d) = -3*m(d) - 7*p(d). Solve l(b) = 0 for b.
-1, 0, 2/9
Solve -1/2*z**4 + 0 + 1/4*z**3 + 1/2*z**2 - 1/4*z = 0.
-1, 0, 1/2, 1
Let x = -148/3 - -50. Let i(m) = -m - 3. Let h be i(-3). Determine g, given that h*g**2 + 0 + 2/3*g**3 - x*g = 0.
-1, 0, 1
Let i(o) be the second derivative of o**7/189 - o**6/45 + o**5/90 + o**4/18 - 2*o**3/27 - 3*o. Find f, given that i(f) = 0.
-1, 0, 1, 2
Suppose -a - 1 = -5. Let z(v) be the second derivative of 1/15*v**3 - 1/30*v**a + 0 - 1/50*v**5 + 2*v + 1/5*v**2. Factor z(d).
-2*(d - 1)*(d + 1)**2/5
Let m(f) be the third derivative of f**7/2940 - f**6/1260 - f**5/210 - f**3/6 + 2*f**2. Let j(b) be the first derivative of m(b). What is p in j(p) = 0?
-1, 0, 2
Let p = 15874/11 + -1442. Factor -2/11*d**4 - 8/11 - 24/11*d - p*d**3 - 26/11*d**2.
-2*(d + 1)**2*(d + 2)**2/11
Let a(f) be the second derivative of f**5/40 + 11*f**4/24 + 19*f**3/12 + 9*f**2/4 - 18*f. Factor a(n).
(n + 1)**2*(n + 9)/2
Let k(u) = -8*u**2 - 2*u + 6. Let q = -7 - -8. Let v(j) = 2*j**2 - 3*j - q + j**2 - 1 + 4*j. Let a(i) = 4*k(i) + 11*v(i). Factor a(o).
(o + 1)*(o + 2)
Suppose 2*f + 0*f - 4 = 4*c, -5*f = -5*c - 10. Suppose -2*q = -q - f. Find z, given that 0*z**2 - 2*z**3 + 2*z**2 - q*z**4 + 2*z**5 - z**2 + z**2 = 0.
-1, 0, 1
Let l(n) be the second derivative of -n**4/12 - 2*n**3/3 - 2*n. Let k be l(-4). Factor k - 2*u**2 - 4/9*u.
-2*u*(9*u + 2)/9
Let m(n) = -9*n**5 - 3*n**4 + 16*n**3 + 21*n**2 - 20*n + 8. Let w(d) = 4*d**5 + 2*d**4 - 8*d**3 - 10*d**2 + 10*d - 4. Let l(x) = -6*m(x) - 13*w(x). Factor l(b).
2*(b - 2)*(b - 1)**3*(b + 1)
Let q(s) be the first derivative of -1 - 2/5*s**2 + 1/10*s**4 + 0*s - 2/15*s**3. Factor q(z).
2*z*(z - 2)*(z + 1)/5
Let b(q) = -7*q**3 - 5*q**2 + 6*q + 9. Let m(h) = 4*h**3 + 3*h**2 - 3*h - 5. Let f(j) = 3*b(j) + 5*m(j). Let f(y) = 0. Calculate y.
-1, 2
Let i(s) = s**2 - 6*s - 4. Let t be i(7). Suppose t*z + 15 = 8*z. Solve 11*f**4 + 18*f**2 - 12*f**2 + 3*f**5 + f**z + 14*f**3 + f**4 = 0.
-2, -1, 0
Let c(f) be the second derivative of -f**4/54 - 2*f**3/9 - f**2 - 2*f. Solve c(q) = 0.
-3
Suppose -2*f = 4, 0*z + f = -z - 2. Factor -3/2*j**4 - 1/2*j**2 + 0*j + 3/2*j**3 + 1/2*j**5 + z.
j**2*(j - 1)**3/2
Let t(m) be the first derivative of -2/9*m**3 + 8/9*m - 4/9*m**2 + 1/9*m**4 + 3 + 2/45*m**5. Factor t(a).
2*(a - 1)**2*(a + 2)**2/9
Let o(j) be the second derivative of -j**5/100 + j**4/15 - j**3/10 + 14*j. Factor o(p).
-p*(p - 3)*(p - 1)/5
Let m(i) be the second derivative of i + 0 + 0*i**3 + 1/270*i**5 - 1/108*i**4 + 3/2*i**2. Let d(f) be the first derivative of m(f). Factor d(q).
2*q*(q - 1)/9
Let m(v) be the second derivative of 0 + 1/12*v**4 + 2/3*v**3 - v + 3/2*v**2. Suppose m(y) = 0. Calculate y.
-3, -1
Let y(j) be the first derivative of -5*j**4/2 - j**3/3 - j**2 - j - 4. Let c be y(-1). Factor d**2 - 10 + c + 2*d.
d*(d + 2)
Let b(n) be the third derivative of n**8/1008 + n**7/140 + n**6/60 + n**5/90 + 6*n**2. Suppose b(g) = 0. What is g?
-2, -1/2, 0
Let k(f) be the second derivative of 1/40*f**6 + 0 - 3/80*f**5 + 0*f**3 + 0*f**2 - 1/16*f**4 + f + 1/56*f**7. Suppose k(q) = 0. Calculate q.
-1, 0, 1
Suppose 10 = 4*d - 2*t, 6*d - 2*t = 5*d + 4. Factor -2/3 - 2/3*v**d - 4/3*v.
-2*(v + 1)**2/3
Let l(k) = k**5 - k**4 - k**2 + 1. Let b(n) = -7*n**5 - 6*n**4 + 2*n**3 + 12*n**2 + 2*n - 3. Let h(a) = -b(a) - 3*l(a). Determine m so that h(m) = 0.
-2, -1, -1/4, 0, 1
Let q(y) be the first derivative of -2*y**5/5 - 7*y**4/2 - 10*y**3 - 9*y**2 + 47. Factor q(s).
-2*s*(s + 1)*(s + 3)**2
Factor -24/7*s**4 - 8/7*s**2 + 32/7 + 4/7*s**5 - 48/7*s + 44/7*s**3.
4*(s - 2)**3*(s - 1)*(s + 1)/7
Let p(j) be the first derivative of -5*j**3/3 + 35*j**2 - 245*j - 64. Find u, given that p(u) = 0.
7
Determine v so that -8/3*v + 2/3*v**4 + 0*v**2 + 2*v**3 + 0 = 0.
-2, 0, 1
Let x = 91/3 + -30. Let c(o) be the first derivative of 2/27*o**3 + x*o**2 + 2 + 4/9*o. Suppose c(t) = 0. What is t?
-2, -1
Let m(p) be the third derivative of -5*p**8/336 + p**7/21 - p**6/24 - 22*p**2. Factor m(k).
-5*k**3*(k - 1)**2
Factor 2/5*s**2 + 0*s - 2/5.
2*(s - 1)*(s + 1)/5
Let j(v) = -v**3 - v**2 + v - 2. Let k be j(-2). Determine f, given that -1/4*f**2 + 0*f + 1/4*f**3 + k = 0.
0, 1
Let b(i) be the third derivative of i**6/720 - i**5/180 - i**4/144 + i**3/18 - 11*i**2. Factor b(y).
(y - 2)*(y - 1)*(y + 1)/6
Let m(n) be the first derivative of -n**6/3 - 2*n**5/5 + n**4 + 4*n**3/3 - n**2 - 2*n - 48. Factor m(r).
-2*(r - 1)**2*(r + 1)**3
Let l(m) = m - 7. Suppose -4*q = -2*k - 36, 2 - 11 = -q - k. Let s be l(q). Find y such that -y**4 - 4*y**4 - 2 + 4*y**s + 3*y**4 = 0.
-1, 1
Let m = 74 - 74. Let u(p) be the second derivative of -1/24*p**3 + m + 0*p**2 - 1/48*p**4 + 2*p. Solve u(g) = 0 for g.
-1, 0
Let p(z) be the first derivative of z**6/480 - z**5/240 - z**4/96 + z**3/3 - 3. Let c(l) be the third derivative of p(l). Factor c(w).
(w - 1)*(3*w + 1)/4
Let u(y) = y**3 - 23*y**2 + 43*y - 29. Let o(x) = -4*x**3 + 116*x**2 - 214*x + 146. Let q(w) = 2*o(w) + 11*u(w). Factor q(l).
3*(l - 3)**2*(l - 1)
Let z(o) be the first derivative of 3*o**4/4 + 4*o**3 - 33*o**2/2 + 18*o + 14. Factor z(j).
3*(j - 1)**2*(j + 6)
Let k be 34/42 - (-5)/15. Let n be (24/140)/3*20. Determine r so that 2/7*r**2 - k*r + n = 0.
2
Let t(p) = 1. Let w(n) = n**5 - 2*n**4 + n**3 - 3. Let s(i) = 3*t(i) + w(i). Solve s(a) = 0.
0, 1
Suppose 0 = 5*m + 25, 4*m + 14 = 3*h - 12. Let s be 0/2 + 0 + 4. Solve s*t**3 - h*t**2 + t + 0*t - 3*t**3 = 0 for t.
0, 1
Factor -1/2*r**3 + 1/6*r**4 + 1/6*r**2 + 1/2*r - 1/3.
(r - 2)*(r - 1)**2*(r + 1)/6
Let t(w) be the first derivative of 3 + 1/10*w**4 + 0*w - 2/25*w**5 + 0*w**2 + 4/15*w**3. Suppose t(c) = 0. Calculate c.
-1, 0, 2
Factor 0*y**2 + 5*y - 7*y**3 + 4*y**2 + 2 - 5*y**3 + 13*y**3.
(y + 1)**2*(y + 2)
Suppose 0*d + d = 2. Suppose d*f + f = 0. Factor 0 + f*r - 2/3*r**3 - 2/3*r**2.
-2*r**2*(r + 1)/3
Let o be ((-72)/(-28))/((-2)/(-14)). Find p, given that 3*p - 3*p**3 - 38 + 23 + o - 3*p**2 = 0.
-1, 1
Let v be (28/49)/((36/70)/3). Factor -1/3*l - 8/3*l**3 + 1/3 - v*l**2.
-(l + 1)*(2*l + 1)*(4*l - 1)/3
Let j(s) be the second derivative of 6*s + 0*s**3 + 1/2*s**2 + 0 - 1/12*s**4. Determine n, given that j(n) = 0.
-1, 1
Let f(o) be the first derivative of 3*o**4/8 - 3*o**3/2 + 3*o**2/2 + 14. Find k, given that f(k) = 0.
0, 1, 2
Let w(s) = -s**3 + 10*s**2 - 7*s - 13. Let t be w(9). Suppose -5*n + g = -2*n - 1, -t*g + 21 = -2*n. Factor -i + 10*i**n + 4*i**3 + 4*i**2 - 3*i - 14*i**4.
-2*i*(i - 1)*(i + 1)*(7*i - 2)
Let g(k) be the third derivative of -1/72*k**4 + 0*k**3 + 0 + 1/180*k**5 + 0*k - k**2. Factor g(m).
m*(m - 1)/3
Suppose 1 - 1 - 3*s**4 - 1537*s**3 + 1546*s**3 - 6*s**2 = 0. Calculate s.
0, 1, 2
Let k(p) be the first derivative of -p**3/3 + 9*p**2/2 + 12*p + 3. Let w be k(10). Solve 2*y - 11*y**2 + 0*y + w + 4*y + 3*y**2 = 0.
-1/4, 1
Factor 0 - 2/3*l - 2/3*l**2.
-2*l*(l + 1)/3
Let w(n) be the first derivative of -n**2 - n + 1. Let q be w(-6). Factor t**2 - 10*t**3 + q*t**3 - 1 + 3*t - 4*t**2.
(t - 1)**3
Let w = -9 + 12. Factor -w*a**3 + 3 - 3*a**2 - a + 0 + 6*a - 2*a.
-3*(a - 1)*(a + 1)**2
Let d be (-24)/48*(1 - (-1)/(-1)). Factor 0 - 2/7*u**2 + d*u + 2/7*u**3.
2*u**2*(u - 1)/7
Let m be 30/105 - 2/7. Let h(b) be the second derivative of -5/6*b**3 + b**2 + m + b - 1/20*b**5 + 1/3*b**4. Factor h(w).
-(w - 2)*(w - 1)**2
Suppose -2*g = -2*x + 7*x - 21, x + g = 6. Let n be x - 40/15 - 0. Determine c so that 0*c + 2/3*c**4 + n*c**3 + 0 - 1/3*c**5 - 2/3*c**2 = 0.
-1, 0, 1, 2
Factor -1/3*j**4 - 2/3*j + 1/3*j**2 + 0 + 2/3*j**3.
-j*(j - 2)*(j - 1)*(j + 1)/3
Let v(g) be the second derivative of g**7/42 + 11*g**6/90 + g**5/4 + g**4/4 + g**3/9 - 9*g. Let v(m) = 0. What is m?
-1, -2/3, 0
Let c(i) be the third derivative of -1/78*i**4 + 0*i - 3*i**2 - 1/390*i**5 + 0 + 0*i**3. Factor c(t).
-2*t*(t + 2)/13
Factor -2*k**2 + 8/3*k - 2/3*k**3 + 0.
-2*k*(k - 1)*(k + 4)/3
Let q(x) = x + 9*x**3 - 3*x**2 - 2*x - 8*x**3 - x**5 + 2*x**2. Let n(u) = u**5 - 16*u**4 + 13*u**3 - 5*u**2 - 5*u. Let t(j) = n(j) - 5*q(j). Factor t(d).
2*d**3*(d - 2)*(3*d - 2)
Let l be 28/(-7) + (2*2 - 0). Solve l - 1/2*r**3 + 1/2*r - 1/2*r**2 + 1/2*r**4 = 0.
-1, 0, 1
Suppose 4*g + 14 = -6. Let p = -2 - g. Factor -x**p - 3*x**3 - x**4 - x**2 - 3*x**3 + 5*x**3.
-x**2*(x + 1)**2
Let u(i) be the first derivative of