such that q(p) = 0.
-1, 0
Let w(a) be the third derivative of a**5/60 - a**4/24 - a**3/3 + 15*a**2. Suppose w(n) = 0. Calculate n.
-1, 2
Solve 4/3*m**4 + 0*m**2 + 0*m + 0 + 2/3*m**5 + 2/3*m**3 = 0.
-1, 0
Let l be (4/(-22))/(-2)*-1. Let f = l + 15/44. Factor -f*p + 1/4*p**3 - 3/4*p**2 + 1/4*p**4 + 1/2.
(p - 1)**2*(p + 1)*(p + 2)/4
Let u(i) be the second derivative of 3*i**5/5 - 5*i**4/6 - i**3/3 + i - 24. Factor u(f).
2*f*(f - 1)*(6*f + 1)
Suppose -t = 3*t - 8. Factor -2*f + f + t + 3*f - 2*f**3 - 2*f**2 + 0*f.
-2*(f - 1)*(f + 1)**2
Find f, given that 10*f - 4*f - 48*f**3 + 45*f**3 - 3*f**2 = 0.
-2, 0, 1
Let l(m) be the first derivative of m**6/105 - m**4/42 - 4*m - 2. Let a(g) be the first derivative of l(g). Determine u so that a(u) = 0.
-1, 0, 1
Let a(h) be the second derivative of -h**4/12 + 4*h**3/3 - 8*h**2 + 6*h. Let a(m) = 0. What is m?
4
Let j(g) be the third derivative of -g**7/210 - g**6/120 + g**5/20 + g**4/24 - g**3/3 - 5*g**2. Factor j(v).
-(v - 1)**2*(v + 1)*(v + 2)
Let m(n) be the third derivative of -n**8/112 + 6*n**7/35 - 6*n**6/5 + 16*n**5/5 + 20*n**2. What is k in m(k) = 0?
0, 4
Let w(n) = n**3. Let h(z) = 5*z**3 + 5*z**2 + z. Let t(c) = h(c) - w(c). Solve t(f) = 0.
-1, -1/4, 0
Let k = 7/16 - -1/16. Determine t, given that 0*t - 1/4*t**2 + k*t**3 - 1/4*t**4 + 0 = 0.
0, 1
Suppose -17 = -2*g + g + 3*q, 0 = -q - 4. Let d(c) be the third derivative of 0*c - 1/36*c**4 - c**2 + 0 + 0*c**3 + 1/90*c**g. Factor d(v).
2*v*(v - 1)/3
Factor -22*j**4 + 18*j**3 + 30*j - 9 + 41*j**4 - 22*j**4 - 36*j**2.
-3*(j - 3)*(j - 1)**3
Suppose 2*m + 2*m = 0. Factor -5*h**3 + 0*h + 6*h**2 + 2*h**3 - 3*h + m*h**3.
-3*h*(h - 1)**2
Let t be (-4 + -2)*(-2)/4. Find k, given that -8*k + 2*k + t*k + k**2 + 2*k = 0.
0, 1
Let v(t) be the second derivative of 2*t + 1/70*t**5 + 1/105*t**6 + 0*t**3 + 0*t**2 + 0 + 0*t**4. Let v(k) = 0. What is k?
-1, 0
Let j(a) be the first derivative of a**6/1620 - a**5/540 - a**4/54 - 4*a**3/3 - 1. Let v(t) be the third derivative of j(t). Factor v(d).
2*(d - 2)*(d + 1)/9
Let r(l) be the second derivative of -l**7/210 + l**5/50 - l**3/30 - 14*l. Find c such that r(c) = 0.
-1, 0, 1
Let s = -406 + 2031/5. Solve -1/5*r**5 + 2/5*r + 0 + s*r**4 - r**2 + 3/5*r**3 = 0.
-2, 0, 1
Let q(f) be the first derivative of -2*f**5/5 - f**4/6 + 4*f**3/9 - 8. Let q(k) = 0. What is k?
-1, 0, 2/3
Let j = -30 - -8. Let h be (-48)/j - (-30)/(-165). Find t such that -1/3 - t - 1/3*t**3 - t**h = 0.
-1
Let l(h) be the second derivative of 5/12*h**3 - 1/12*h**4 - 1/5*h**5 + 0 - 2*h - 1/4*h**2. What is f in l(f) = 0?
-1, 1/4, 1/2
Let u = -156 + 627/4. Let i(w) be the first derivative of w + 2 + 1/6*w**3 + u*w**2. Factor i(y).
(y + 1)*(y + 2)/2
Let y = 1648/2463 + -2/821. Solve 2/3*f**2 + y + 4/3*f = 0.
-1
Let a(y) be the second derivative of -y**5/10 - y**4 - 3*y**3 - 4*y**2 - 2*y. Factor a(d).
-2*(d + 1)**2*(d + 4)
Let c(p) be the third derivative of -3*p**5/20 - p**4/6 + p**3/2 + 5*p**2. Let g(w) = -w**2 + 1. Let u(j) = -c(j) + 3*g(j). Factor u(r).
2*r*(3*r + 2)
Let 2*v**2 + 2 - 2 - 9 - 1 + 8*v = 0. What is v?
-5, 1
Let c(d) be the second derivative of d**7/14 + d**6/10 - 3*d**5/10 - d**4/2 + d**3/2 + 3*d**2/2 + 9*d. Factor c(x).
3*(x - 1)**2*(x + 1)**3
Find j, given that -j + 36*j**3 - 5*j**4 - 30*j**3 + 3*j**4 - 7*j = 0.
-1, 0, 2
Let k(r) be the second derivative of r**4/4 + r**3/3 + r**2/2 - r. Let p be k(-1). Factor -3*o**3 - 2*o**3 + 0*o**2 + 2*o**4 + o**3 + 2*o**p.
2*o**2*(o - 1)**2
Let r(i) be the third derivative of i**6/180 - i**4/9 + 2*i**2. Factor r(l).
2*l*(l - 2)*(l + 2)/3
Let q(c) = 15*c - 7 - c - 6*c - c**2. Let b be q(7). Factor -1/2*w + b - 9/4*w**2 - 7/4*w**3.
-w*(w + 1)*(7*w + 2)/4
Let a(g) be the third derivative of -g**7/5040 - g**6/720 + g**4/36 + 4*g**3/3 - g**2. Let s(n) be the first derivative of a(n). Solve s(c) = 0.
-2, 1
Suppose -5*u - 3*o = -7*u + 12, u - 5*o - 20 = 0. Let c = u + 3. Factor -2*r**c + 4*r**3 + 4*r**4 - 6