g + 7)/4
Let s(f) be the first derivative of -f**6/6 + 4*f**5/5 + 3*f**4 + 2*f**3/3 - 11*f**2/2 - 6*f - 12. Factor s(i).
-(i - 6)*(i - 1)*(i + 1)**3
Factor 34/7*q - 4/7*q**2 + 38/7.
-2*(q + 1)*(2*q - 19)/7
Let r(k) be the second derivative of k**7/357 - 4*k**6/85 + 11*k**5/85 + 14*k**4/17 + 49*k**3/51 + 69*k. Determine h, given that r(h) = 0.
-1, 0, 7
Let c(s) be the second derivative of -1/8*s**4 + s**3 - s**2 - 9/40*s**6 + 0 - 3/5*s**5 + 5*s. Let x(y) be the first derivative of c(y). Factor x(j).
-3*(j + 1)*(3*j - 1)*(3*j + 2)
Let k = 10090 + -10087. Factor 0 + 3/4*a**4 - 3/2*a**2 - 3/4*a**k + 0*a.
3*a**2*(a - 2)*(a + 1)/4
Suppose 3*f + 22 = 2*f. Let c = -18 - f. Determine l so that 9*l**2 - 15*l**3 - 55*l**c + 3 + 13*l + 2*l + 43*l**4 = 0.
-1, -1/4, 1
Suppose 27 = -2*u - 3*q, -24*q = 3*u - 19*q + 45. Let t be (-4)/(-18)*(-3)/(-1). Factor r**4 + 0*r**2 - t*r**3 + 0*r + u.
r**3*(3*r - 2)/3
Let c(w) = -4*w**2 + 112*w + 192. Let b(a) = a**2 - 37*a - 64. Let q be 1/1*(-2 + -14). Let f(u) = q*b(u) - 5*c(u). Factor f(k).
4*(k + 4)**2
Suppose 27 = -3*c - m, 0 = 11*c - 8*c + 3*m + 27. Let w be -2*(15/(-10))/(c/(-12)). Let 3/2*r**w + 0*r**2 - 3*r**3 - 3/2 + 3*r = 0. Calculate r.
-1, 1
Let c = -462 + 465. Let y = 48 + -333/7. Factor -9/7*u**c - 9/7*u**4 + 0 - y*u**2 - 3/7*u**5 + 0*u.
-3*u**2*(u + 1)**3/7
Let w be (1/(-5) + -1)/(264/(-440)). Suppose 6/5*f + 0 + 2/5*f**w = 0. What is f?
-3, 0
Let j be (-2)/6 + 16/12. Let k be (-3 + 1/j)/(-1). Factor 4*m - 3*m**2 + 3*m**2 - 8 + 0*m**k + 4*m**2.
4*(m - 1)*(m + 2)
Suppose s - 4*s - 4*y = 6, 5*s + 3*y = 1. Let r(f) = f**2 - 34*f - 670. Let u be r(48). Factor -2/3*i + 2*i**s + 2/3*i**4 - u*i**3 + 0.
2*i*(i - 1)**3/3
Let n(x) be the third derivative of -x**6/30 + 7*x**5/60 + 7*x**4/24 - 4*x**2. Let l(p) = -p. Let m(d) = -5*l(d) - n(d). Factor m(v).
v*(v - 2)*(4*v + 1)
Find u, given that 3/5*u**2 + 21/5*u - 24/5 = 0.
-8, 1
Let h(m) be the third derivative of m**6/30 - 11*m**5/15 + 35*m**4/6 - 50*m**3/3 + 6*m**2 + 4. Solve h(s) = 0 for s.
1, 5
Determine d so that 5/6*d - 1 - 1/6*d**2 = 0.
2, 3
Suppose 3*a - c + 265 = 716, 3*c + 137 = a. Let u be 4/a*198 - 5. Factor -2/19*h**2 - u - 6/19*h.
-2*(h + 1)*(h + 2)/19
Let l be 55/(-210) - (-8)/16. Let t(x) be the first derivative of 0*x + l*x**6 + 2 - 26/35*x**5 + 2/7*x**4 + 8/21*x**3 + 0*x**2. Solve t(z) = 0 for z.
-2/5, 0, 1, 2
Determine f, given that -42*f - 12*f**2 - 3*f**3 + 39*f**3 + f**4 + 6*f + 32 - 25*f**2 + 4*f**4 = 0.
-8, -1, 4/5, 1
Find q such that 273504080*q + 52320*q**3 + 0*q**5 + 69*q**4 - 499*q**4 + 50044*q**3 + q**5 - 6360560*q**2 - 4704270176 - 28404*q**3 = 0.
86
Factor 4/7*z**4 + 92/7*z**2 + 2/7*z**5 - 16 + 40/7*z - 58/7*z**3.
2*(z - 2)**3*(z + 1)*(z + 7)/7
Find h, given that 2/7*h**5 - 4/7*h**4 - 6/7*h**3 + 16/7*h**2 + 0 - 8/7*h = 0.
-2, 0, 1, 2
Suppose 20*p - 22*p + 10 = 0. Suppose 5*q - x - 30 = 53, 0 = -p*q - 2*x + 74. Find g such that 3*g**3 + q*g - g**3 - 32 + 20*g**2 - 6*g**2 = 0.
-4, 1
Let i be 37 - 29 - (-1 - (-4 - 1)). Suppose -10*a = i*a - 18*a. Factor 2/5 + a*o - 2/5*o**2.
-2*(o - 1)*(o + 1)/5
Let n(p) = p**2 + 4*p + 5. Let s be n(-3). Let i be (14/245*5)/(1/s). Factor -2/7 + 0*r**2 - 4/7*r**3 + 2/7*r**4 + i*r.
2*(r - 1)**3*(r + 1)/7
Let 14*d**2 + 26*d**2 - 26*d**3 + 21*d**3 - 60*d = 0. What is d?
0, 2, 6
Let q(v) be the first derivative of -v**3/15 + v**2/2 + 370. Suppose q(m) = 0. Calculate m.
0, 5
Let o = -5666/5 - -1134. Factor 0 + 0*x - o*x**3 - 2/5*x**4 - 2/5*x**2.
-2*x**2*(x + 1)**2/5
Let d(g) be the first derivative of g**6/900 - g**5/75 + 14*g**3/3 + 4. Let y(r) be the third derivative of d(r). Determine z so that y(z) = 0.
0, 4
Suppose -6*i - 1668 = -10*i. Factor 5*r**3 - r + i*r**5 - 10*r**4 + r - 412*r**5.
5*r**3*(r - 1)**2
Let c(u) be the third derivative of -u**8/8064 + u**7/336 + 7*u**5/10 + 28*u**2. Let k(a) be the third derivative of c(a). Determine g so that k(g) = 0.
0, 6
Solve -20/7*h**2 + 92/7*h + 40/7 = 0 for h.
-2/5, 5
Let h = -623280149/441 - -1413333. Let c = -2/441 - h. Solve -4/3*p**2 + 4/3*p**3 + c*p**5 - 2/3 + 2*p**4 - 2*p = 0.
-1, 1
Let g(n) be the third derivative of 0*n - 1/84*n**4 - 1/420*n**5 + 0 - 16*n**2 + 1/1470*n**7 + 0*n**3 + 1/420*n**6. Solve g(l) = 0.
-2, -1, 0, 1
Suppose 8 = 4*t - 4*j, 18 = -2*t + 3*j + 22. Suppose 10/3*n + t - 2/3*n**3 + 2/3*n**2 = 0. Calculate n.
-1, 3
Suppose -4*m + 6*m + 5*w = 6, 5*m - 4*w = 15. Let 0*a**2 - m*a**2 - 6*a + 40 + 5*a**2 - 48 = 0. What is a?
-1, 4
Let h(s) be the third derivative of s**8/112 - s**6/5 + 2*s**4 + 275*s**2. Factor h(d).
3*d*(d - 2)**2*(d + 2)**2
Let y(u) be the third derivative of u**9/151200 - u**8/25200 - u**7/12600 + u**6/900 + u**5/20 - 19*u**2. Let i(x) be the third derivative of y(x). Factor i(j).
2*(j - 2)*(j - 1)*(j + 1)/5
Let a(x) be the first derivative of -17*x**5/5 + 151*x**4/4 - 147*x**3 + 405*x**2/2 + 54*x - 844. Factor a(h).
-(h - 3)**3*(17*h + 2)
Let g(v) be the first derivative of -3*v**8/280 + 4*v**7/175 + 11*v**6/300 + v**5/75 + 41*v**2/2 - 15. Let t(y) be the second derivative of g(y). Factor t(b).
-2*b**2*(b - 2)*(3*b + 1)**2/5
Suppose -2*q - 3*q = -c - 5, -3*q = 4*c - 3. Suppose 0 = -3*s + m + 12, s + c*s - 3*m = 12. Factor -i**s + 3*i**3 - 2*i**2 - 4*i**3.
-2*i**2*(i + 1)
Let b(h) = -2*h**2 - 40*h + 117. Let s(l) = l**2 + 18*l - 58. Let f(y) = 4*b(y) + 10*s(y). Factor f(t).
2*(t - 4)*(t + 14)
Factor 70/3*g + 0 + 1/3*g**3 + 71/3*g**2.
g*(g + 1)*(g + 70)/3
Let l(i) be the second derivative of i**5/35 - i**4/3 + 23*i + 1. Suppose l(b) = 0. Calculate b.
0, 7
Let d(q) = -7*q**2 - 6*q - 5. Let z(r) = -3*r**2 - 3*r - 2. Suppose 12 = -3*i - 0*i. Let a = 13 + i. Let b(v) = a*z(v) - 4*d(v). Factor b(c).
(c - 2)*(c - 1)
Factor -15*u**3 - 19*u**3 + 30*u**3 - 24*u**2.
-4*u**2*(u + 6)
Solve -6/17*m**2 - 8/17*m + 0 + 2/17*m**3 = 0.
-1, 0, 4
Let n(l) be the second derivative of l**4/4 - 15*l**3 + 87*l**2/2 + 5*l - 2. Find m, given that n(m) = 0.
1, 29
Let k = -28 + 110. Let q be k/22 - 9/3. Determine f so that 16/11*f**2 + q*f + 0 - 6/11*f**3 - 18/11*f**4 = 0.
-2/3, 0, 1
Let x be 48/(-36) - 3/(11340/(-5044)). Let l(a) be the third derivative of 0*a**4 + 2*a**2 + 0*a + 1/135*a**5 + 1/180*a**6 + 0 + x*a**7 + 0*a**3. Factor l(b).
2*b**2*(b + 1)*(b + 2)/9
Suppose -46*b = -3*b - 129. What is k in 0 + 3/4*k**b + 3/4*k**4 + 0*k + 0*k**2 = 0?
-1, 0
Suppose 2*m + 5 = -3*q, 3*m + 0*m - 3*q = 30. Find t, given that 4*t**4 - 4*t**2 + 78*t**5 - 4*t - 76*t**m + 2*t = 0.
-1, 0, 1
Let z = -1223/8 - -153. Let y(o) be the third derivative of 1/40*o**6 + 0*o + 1/2*o**3 + o**2 + 0 - z*o**4 - 1/20*o**5. Factor y(t).
3*(t - 1)**2*(t + 1)
Let u(x) = 2*x**3 - x**2 - 1. Let i(d) = 65*d**3 - 155*d**2 + 75*d + 15. Let q(n) = -i(n) + 25*u(n). Factor q(b).
-5*(b - 8)*(b - 1)*(3*b + 1)
Let f be 10*(-11)/(275/(-30)). Let j(s) be the second derivative of -1/24*s**4 + 0 + f*s + 0*s**3 + 0*s**2 - 1/80*s**5. Solve j(i) = 0.
-2, 0
Suppose -4*n - k = -8, n = 6*n - k - 10. Let x = 256/565 + -6/113. Factor 4/5 + 2/5*q - x*q**n.
-2*(q - 2)*(q + 1)/5
Let z(s) = -s - 6. Let f be z(0). Let v be f/4*(-10)/3. Suppose -4*o**2 - 2*o**2 - o + v*o**2 = 0. Calculate o.
-1, 0
Let k(s) be the second derivative of 2*s**7/105 - s**6/15 + s**5/15 - s**2/2 - 13*s. Let h(g) be the first derivative of k(g). Determine r so that h(r) = 0.
0, 1
Let l(a) = a**5 - a**4 - a. Let n(i) = 3*i**5 + 21*i**4 - 69*i**3 + 33*i**2 + 66*i - 60. Let u(s) = -6*l(s) + n(s). Determine c, given that u(c) = 0.
-1, 1, 2, 5
Let p(v) be the second derivative of -v**5/180 - v**4/24 - v**3/9 - 4*v**2 - 10*v. Let q(o) be the first derivative of p(o). Factor q(z).
-(z + 1)*(z + 2)/3
Let a(s) be the second derivative of s**4/78 + 35*s**3/39 + 34*s**2/13 - s + 3. Solve a(y) = 0 for y.
-34, -1
Find s, given that 0 + 3/5*s**2 + 27/5*s = 0.
-9, 0
Let h(x) be the third derivative of x**8/43680 - x**6/4680 + 5*x**4/24 + 5*x**2. Let w(b) be the second derivative of h(b). Suppose w(v) = 0. What is v?
-1, 0, 1
Suppose 20 - 25*x**3 - 125/4*x**4 + 120*x**2 + 100*x = 0. What is x?
-2, -2/5, 2
Find q such that 0 - 3*q**2 - 1/2*q + 1/8*q**3 + 3/4*q**4 = 0.
-2, -1/6, 0, 2
Let n(r) = r - 7. Let m be n(9). Factor 4*o**2 - 25*o + 3*o**m - 12*o**2.
-5*o*(o + 5)
Let v(g) be the first derivative of -g**3/5 - 3*g**2/2 + 108*g/5 - 175. Factor v