-3*a + 8. Factor 0 + t*b - 1/2*b**a + 9/4*b**3.
b**2*(9*b - 2)/4
Let a(o) = -2*o**2 + 8*o + 14. Let s(q) = -q - 1. Let z(u) = -2*a(u) - 28*s(u). Find l, given that z(l) = 0.
-3, 0
Suppose -6*g = -22*g. Let r(a) be the second derivative of 0*a**2 - 1/48*a**4 + 1/80*a**5 + 4*a + 0*a**3 + g. Factor r(n).
n**2*(n - 1)/4
Let m(i) be the first derivative of i**8/7560 - i**7/3780 - i**6/540 + i**5/108 - i**4/54 + i**3/3 - 4. Let k(p) be the third derivative of m(p). Factor k(j).
2*(j - 1)**3*(j + 2)/9
Let i(l) be the second derivative of 4*l - 1/4*l**3 + 0 - 1/2*l**2 - 1/24*l**4. Factor i(d).
-(d + 1)*(d + 2)/2
Determine x so that -3/4*x**2 + 1/4*x**3 + 3/4 - 1/4*x = 0.
-1, 1, 3
Let f(q) be the first derivative of 0*q**3 + 0*q**2 - q - 3 + 0*q**4 - 2/15*q**6 + 1/10*q**5 + 1/21*q**7. Let l(k) be the first derivative of f(k). Factor l(v).
2*v**3*(v - 1)**2
Let q(z) be the second derivative of -z**5/20 - z**4/12 + z**3/6 + z**2/2 + 6*z. Find n, given that q(n) = 0.
-1, 1
Let q(h) be the first derivative of h**9/15120 - h**7/1400 - h**6/900 + 8*h**3/3 + 2. Let d(s) be the third derivative of q(s). Factor d(t).
t**2*(t - 2)*(t + 1)**2/5
Suppose -2 = 2*i - 0. Let k(z) be the third derivative of z**6/120 + z**4/24 + z**3/6 + 2*z**2. Let d(h) = -h**4 + h + 1. Let f(a) = i*k(a) + d(a). Factor f(b).
-b**3*(b + 1)
Let g = -1627/4 + 408. Solve -1/4*v**4 + 3/4*v - 7/4*v**2 + 0 + g*v**3 = 0.
0, 1, 3
Suppose -4*y - 708 = -4*n, 3*y - 2*n + 571 = -7*n. Let s = 1276/7 + y. Factor -4/7 - 6/7*d - s*d**2.
-2*(d + 1)*(d + 2)/7
Let i = 23/60 - 2/15. What is y in -i*y**4 - 1/4*y**5 + 0*y + 0 + 1/4*y**2 + 1/4*y**3 = 0?
-1, 0, 1
Suppose -2*r = 4*r. Let q be (3/(-2) + 2)*r. Factor 4/3*w**3 + 0 - 2/3*w + 0*w**2 - 2/3*w**5 + q*w**4.
-2*w*(w - 1)**2*(w + 1)**2/3
Let 2/9*o**2 + 0 - 4/9*o = 0. What is o?
0, 2
Let z(f) be the second derivative of -f**6/40 - f**5/30 + f**4/8 + f**3/3 + 2*f**2 - 2*f. Let y(v) be the first derivative of z(v). What is j in y(j) = 0?
-1, -2/3, 1
Let w(x) be the third derivative of -1/54*x**5 + 0*x**3 + 0*x + 0 + 1/54*x**4 - 2*x**2. Find v, given that w(v) = 0.
0, 2/5
Factor 1/3*l + 1/3*l**3 + 0 + 2/3*l**2.
l*(l + 1)**2/3
Let j(h) = -4*h**3 - 4*h**2 - 6*h - 7. Suppose 0 = 4*s - 6*s - 4. Let k(a) = a**2 + a + 1. Let l(o) = s*j(o) - 14*k(o). Determine m, given that l(m) = 0.
-1/4, 0, 1
Let b(p) = -2*p**4 + 20*p**3 - 30*p**2 + 14*p + 2. Let o(r) = r**4 - 20*r**3 + 29*r**2 - 13*r - 3. Let g(c) = 3*b(c) + 2*o(c). Factor g(m).
-4*m*(m - 2)**2*(m - 1)
Let w(u) = u**2 - u. Suppose 0*o = 2*o + 4*c + 2, 2*c - 17 = 5*o. Let n(z) = 3*z**4 + 8*z**3 + 12*z**2 - 3*z. Let g(t) = o*n(t) + 15*w(t). Factor g(i).
-3*i*(i + 1)**2*(3*i + 2)
Let f = 3 - 0. Let t be 0/(0 + (0 - 2)). Factor 7/2*d**2 + 3/2*d**4 - 4*d**f - d + t.
d*(d - 1)**2*(3*d - 2)/2
Let o = 13 + -47/5. Let 16/5*p - 2/5 + 48/5*p**3 - o*p**4 - 44/5*p**2 = 0. What is p?
1/3, 1
Let o(i) be the first derivative of -1/20*i**4 - 1/5*i - 1/5*i**3 - 2 - 3/10*i**2. Factor o(k).
-(k + 1)**3/5
Solve 2*d**2 - 2*d**2 + 3*d**4 - 2*d**5 - 6*d**3 + 5*d**5 = 0.
-2, 0, 1
Let a(q) = q**2 - 5*q + 5. Let w be a(5). Let z = 7 - 5. Factor w*v**2 + 2*v**4 + 6*v**z - 5*v**2 - v**3 - 2*v - 5*v**3.
2*v*(v - 1)**3
Let t(w) = -w**3 + w - 1. Let d(r) = -r**4 - 5*r**2 + 1. Let o(g) = d(g) - 5*t(g). Suppose o(i) = 0. Calculate i.
-1, 1, 2, 3
Suppose 5 = -5*w, -w - 14 = -3*d - 1. Factor v**5 - 9*v**4 - 3 + 13*v**d + 3 + 4*v**3.
v**3*(v + 2)**2
Suppose 3*l = -0*t - 4*t + 20, t - 2 = 0. Factor -c + c**3 + c**2 - c**l + 8 - 8.
-c*(c - 1)**2*(c + 1)
Factor -1/3*k - 1/6 - 1/6*k**2.
-(k + 1)**2/6
Let x(h) = 9*h**4 - 4*h**3 - 44*h**2 - 4*h + 76. Let v(d) = -8*d**4 + 3*d**3 + 43*d**2 + 3*d - 77. Let c(i) = -4*v(i) - 3*x(i). Solve c(l) = 0.
-2, 2
Let z(i) be the first derivative of -2*i + 1/3*i**3 + 3 - 1/2*i**2. Let u(j) = -2*j**2 + 2*j + 4. Let p(l) = 6*u(l) + 14*z(l). Factor p(a).
2*(a - 2)*(a + 1)
Let c(u) be the second derivative of 3/10*u**5 + 0*u**2 + 3/10*u**6 + 0 + 0*u**4 + 0*u**3 + 5*u + 1/14*u**7. What is a in c(a) = 0?
-2, -1, 0
Let f be (-3)/2 + 9/6. Let m(c) be the second derivative of 1/70*c**5 - 2/105*c**6 + c - 1/49*c**7 + f*c**4 + 0*c**2 + 0*c**3 + 0. Solve m(o) = 0.
-1, 0, 1/3
Let r(i) be the third derivative of -i**8/3360 + i**7/560 - i**6/240 + i**5/240 - i**3/3 - 2*i**2. Let q(f) be the first derivative of r(f). Solve q(y) = 0.
0, 1
Let c(l) = -l**5 - 3*l**4 + 3*l**3 - 2*l**2 - 3. Let d(p) = -2*p**5 - 2*p**4 + 2*p**3 - 2*p**2 - 4. Let b(r) = -4*c(r) + 3*d(r). Factor b(i).
-2*i**2*(i - 1)**3
Let g(f) = -11*f**3 - 29*f**2 - 12*f + 3. Let w(o) = -o**3 + o**2 - 1. Let u(m) = g(m) + 5*w(m). Factor u(d).
-2*(2*d + 1)**3
Let x(o) = -o**3 - o - 1. Let y(f) = 8*f**3 - 20*f**2 + 4*f + 26. Let a(l) = -6*x(l) - y(l). Find p such that a(p) = 0.
-1, 1, 10
Find w such that 0*w**3 + 7*w**2 - 4*w**2 - 4*w**2 + w**3 = 0.
0, 1
Let j(f) = -f**3 + 5*f**2 + 1. Let p be j(5). Let h(o) = -303*o**3 - 174*o**2 + 48*o + 36. Let q(z) = z**3 - z + 1. Let k(y) = p*h(y) - 12*q(y). Solve k(c) = 0.
-2/3, -2/7, 2/5
Let z = 5/19 + -1/76. Determine a so that 1/4*a**3 + 3/4*a**2 - 1/2 - 1/4*a - z*a**4 = 0.
-1, 1, 2
Let f(h) be the third derivative of -h**5/20 + h**4/8 - 53*h**2. Factor f(a).
-3*a*(a - 1)
Find x, given that -2/3*x**2 + 2/3*x - 2/3*x**3 + 2/3 = 0.
-1, 1
Suppose -66 = 4*s + 2*q, 16 = -2*s + 5*q - 23. Let j = s - -89/5. Factor 4/5*d - 6/5*d**2 - 1/5 + j*d**3 - 1/5*d**4.
-(d - 1)**4/5
Let o(t) = -22*t**2 + 70*t - 100. Let s(j) = -9*j**2 + 28*j - 40. Let g(c) = -5*o(c) + 12*s(c). Solve g(w) = 0.
2, 5
Factor 12/7*x + 8/7 + 4/7*x**2.
4*(x + 1)*(x + 2)/7
Let z(w) be the first derivative of -w**5/5 - 9*w**4/28 - 2*w**3/21 - 7. Factor z(i).
-i**2*(i + 1)*(7*i + 2)/7
Let g be 255/70*2 + 3/(-2). Let w(j) be the first derivative of -40/7*j**2 - 78/7*j**3 - 3 - g*j**4 - 8/7*j. Factor w(b).
-2*(b + 1)*(9*b + 2)**2/7
Suppose 7*a - 2*a - 10 = 0. Suppose -7*f - 40 = -5*t - a*f, -3*f = 2*t + 9. Determine x, given that 2/3*x**t + 0 + 0*x + 2/3*x**2 - 2/3*x**4 - 2/3*x**5 = 0.
-1, 0, 1
Let t(g) be the third derivative of g**9/3024 - g**7/420 + g**5/120 + 2*g**3/3 + 4*g**2. Let u(k) be the first derivative of t(k). Solve u(h) = 0.
-1, 0, 1
Let v be (-1)/4 - (-34)/8. Suppose -5*k - l - l + 15 = 0, v*l = 0. Factor -c + c**2 - 1 + k + 0 - 2*c**2.
-(c - 1)*(c + 2)
Let i(r) = -2*r**2 + 2*r + 2. Let l(a) = -2. Let y(w) = -2*i(w) + 10*l(w). Factor y(t).
4*(t - 3)*(t + 2)
Factor -479*z**2 + z**4 - 4*z**4 + 491*z**2.
-3*z**2*(z - 2)*(z + 2)
Suppose -p + 5*p = 24. Let x(u) = -9*u**2 - 9*u + 11. Let l(y) = -5*y**2 - 5*y + 6. Let h(d) = p*x(d) - 11*l(d). Solve h(w) = 0.
-1, 0
Suppose 2*q = -4*x + 6*q - 20, 4*x - 3*q = -16. Let z be x/(-1)*0/(-1). Factor -2/5*y + z + 2/5*y**2.
2*y*(y - 1)/5
Let d be -5 - (88/(-15) + (-10)/(-15)). Factor -3/5*c**5 - c**4 + d*c**2 - 1/5*c**3 + 0*c + 0.
-c**2*(c + 1)**2*(3*c - 1)/5
Suppose 18*l + 6*l = 96. Let u be ((-1)/9)/(1/(-3)). Factor o**2 + u*o**l - o**3 - 1/3*o + 0.
o*(o - 1)**3/3
Let w be (-32)/112 + (-32)/(-14). Factor -2*j - w*j**2 - 2*j + 2*j.
-2*j*(j + 1)
Let s(h) be the second derivative of h**7/147 - h**6/105 - h**5/70 + h**4/42 - 4*h. Factor s(t).
2*t**2*(t - 1)**2*(t + 1)/7
Let c(v) be the second derivative of v**6/120 - v**5/20 + 5*v**4/48 - v**3/12 - 3*v. Factor c(l).
l*(l - 2)*(l - 1)**2/4
Let n(g) be the second derivative of -1/21*g**7 - 2/3*g**3 + 0 - 1/15*g**6 + 3*g + 0*g**2 + 1/6*g**4 + 3/10*g**5. Suppose n(l) = 0. Calculate l.
-2, -1, 0, 1
Solve 4/3 - 14/3*k + 4*k**2 - 4/3*k**4 + 2/3*k**3 = 0 for k.
-2, 1/2, 1
Let b(p) be the second derivative of -p**4/6 + p**3/3 + p. Factor b(v).
-2*v*(v - 1)
Let l be 24/66 - -3 - (0 - -3). Factor 2/11*k**4 + 0 + l*k**3 + 2/11*k**2 + 0*k.
2*k**2*(k + 1)**2/11
Let s(p) be the third derivative of 0*p + 0 - p**2 - 7/72*p**4 - 1/90*p**5 - 1/9*p**3 + 1/120*p**6. Factor s(k).
(k - 2)*(k + 1)*(3*k + 1)/3
Let b(y) = -4*y + 2*y**3 - 11 - y**3 - 10*y**2 + 0*y**3 - 6*y. Let z be b(11). Factor -2/5*d + 4/5*d**3 + 0 + 0*d**4 + z*d**2 - 2/5*d**5.
-2*d*(d - 1)**2*(d + 1)**2/5
Factor 6*y**3 + 6*y**4 + 3/2*y**5 - 15/2*y - 3 - 3*y**2.
3*(y - 1)*(y + 1)**3*(y + 2)/2
Let b be 3/36*-34 - -3. Let n(o) be the first derivative of b*o**3 + 2 + 1/2*o + 1/2*o**2. Solve n(y) = 0.
-1
Factor -18/5*i**3 + 0 - 9/5*i + 24/5*