
Suppose 15*v = 6 - 6. Let w(u) be the third derivative of 0*u**4 - 2*u**2 + 1/20*u**6 + 0*u + 1/35*u**7 + 0*u**3 + 1/168*u**8 + 1/30*u**5 + v. Factor w(f).
2*f**2*(f + 1)**3
Suppose 2/7*h + 8/7*h**2 + 12/7*h**3 + 8/7*h**4 + 0 + 2/7*h**5 = 0. Calculate h.
-1, 0
Let n(l) be the second derivative of -l**5/20 - l**4/4 + 2*l**2 - 2*l. Let s be n(-3). Suppose 2*g + 2*g**3 - s*g**3 - 2*g**3 + 2*g**5 = 0. What is g?
-1, 0, 1
Let k(v) be the second derivative of -v**5/110 - 5*v**4/66 - 2*v**3/33 + 8*v**2/11 + 5*v. Find p such that k(p) = 0.
-4, -2, 1
Let z be (-14)/(-4)*12/14. What is j in -4*j**2 + 2 + j - 4*j**2 + 0*j + 3*j**2 - j**3 + z*j**4 = 0?
-1, -2/3, 1
Let o(p) be the third derivative of p**6/30 + 7*p**5/15 + 8*p**4/3 + 8*p**3 - 17*p**2. Factor o(m).
4*(m + 2)**2*(m + 3)
Let k(m) = 6*m**3 + 63*m**2 + 32*m. Let i(u) = 3*u**3 + 32*u**2 + 16*u. Let h(z) = 11*i(z) - 6*k(z). Factor h(q).
-q*(q + 8)*(3*q + 2)
Let r(s) be the second derivative of s**4/6 - 4*s**3/3 + 4*s**2 + 4*s. Factor r(j).
2*(j - 2)**2
Let b(g) = g**2 + 8*g + 9. Let p be b(-7). Factor -1/5*j**p - 9/5 - 6/5*j.
-(j + 3)**2/5
Let b(v) be the third derivative of v**9/6048 - v**8/3360 - v**7/1680 + v**6/720 - v**3/6 - 7*v**2. Let i(a) be the first derivative of b(a). Factor i(c).
c**2*(c - 1)**2*(c + 1)/2
Let i(s) = 8*s + 10*s - 9*s + s**2. Let m be i(-9). Factor m + 2/9*d**2 + 0*d.
2*d**2/9
Factor 2 + 2*h**2 - 6*h + 14*h + 4.
2*(h + 1)*(h + 3)
Factor 2/7*u**3 - 2/7*u + 2/7 - 2/7*u**2.
2*(u - 1)**2*(u + 1)/7
Factor 0 + 0*w + 5*w**2 - 5/2*w**3.
-5*w**2*(w - 2)/2
Let d(p) = p**4 + 1. Let i = -3 + 8. Suppose 2*u = -i*v - 12, -4*v = 2 + 6. Let s(m) = 7*m**4 - 2*m**2 + 5. Let z(j) = u*s(j) + 5*d(j). Factor z(t).
-2*t**2*(t - 1)*(t + 1)
Factor 13 - 25*p + 5*p**2 + 0 + 2 + 5*p**3.
5*(p - 1)**2*(p + 3)
Let t(s) = 7*s**4 + 6*s**3 - s**2. Let p = 1 + 3. Let j(h) = 6*h**4 + 6*h**3. Let k(f) = p*j(f) - 3*t(f). Suppose k(c) = 0. What is c?
-1, 0
Let o(u) be the first derivative of 8*u**5/5 + 7*u**4 + 16*u**3/3 - 8*u**2 - 5. Factor o(l).
4*l*(l + 2)**2*(2*l - 1)
Let l(g) be the second derivative of -g**4/4 - 8*g - 2. Find j such that l(j) = 0.
0
Let i(t) be the first derivative of -t**7/180 - t**6/45 - t**5/60 + t**4/18 + t**3/3 - 3. Let p(a) be the third derivative of i(a). Factor p(f).
-2*(f + 1)**2*(7*f - 2)/3
Let r = -2/877 + 2645/6139. Suppose 6/7*l**2 + 9/7*l**3 + 0 - r*l = 0. Calculate l.
-1, 0, 1/3
Let i = -2 + 2. Let z(d) be the first derivative of 0*d - 1/6*d**6 - 2 + i*d**2 - 1/2*d**4 - 1/6*d**3 - 1/2*d**5. Find j such that z(j) = 0.
-1, -1/2, 0
Let m(k) = -6*k**3 - 6*k**2 + 3*k + 6. Let n(q) = -6*q**3 - 7*q**2 + 2*q + 5. Let u(b) = 2*m(b) - 3*n(b). Determine w, given that u(w) = 0.
-1, 1/2
Let r = 1/10109 + 5731783/202180. Let c = r - 107/4. Solve c*s**4 + 2/5*s**2 - 8/5*s**3 + 0*s + 0 = 0.
0, 1/2
Let c(d) be the first derivative of -d**6/40 - d**5/80 + d**4/24 - 3*d + 4. Let i(p) be the first derivative of c(p). Factor i(u).
-u**2*(u + 1)*(3*u - 2)/4
Let k(o) be the second derivative of o**5/40 - o**4/12 + o**3/12 - 6*o. Factor k(j).
j*(j - 1)**2/2
Let d be 1*(-14 + (2 - -2)). Let m be (d/150)/(1/(-3)). Factor 0 + 2/5*k - 3/5*k**2 + m*k**3.
k*(k - 2)*(k - 1)/5
Suppose 2 + 14 = 4*a. Let h be a/14 - 90/(-28). Factor -h*i**2 + 0 - i.
-i*(7*i + 2)/2
Let l(u) be the second derivative of -u**9/4536 - u**8/1260 + u**6/270 + u**5/180 - u**3/2 - u. Let h(r) be the second derivative of l(r). Factor h(i).
-2*i*(i - 1)*(i + 1)**3/3
Factor 4/3*w**3 + 2/3*w**4 - 8/3*w + 8/3 - 2*w**2.
2*(w - 1)**2*(w + 2)**2/3
Let w(z) = -4*z**4 + 10*z**3 - 6*z**2 + 6*z - 6. Let v(j) = 12*j**4 - 31*j**3 + 19*j**2 - 17*j + 17. Let p(x) = -6*v(x) - 17*w(x). Let p(m) = 0. What is m?
0, 1, 3
Let w(v) be the first derivative of -1 - 1/6*v**2 - 4/9*v**3 + 0*v. Solve w(l) = 0 for l.
-1/4, 0
Factor -r**3 - 11*r - r**3 + 13*r.
-2*r*(r - 1)*(r + 1)
Factor -10 + 32*y + 12 - 14*y**2 - 10.
-2*(y - 2)*(7*y - 2)
Suppose 8 = 3*l + l. Let r = 0 + l. Let -1/2 + 1/4*v**r + 1/4*v = 0. Calculate v.
-2, 1
Let r(f) be the third derivative of -f**7/945 + f**5/135 - f**3/27 + 41*f**2. Factor r(k).
-2*(k - 1)**2*(k + 1)**2/9
Let x(h) = -h**5 + 17*h**4 + 9*h**3 - 17*h**2 - 8*h. Let n(l) = -2*l**5 + 26*l**4 + 14*l**3 - 26*l**2 - 12*l. Let z(y) = -5*n(y) + 8*x(y). Factor z(j).
2*j*(j - 1)*(j + 1)**2*(j + 2)
Let z(y) be the second derivative of 3*y - 1/30*y**6 + 0*y**5 + 1/12*y**4 + 0*y**2 + 0*y**3 + 0. Find x such that z(x) = 0.
-1, 0, 1
Let v(y) be the second derivative of -y**7/14 + 7*y**6/10 - 57*y**5/20 + 25*y**4/4 - 8*y**3 + 6*y**2 - 24*y. Suppose v(d) = 0. Calculate d.
1, 2
Let m(x) be the first derivative of 2*x**5/5 - x**4/2 - 2*x**3 + 5*x**2 - 4*x - 32. Solve m(g) = 0 for g.
-2, 1
Suppose -7*m + 2 = -12. Let y(p) be the third derivative of 0 - 1/15*p**3 + 0*p - 1/150*p**5 + m*p**2 + 1/30*p**4. Factor y(k).
-2*(k - 1)**2/5
Let l(p) be the second derivative of p**5/5 + 4*p**4/3 + 10*p**3/3 + 4*p**2 + 2*p. Solve l(n) = 0.
-2, -1
Let q(d) be the first derivative of d**4/4 + d**3/2 + 4*d - 4. Let k(r) be the first derivative of q(r). Suppose k(g) = 0. Calculate g.
-1, 0
Let i(o) be the third derivative of -4/21*o**3 + 0*o + 1/30*o**5 - o**2 + 0 - 1/7*o**4. Factor i(a).
2*(a - 2)*(7*a + 2)/7
Let -4*x + 2*x**2 + 0*x - 3*x**3 + 7*x**3 - 2*x**4 + 0*x = 0. What is x?
-1, 0, 1, 2
Find k, given that 6 - 6*k**4 + 0*k**4 - 4*k**3 - 6 - 4*k + 14*k**2 = 0.
-2, 0, 1/3, 1
Determine x so that -9/4*x + 3/4 - 3/4*x**3 + 9/4*x**2 = 0.
1
Let j(v) be the first derivative of 5*v**4/24 - 10*v**3/9 - 5*v**2/12 + 10*v/3 - 15. Factor j(w).
5*(w - 4)*(w - 1)*(w + 1)/6
Let g(n) = -n**2 - 3*n + 1. Let q be g(-4). Let k be q/(-7)*(-20)/(-6). Factor -4/7 - k*j + 4/7*j**2 + 10/7*j**3.
2*(j - 1)*(j + 1)*(5*j + 2)/7
Let v(g) = 5*g**4 + 11*g**3 - 31*g**2 + 21*g - 6. Let z(t) = -10*t**4 - 23*t**3 + 63*t**2 - 43*t + 13. Let k(u) = -13*v(u) - 6*z(u). Factor k(h).
-5*h*(h - 1)**2*(h + 3)
Let j(d) be the second derivative of 1/10*d**5 + 1/15*d**6 + 0*d**2 + 3*d + 0 + 0*d**3 + 1/18*d**4 + 1/63*d**7. Factor j(f).
2*f**2*(f + 1)**3/3
Let i(v) be the second derivative of -v**4/12 - 4*v. Let r(t) = 10*t**2 - 2*t. Let k(q) = 18*i(q) + 2*r(q). Factor k(x).
2*x*(x - 2)
Let h(p) = p**3 + 3*p**2 - 2*p - 6. Let k be h(-3). Factor 0*f**2 + 0 - 1/4*f**3 + k*f + 1/4*f**4.
f**3*(f - 1)/4
Factor 0*v**2 - 1/7*v + 0 + 1/7*v**3.
v*(v - 1)*(v + 1)/7
Let c = -54078/25 - -26170527/12100. Let q = -2/121 - c. Factor -q*j - 1/2*j**2 + 3/4*j**3 + 0.
j*(j - 1)*(3*j + 1)/4
Let l(y) = -y**2 + 6*y - 5. Let r be l(4). Suppose -6*o = -r*o - 9. Find w, given that 0 + 0*w + 1/2*w**4 - 1/2*w**2 - 1/2*w**5 + 1/2*w**o = 0.
-1, 0, 1
Let n(b) be the third derivative of -b**5/90 + b**4/36 + 2*b**3/9 + 5*b**2. Determine o so that n(o) = 0.
-1, 2
Let g be 609/14*8/18. Let z = g - 19. Let 0*j**2 + 1/3*j**5 + 0*j**4 + 0 - 2/3*j**3 + z*j = 0. Calculate j.
-1, 0, 1
Let j = 4037/4 - 1009. Let 1/2 + 3/4*z + j*z**2 = 0. Calculate z.
-2, -1
Let w(n) be the second derivative of n**7/21 + 4*n**6/15 - n**5/10 - 2*n**4/3 - 5*n. Suppose w(z) = 0. Calculate z.
-4, -1, 0, 1
Let y(v) = -v**2 + 4*v**5 - v**5 - 2*v**5. Let u(o) = -4*o**5 - 2*o**4 + 5*o**2 + o. Let r be 6/57 - (-168)/(-152). Let a(m) = r*u(m) - 3*y(m). Factor a(f).
f*(f - 1)*(f + 1)**3
Let i(v) = -3*v**3 + 2*v**2 - 1. Let s be i(1). Let p be 24/s*4/(-12). Factor -n**2 + 2*n + p + 6*n**4 - 2*n**2 - 2*n**3 - 7*n**2.
2*(n - 1)**2*(n + 1)*(3*n + 2)
Let x be (-1)/((-8)/25) + -3. Let a(s) be the first derivative of x*s**4 + 1/12*s**3 + 0*s + 1/20*s**5 + 0*s**2 + 3. Factor a(i).
i**2*(i + 1)**2/4
Let q be ((-6)/420*-8)/((-6)/(-21)). Let -2/5*x**2 + 0*x + q = 0. Calculate x.
-1, 1
Let f(b) be the second derivative of -4*b + 0 - 1/24*b**3 + 0*b**2 + 1/24*b**4 - 1/80*b**5. Factor f(g).
-g*(g - 1)**2/4
Let u(d) = -3*d - 2. Let m be u(-2). Let i = -16 + 22. Factor i*q**2 - m - 7*q - 5*q + 2*q**2 - 2*q.
2*(q - 2)*(4*q + 1)
Let m = 8 + -22/3. Suppose m*k + k**2 + 5/3*k**5 + 0 - 7/3*k**3 - k**4 = 0. Calculate k.
-1, -2/5, 0, 1
Suppose -5 = -m - 2. Let s be m/24*2*1. Solve -1/4*o**3 + 0*o - 1/4*o**4 + s*o**2 + 0 + 1/4*o**5 = 0.
-1, 0, 1
Let t(z) be the third derivative of -z**8/840 + z**7/140 - z**5/15 - 2*z**3/3 + 4*z**2. Let f(c) be the first derivative of t(c). Factor f(j).
-2*j*