+ 3)
Let j(p) be the third derivative of -1/245*p**7 - 1/420*p**6 + 0 + 0*p**3 + 1/42*p**4 + 3*p**2 + 1/70*p**5 + 0*p - 1/1176*p**8. Find k such that j(k) = 0.
-2, -1, 0, 1
Let o(s) be the third derivative of 0*s + s**2 + 0*s**3 + 1/60*s**6 + 0 + 0*s**4 + 1/30*s**5. Factor o(h).
2*h**2*(h + 1)
Let l be 6071/(-492) - (-42)/(-56). Let h = 10/41 - l. Find c such that 0 - 22*c**3 - h*c**2 - 8/3*c - 44/3*c**4 - 10/3*c**5 = 0.
-2, -1, -2/5, 0
Let r(q) = 9*q**3 - 15*q**2 + 4*q + 20. Let x(u) = -125*u**3 + 210*u**2 - 55*u - 280. Let l(g) = -55*r(g) - 4*x(g). Find d such that l(d) = 0.
-1, 2
Suppose -3*k + 16 - 4 = 0. Suppose o + 3*o - s = 21, 12 = k*s. Let 3*p**5 + 0*p**4 - 2*p**5 - 4*p**4 + o*p**3 - 4*p**2 + p = 0. Calculate p.
0, 1
Let a be 16/12*-1*3. Let n(j) = -j**2 + 4*j - 1. Let t(o) = -o**2 + 5*o - 1. Let u(r) = a*t(r) + 6*n(r). Suppose u(c) = 0. Calculate c.
1
Suppose 0 = -4*v - 2 - 18. Let h = v + 7. Factor -2/3*d - 4/3*d**h - 2/3*d**5 + 2/3*d**4 + 4/3*d**3 + 2/3.
-2*(d - 1)**3*(d + 1)**2/3
Let u = -189 - -192. Let p(j) be the third derivative of j**2 + 0*j + 1/40*j**6 + 0*j**5 + 0 + 0*j**7 + 0*j**u + 0*j**4 - 1/112*j**8. Factor p(i).
-3*i**3*(i - 1)*(i + 1)
Let a(f) be the third derivative of -f**5/100 + f**4/20 - f**3/10 - 7*f**2. Solve a(n) = 0 for n.
1
Determine h so that -7/2*h + 37/2*h**3 + 1 - 10*h**4 - 6*h**2 = 0.
-2/5, 1/4, 1
Factor 4/3*p**3 - 1/3*p + 0 + 1/6*p**2 + 5/6*p**4.
p*(p + 1)**2*(5*p - 2)/6
Let c(u) = -7*u**2 - u**3 + u**2 + 0 - 5*u + 2. Let n be c(-5). Factor -2*o**n - 5*o**3 - 2*o**2 + 3*o**5 + 2*o + 3*o**2 + o**4.
o*(o - 1)*(o + 1)**2*(3*o - 2)
Let q(z) = z**2 + 6*z - 4. Let d be q(-7). Factor 3*u**2 + u - d + 0*u**4 - u**3 + 0*u - 2*u**4 + 2.
-(u - 1)*(u + 1)**2*(2*u - 1)
Suppose 0*i + 6 = -i. Let x(t) = 1 - 10*t**2 - 4 - 2*t**3 - 11*t + 15*t**2. Let n(s) = -s**3 + 3*s**2 - 6*s - 2. Let q(b) = i*x(b) + 11*n(b). Factor q(f).
(f - 1)*(f + 2)**2
Let f(d) be the third derivative of d**5/110 - 5*d**4/44 + 4*d**3/11 - 2*d**2 + 2. Factor f(r).
6*(r - 4)*(r - 1)/11
Factor -8*b**4 + 198*b - 198*b + 2*b**3.
-2*b**3*(4*b - 1)
Let r(h) = h**2 - 11*h - 11. Let l(j) = 3*j**2 - 23*j - 23. Suppose -12 = -7*k + 11*k. Let p(d) = k*l(d) + 7*r(d). Suppose p(q) = 0. What is q?
-2
Let k be 0*(8 + -3)/(-5). Let h(y) be the second derivative of -9/40*y**5 - 7/8*y**4 + k + 0*y**3 - 3*y + 3*y**2. Determine z so that h(z) = 0.
-2, -1, 2/3
Let y(w) be the second derivative of -4/7*w**2 - 8/3*w**3 + 0 - 499/70*w**5 - 407/105*w**6 - 121/147*w**7 - 265/42*w**4 + 11*w. Factor y(n).
-2*(n + 1)**3*(11*n + 2)**2/7
Let y(o) be the second derivative of -o**5/4 - 5*o**4/6 + 5*o**3/6 + 5*o**2 + 11*o. Factor y(f).
-5*(f - 1)*(f + 1)*(f + 2)
Suppose 2*w + 5*h - 11 = -0, -4*w - 2*h = -14. Let m be 9/w + 8 + -11. Factor -2/3*i**2 + 0 + m*i - i**3 - 1/3*i**4.
-i**2*(i + 1)*(i + 2)/3
Let l(n) be the third derivative of n**5/120 + n**4/16 + 19*n**2. Factor l(q).
q*(q + 3)/2
Let y(x) = -7*x**5 + 11*x**4 - x**3 + 2*x**2 + 5*x - 5. Let b(n) = 6*n**5 - 10*n**4 + 2*n**3 - 2*n**2 - 4*n + 4. Let i(q) = -5*b(q) - 4*y(q). Factor i(k).
-2*k**2*(k - 1)**3
Let j(t) be the first derivative of -t**3/5 - 9*t**2/5 + 21*t/5 - 27. Factor j(y).
-3*(y - 1)*(y + 7)/5
Suppose -4 + 2*k**2 - 14/3*k = 0. What is k?
-2/3, 3
Let m(p) be the second derivative of p**6/50 + 3*p**5/50 + p**4/20 + 8*p. Find g, given that m(g) = 0.
-1, 0
Let p(a) be the third derivative of a**8/336 + 2*a**7/105 - a**6/120 - a**5/15 - 27*a**2 - 2. Suppose p(z) = 0. What is z?
-4, -1, 0, 1
Let o(u) be the second derivative of 1/360*u**6 - 1/180*u**5 - u + 0*u**4 - 1/2*u**2 + 0*u**3 + 0. Let m(y) be the first derivative of o(y). Factor m(d).
d**2*(d - 1)/3
Suppose -2*l + 2*x + 12 = -6, 0 = -4*l - x + 11. Determine o, given that -3 + 277*o**5 + 264*o**3 - 9*o + 48*o**2 - 37*o**5 + 300*o**l + 154*o**4 - 22*o**4 = 0.
-1/2, 1/5
Factor 2/5*a - 2*a**3 - 6/5*a**2 + 2/5 - 4/5*a**4.
-2*(a + 1)**3*(2*a - 1)/5
Let u be (4/60)/(-2 + 4). Let o(q) be the third derivative of 0 - u*q**5 + 0*q - q**2 + 0*q**4 + 1/3*q**3. Find b such that o(b) = 0.
-1, 1
Let m = -142/3 + 995/21. Let j(v) be the second derivative of m*v**3 + 0*v**2 + 2*v + 1/42*v**4 + 0. Factor j(l).
2*l*(l + 1)/7
Let t = -2/1797 - -8392/5391. Suppose 40/9*v - 46/9*v**2 - 8/9 + t*v**3 = 0. What is v?
2/7, 1, 2
Let r be (-45)/27*3*-1. Factor 2*s**2 + 6 - 5*s - r + 3 - s.
2*(s - 2)*(s - 1)
Let n(i) be the first derivative of 25*i**5 - 135*i**4/4 - 115*i**3/3 + 135*i**2/2 - 10*i + 7. Determine y, given that n(y) = 0.
-1, 2/25, 1
Let z(r) be the first derivative of -4*r**5/5 + 7*r**4/4 - 2*r**3/3 - r**2/2 - 9. Let z(x) = 0. Calculate x.
-1/4, 0, 1
Factor -2/17*b**4 - 2/17 + 0*b + 4/17*b**2 + 0*b**3.
-2*(b - 1)**2*(b + 1)**2/17
Let z be 1/6 - (-46)/12. Let g(y) be the second derivative of 1/2*y**3 + 0*y**z - 1/20*y**5 + 0 + 2*y - y**2. Factor g(o).
-(o - 1)**2*(o + 2)
Let a = 32605/76 + -429. Let z = 159/532 - a. Suppose -4/7 + 2/7*n + 4/7*n**2 - z*n**3 = 0. What is n?
-1, 1, 2
Let f be ((-5)/(-15) - 0) + 5/(-15). Determine m, given that 0*m**2 - 1/3*m + f + 1/3*m**3 = 0.
-1, 0, 1
Let h(o) be the first derivative of o**6/540 - o**5/90 + o**4/36 + 2*o**3/3 - 3. Let x(f) be the third derivative of h(f). Determine r, given that x(r) = 0.
1
Factor 1/5*u**2 + 2/5*u + 0 - 1/5*u**4 - 2/5*u**3.
-u*(u - 1)*(u + 1)*(u + 2)/5
Suppose -10/3*t**2 + 4/3*t**3 - 5/3*t**5 + 1/3*t + 2/3 + 8/3*t**4 = 0. What is t?
-1, -2/5, 1
Let -c**2 + 7*c + c**3 - 3 + 2*c**2 - 6*c**2 = 0. Calculate c.
1, 3
Suppose -y + 9 = 2*y. Let d(t) be the first derivative of -8/9*t**y + 0*t - 1/9*t**6 - t**4 - 8/15*t**5 - 1/3*t**2 - 2. Let d(a) = 0. Calculate a.
-1, 0
Suppose k - 5*y = -21, 22*y - 6 = -4*k + 24*y. Factor 3/4*x**2 + 0 + 3/4*x**k + 3/2*x**3 + 0*x.
3*x**2*(x + 1)**2/4
Suppose -5*o - 5*u = 5, -u - 2*u - 13 = -2*o. What is p in -12*p**o - 6*p**4 - 1 + 8 - 24*p + 22*p**3 + 9 = 0?
-1, 2/3, 2
Let x = -9 + 11. Let q(f) = -f**3 - 6*f**2 + 8. Let r(c) = 6*c**2 - 8. Let j(n) = x*q(n) + 3*r(n). Factor j(m).
-2*(m - 2)**2*(m + 1)
Let s = -5 - -7. Factor -4*t**2 + 9*t**4 + s*t**2 - 4*t**2 - 3*t**5 + 3*t - 3*t**4.
-3*t*(t - 1)**3*(t + 1)
Let b be 50 + -38 - (2/1 + 2). Suppose b*m**2 + 32/3*m**3 + 1/6 + 2*m = 0. What is m?
-1/4
Factor 4/5*h**3 - 4/5*h**2 + 4/5 - 4/5*h.
4*(h - 1)**2*(h + 1)/5
Let z(r) be the third derivative of r**8/672 + r**7/420 + 15*r**2. Factor z(c).
c**4*(c + 1)/2
Let w(u) = 7*u**2 - 19*u + 77. Let m(j) = 10*j**2 - 29*j + 115. Let r(q) = 5*m(q) - 7*w(q). Let r(n) = 0. What is n?
6
Factor 4/3*v**3 + 0 + 0*v + 2/3*v**4 + 2/3*v**2.
2*v**2*(v + 1)**2/3
Let k(m) be the third derivative of m**6/80 - 3*m**5/40 + m**4/8 - 12*m**2. Solve k(a) = 0.
0, 1, 2
Factor 0*g**2 - 2/3*g**3 + 0*g + 0.
-2*g**3/3
Factor -26*p + p**4 + 66*p**2 - 21*p**3 - 15*p**2 - 25*p + 2*p**4 + 18.
3*(p - 3)*(p - 2)*(p - 1)**2
Let f(s) be the second derivative of 0*s**4 + 1/105*s**6 + 0 + 6*s + 0*s**3 + 1/70*s**5 + 0*s**2. Factor f(u).
2*u**3*(u + 1)/7
Let r(n) be the third derivative of n**8/896 - n**7/112 + n**6/160 + 7*n**5/80 - 3*n**4/64 - 9*n**3/16 - 9*n**2. What is d in r(d) = 0?
-1, 1, 3
Suppose -23*x = 7*x - 90. Factor 4/7*y**x + 0*y**4 - 2/7*y**5 + 0*y**2 + 0 - 2/7*y.
-2*y*(y - 1)**2*(y + 1)**2/7
Let c(u) be the second derivative of u**6/195 - 7*u**5/130 + 3*u**4/13 - 20*u**3/39 + 8*u**2/13 - 11*u. Find j, given that c(j) = 0.
1, 2
Let i be 1/(-2 + (-9)/(-4)). Suppose 23 = -i*s + 3. Let p(n) = -2*n**3 + 2. Let c(q) = -4*q**3 + q**2 + 5. Let w(g) = s*p(g) + 2*c(g). Solve w(u) = 0 for u.
-1, 0
Let f(y) be the second derivative of y**4/30 - 4*y**2/5 + 7*y. Factor f(l).
2*(l - 2)*(l + 2)/5
Let q be (-1*2)/(1 - 3). Let t be (q/3)/((-3)/(-27)). Factor 6*x**2 + t + 2*x - 18*x**3 + 14*x - 11.
-2*(x + 1)*(3*x - 2)**2
Let y = 1/8 + 11/40. Factor 0*h**3 - 4/5*h**2 - 2/5*h**5 + y*h + 4/5*h**4 + 0.
-2*h*(h - 1)**3*(h + 1)/5
Let l(d) = 32*d + 195. Let u be l(-6). Suppose 0 - 1/4*i**u + 1/4*i**2 + 0*i = 0. Calculate i.
0, 1
Suppose 19*p**3 - 77*p**3 - 18 + 12*p + 26*p**3 + 2*p**4 + 20*p**3 + 16*p**2 = 0. What is p?
-1, 1, 3
Solve 0 - 1/5*p**3 + 1/5*p**5 + 0*p - 1/5*p**4 + 1/5*p**2 = 0.
-1, 0, 1
Let l(p) be the first derivative of 0*p - p**2 + 2 + 1/3*p**3 + 1/4*p**4. Let l(a) = 0. What is a?
-2, 0, 1
Let o(c) = 3*c**2 + 7*c + 4. Let 