0.
-1, 1/2
Let b(p) be the first derivative of p**4/20 + p**3/15 - p**2/2 + 3*p/5 - 4. Let b(x) = 0. What is x?
-3, 1
Suppose -i + 2*j = -12, -23 = -i + 5*j + 1. Let g(f) = -f + 4. Let w be g(i). Solve 1/3*h**2 + w*h + 0 = 0 for h.
0
Let j(i) = -2*i**5 - 5*i**4 - 2*i**3 + 20*i**2 + 5*i - 13. Suppose -5*r - 3 - 12 = 0. Let n(v) = -v**4 + v - 1. Let q(l) = r*n(l) - j(l). Factor q(w).
2*(w - 1)**2*(w + 2)**3
Let u = -817/5 + 164. Factor 1/5*h**2 - u*h + 2/5.
(h - 2)*(h - 1)/5
Let u(t) be the first derivative of 6*t**5/35 + 4*t**4/7 + 4*t**3/7 - 2*t/7 + 3. What is j in u(j) = 0?
-1, 1/3
Let v(k) = -3*k**3 + 2*k**2. Let t(c) be the second derivative of c**5/20 - c**4/12 - 2*c. Let q(g) = -10*t(g) - 4*v(g). Factor q(i).
2*i**2*(i + 1)
Factor 23*o**2 + 9/2*o**4 + 9/2 - 1/2*o**5 - 15*o**3 - 33/2*o.
-(o - 3)**2*(o - 1)**3/2
Suppose 0 = 3*d - 5*n - 7 - 5, 4*d = 2*n + 16. Let t be 11/d + (-9 - -7). Factor -7/4*a**3 - 1/2 - t*a + 3*a**2.
-(a - 1)**2*(7*a + 2)/4
Let h = 30 - 27. Let b(t) be the first derivative of h - 7/15*t**3 - 1/5*t**2 + 0*t - 1/4*t**4. Factor b(r).
-r*(r + 1)*(5*r + 2)/5
Let v(g) be the second derivative of 2*g - 1/6*g**3 - 1/36*g**4 + 0*g**2 + 0. Factor v(y).
-y*(y + 3)/3
Let i(d) = d**3 + 8*d**2 + d + 11. Let m be i(-8). Suppose o**m - 2*o**2 + o**2 - o**4 - o**5 + 2*o**2 = 0. Calculate o.
-1, 0, 1
Let w be (1/(-168))/(4/(-1014)). Let y = -15/16 + w. Factor y - 2/7*k**3 - 10/7*k + 8/7*k**2.
-2*(k - 2)*(k - 1)**2/7
Let l = 7849/12 + -2451/4. Let v = l - 41. Factor -2/3*m + v + 1/3*m**2.
(m - 1)**2/3
Suppose 6 = 2*x - 0. Let o(n) be the second derivative of 0 + 0*n**2 + 0*n**5 - 3*n + 0*n**x + 1/20*n**6 + 0*n**4 + 1/7*n**7. Factor o(u).
3*u**4*(4*u + 1)/2
Find h such that -48*h + 238 + 159*h**4 + 15*h**2 + 20*h**5 + 168*h**3 - 250 + 22*h**5 = 0.
-2, -1, -2/7, 1/2
Let a = -59 - -61. Let h(l) be the third derivative of l**a + 0*l + 1/12*l**4 + 0*l**3 - 2/15*l**5 + 0. Factor h(v).
-2*v*(4*v - 1)
Let u be (-8)/((-8)/12*3). Let n(w) be the third derivative of 0 + 1/21*w**3 - w**2 + 0*w - 1/42*w**u + 1/210*w**5. Let n(f) = 0. What is f?
1
Let u(k) be the second derivative of -k**7/147 + 4*k**6/105 + k**5/35 - 2*k**4/7 - 3*k**3/7 - 17*k. Factor u(h).
-2*h*(h - 3)**2*(h + 1)**2/7
Let z(t) = -t**3 - 2*t**2 + 2*t + 3. Let l be z(-4). Let i be l/6 - (-6)/(-4). Factor 2/5 + 0*n**2 - 4/5*n**i + 4/5*n - 2/5*n**4.
-2*(n - 1)*(n + 1)**3/5
Let l(n) = -3*n**3 + 5*n**2 + n + 2*n**3 + n**2 - 5 - n**2. Let z(y) = y**2 - 1. Let u(i) = -l(i) + 6*z(i). Factor u(k).
(k - 1)*(k + 1)**2
Let z(o) be the third derivative of o**7/210 - o**6/80 - o**5/30 + o**4/16 + o**3/6 - 12*o**2. Find x such that z(x) = 0.
-1, -1/2, 1, 2
Let h(w) be the second derivative of 0*w**5 - 2/3*w**3 + 0*w**2 + 1/15*w**6 - 3*w + 0 - 1/2*w**4. Find q such that h(q) = 0.
-1, 0, 2
Factor -5*k**3 - 111*k**2 + 7*k**3 + 99*k**2 + 10*k.
2*k*(k - 5)*(k - 1)
Factor 5*m**5 + m**3 - 22*m**3 - 10*m**2 + 6*m**3.
5*m**2*(m - 2)*(m + 1)**2
Suppose -4*k = -2*g, 5*g - 3*g + k = 15. Suppose 12 - 10*p + 22*p - 3*p**2 + g*p**2 = 0. Calculate p.
-2
Suppose 0 = -0*b - b + 4. Suppose n + 4*k + 8 = -3*n, -5*n - b*k - 6 = 0. Factor -n*w**2 - 3*w + 3*w - 2*w.
-2*w*(w + 1)
Let x be 26/4 - 6/12. Let r(i) = i**2 + 10*i - 3. Let u(a) = a - 1. Let s(k) = x*u(k) - r(k). Factor s(p).
-(p + 1)*(p + 3)
Let j(r) be the third derivative of -r**8/672 + r**7/105 - r**6/240 - 7*r**5/60 + 5*r**4/12 - 2*r**3/3 + r**2. Find u such that j(u) = 0.
-2, 1, 2
Let t be (-9)/315*-7*(-15)/(-4). Factor t*s**2 + 0 - 3/4*s.
3*s*(s - 1)/4
Let i(w) be the second derivative of w**5/16 + 13*w**4/48 - w**3/4 + 2*w. Factor i(m).
m*(m + 3)*(5*m - 2)/4
Let q be (-3)/(-150)*(-5)/(-6). Let o(k) be the third derivative of 1/72*k**6 + 0*k - 1/36*k**4 - 3*k**2 + 0*k**3 + 0 + q*k**5. Find y, given that o(y) = 0.
-1, 0, 2/5
Let t(l) be the first derivative of 2*l**5/25 + l**4/5 - 2*l**3/5 - 4*l**2/5 + 8*l/5 - 10. Determine u, given that t(u) = 0.
-2, 1
Let -o**5 + 2*o**3 + 112*o**4 - 114*o**4 + 0*o**5 - 3*o**3 = 0. What is o?
-1, 0
Let x(b) = b**4. Let j(h) = 3*h**5 + 13*h**4 + 3*h**3 - 3*h**2 - 2*h. Let s(o) = -j(o) + 6*x(o). Find c such that s(c) = 0.
-1, 0, 2/3
Let m = 21 - 20. Let -49/4*w**2 + 7*w - m = 0. Calculate w.
2/7
Let x be ((-15)/6)/(2/(-4)). Let k = -3 + x. What is q in 6/7*q**k - 2/7*q**3 + 0 - 4/7*q = 0?
0, 1, 2
Factor -2/7*m**4 - 20/7*m**3 - 80/7*m - 66/7*m**2 - 32/7.
-2*(m + 1)**2*(m + 4)**2/7
Suppose 2*y = -m - 0*m + 1, -3*y = 4*m + 11. Factor 6*c**3 - 6*c**3 + 2*c**4 - 4*c**y.
2*c**3*(c - 2)
Factor 1/2*d**2 - 1/2*d**3 - 1/4*d**4 + 1/4*d**5 - 1/4 + 1/4*d.
(d - 1)**3*(d + 1)**2/4
Let r(s) be the first derivative of s**8/5880 + s**7/1470 - s**5/210 - s**4/84 + 4*s**3/3 - 6. Let d(l) be the third derivative of r(l). Factor d(f).
2*(f - 1)*(f + 1)**3/7
Factor -y**2 - 2*y + 1/3*y**3 + 8/3.
(y - 4)*(y - 1)*(y + 2)/3
Let n(m) be the third derivative of m**6/60 + m**5/5 + 11*m**4/12 + 2*m**3 + 3*m**2. Suppose n(a) = 0. Calculate a.
-3, -2, -1
Suppose f - m + 2 = 3*f, 4*m + 16 = 0. Let l = 5 - f. Factor -2*q**4 + 2/3*q**5 + 0*q + 2*q**3 - 2/3*q**l + 0.
2*q**2*(q - 1)**3/3
Let o = -1 - -2. Suppose -3*c + 9 = i + o, 10 = 5*c. Factor -q - 6*q**2 + 5*q**2 + i + 0.
-(q - 1)*(q + 2)
Let w(j) be the second derivative of j**4/4 - 5*j**3/2 + 6*j**2 + 5*j. Factor w(l).
3*(l - 4)*(l - 1)
Let f(b) be the first derivative of -1/12*b**3 + 3/4*b**2 - 9/4*b + 11. Factor f(c).
-(c - 3)**2/4
Let n(l) be the third derivative of 5*l**8/336 - l**6/12 + 5*l**4/24 - 8*l**2. Factor n(s).
5*s*(s - 1)**2*(s + 1)**2
Let z(c) = 36*c**4 + 33*c**3 - c**2 - 4*c + 3. Let x(v) = 36*v**4 + 32*v**3 - 4*v + 4. Let d(o) = -3*x(o) + 4*z(o). Let d(b) = 0. Calculate b.
-1, -1/3, 0, 1/3
Let o be 20/(-6)*(-15)/(-10). Let a = 7 + o. Factor 1/4*c**a - 1/2*c + 0.
c*(c - 2)/4
Suppose -n - 10 = -3*v + n, 3*v + 5*n = -4. Factor -2 + 8*d**2 + 5*d**3 + 8*d - 3*d**3 + 6 + v*d.
2*(d + 1)**2*(d + 2)
Let w(a) be the second derivative of -a**4/72 - a**3/36 + a**2/6 - 12*a. Let w(h) = 0. Calculate h.
-2, 1
Let r = 1 + 3. Factor 5*m**3 - 3*m**2 - 2*m + 3*m**r - 2*m**3 - m.
3*m*(m - 1)*(m + 1)**2
Let k(a) be the first derivative of -a**8/840 - a**7/140 - a**6/60 - a**5/60 + a**3/3 - 2. Let u(h) be the third derivative of k(h). Factor u(g).
-2*g*(g + 1)**3
Let o(g) be the first derivative of 4*g**5/5 + 4*g**4 + 54. Factor o(u).
4*u**3*(u + 4)
Let r(m) be the third derivative of 2*m**7/105 - 2*m**6/15 - m**5/3 + 8*m**2. Factor r(w).
4*w**2*(w - 5)*(w + 1)
Factor -16/3*y + 4/3*y**4 - 16/3*y**3 + 4/3 + 8*y**2.
4*(y - 1)**4/3
Let h(a) = -13*a**2 - 5*a - 4. Let w(z) = -7*z**2 - 3*z - 2. Let s(n) = 6*h(n) - 11*w(n). Factor s(p).
-(p - 2)*(p - 1)
Suppose -4*r + 0*r = -56. Let m be (r/5)/(5/25). Factor 2 - 3 + m*j**3 + 1 + 4*j**2 + 10*j**4.
2*j**2*(j + 1)*(5*j + 2)
Let n be ((-168)/27 - -6)*-3. Factor n*u**2 + 2/3*u + 0.
2*u*(u + 1)/3
Let v(d) be the first derivative of -d**8/504 - d**7/135 - d**6/108 - d**5/270 + 5*d**2/2 + 2. Let p(q) be the second derivative of v(q). Factor p(y).
-2*y**2*(y + 1)**2*(3*y + 1)/9
Let a(p) be the second derivative of 5*p - 3/5*p**6 + 0*p**2 + 5/6*p**4 - 1/3*p**3 - 3/10*p**5 + 0. What is n in a(n) = 0?
-1, 0, 1/3
Let 3/4*t**2 - 15/4 - 3*t = 0. What is t?
-1, 5
Suppose 7 = 2*n + d, 0 = -d - 2 - 3. Let t = -4 + n. Determine x so that 2 + 3*x**5 + 2*x**4 + 0*x - t*x - 4*x**2 + 5*x - 6*x**3 = 0.
-1, -2/3, 1
Let b be 0 - (24/10 - -1). Let c = b - -56/15. Let 1/3*f**4 + f**2 + f**3 + c*f + 0 = 0. Calculate f.
-1, 0
Let o(i) = -13*i**2 - 3*i - 4. Let h be o(-4). Let f be (-2)/3 + h/(-210). Let 0 + f*w**3 + 2/7*w**2 - 2/7*w - 2/7*w**4 = 0. Calculate w.
-1, 0, 1
Let b(o) be the first derivative of 0*o**2 - 1 + 1/3*o**3 - o - 1/6*o**4. Let u(g) be the first derivative of b(g). Factor u(q).
-2*q*(q - 1)
Suppose 4*l + l - 10 = 0. Factor -1 - 2*u + u**2 + l*u.
(u - 1)*(u + 1)
Let z(t) = 7*t**3 - 3*t**2 - 7*t - 2. Let n(s) = -s + 3*s**2 - 1 - 2*s - 4*s**2 + 3*s**3. Let p = 6 - 1. Let b(w) = p*n(w) - 2*z(w). Factor b(j).
(j - 1)*(j + 1)**2
Let v = -68879/120 - -574. Let u(t) be the third derivative of 0*t - v*t**5 + t**2 + 1/24*t**4 + 0 - 1/12*t**3. Let u(b) = 0. Calculate b.
1
Let m = 14 + -10. Suppose -4 = -n - m*n - 2*z, 3*z + 9 = 0. Solve 4/5*f + 0*f**3 - 2/5*f**4 + 0 + 6/5*f**n = 0 fo