a) = a**5 - a**4 - 1. Let r(i) = 33*i**4 - 135*i**3 + 150*i**2 - 3. Let w(d) = 3*f(d) - r(d). Find h such that w(h) = 0.
0, 2, 5
Let d = -941 - -943. Factor -18/7*a**3 - 12/7*a**4 + 0*a**d + 0*a + 0 - 2/7*a**5.
-2*a**3*(a + 3)**2/7
Let i(g) = g**2 + 17*g - 5. Let j(b) = -8*b + 2. Let a(n) = 2*i(n) + 5*j(n). Factor a(q).
2*q*(q - 3)
Let d(z) be the first derivative of z**6/9 - z**5/3 + z**4/4 + z**3/9 - z**2/6 - 39. Factor d(p).
p*(p - 1)**3*(2*p + 1)/3
Let n(z) = 12*z**2 + 254*z + 42. Let x be n(-21). Factor 9/4*h**2 + 3/4*h**3 - 1/4*h**4 + 5/4*h + x.
-h*(h - 5)*(h + 1)**2/4
Suppose u - 5*f = 16, f + 2 + 6 = u. Let h(g) be the second derivative of -1/3*g**3 - 1/4*g**4 - 1/6*g**2 + u*g + 0 - 1/15*g**5. Let h(a) = 0. What is a?
-1, -1/4
Factor 160/3*j + 5/3*j**3 + 160/3 + 50/3*j**2.
5*(j + 2)*(j + 4)**2/3
Let h(y) be the first derivative of y**6/6 + 2*y**5 - 7*y**4/2 - 28*y**3/3 + 53*y**2/2 - 22*y + 886. Factor h(s).
(s - 1)**3*(s + 2)*(s + 11)
Let u(k) be the third derivative of k**7/210 - 3*k**6/40 + 13*k**5/60 + 15*k**4/8 - 25*k**3/3 + 6*k**2 - 7. Factor u(r).
(r - 5)**2*(r - 1)*(r + 2)
Let s(x) = 3*x**2 - x - 3. Let v be s(2). Suppose k = v*k. Let k*a + 0 - 2/9*a**4 - 4/9*a**3 - 2/9*a**2 = 0. What is a?
-1, 0
Let v(b) be the second derivative of -2*b - 1/6*b**4 - 2/3*b**3 - b**2 + 0. Let v(a) = 0. Calculate a.
-1
Suppose -114*f + 117*f - 9 = 0. Let o(w) be the second derivative of 0*w**2 + 2/9*w**f - 5*w + 0 + 1/45*w**6 + 5/18*w**4 + 2/15*w**5. Factor o(u).
2*u*(u + 1)**2*(u + 2)/3
Let b = 6 - 0. Let r be b/21 - (-78)/21. What is d in 3*d**3 - d**r - 2*d**4 - d + d = 0?
0, 1
Suppose 0*j - 4*j = -5*y - 159, 2*y + 78 = 2*j. Suppose j = 5*n + 4*x, -3*n = -x - 4*x + 8. Determine d so that -4*d**4 - 3 + 6 - 2*d + 3*d**2 + 4*d**3 - n = 0.
-1/2, 1
Let b(z) be the first derivative of -40*z**2 - 16*z + 7 + 84/5*z**5 - 68/3*z**3 + 20*z**4. Let b(y) = 0. Calculate y.
-1, -2/3, -2/7, 1
Let q(b) be the first derivative of -b**3/8 + 15*b**2/4 - 153*b/8 + 25. Suppose q(f) = 0. What is f?
3, 17
Let f be ((-2)/8)/(2/(-102)). Let j = f + -12. Solve -1/2*l + 0 + 3/4*l**4 + 1/4*l**3 - j*l**2 + 1/4*l**5 = 0.
-2, -1, 0, 1
Suppose 4*g + 2*a - 58 + 20 = 0, g = -2*a + 2. Determine n, given that -g*n - 27*n - 23 + 38*n**2 + 9*n**3 + 5 + 10*n**2 = 0.
-6, -1/3, 1
Let u = -477 - -484. Let k(r) be the second derivative of 5*r + 1/10*r**6 + 3/2*r**2 - 3/10*r**5 + 1/14*r**u + 1/2*r**3 - 1/2*r**4 + 0. Factor k(i).
3*(i - 1)**2*(i + 1)**3
Suppose -4*s - a = -25, 3*s - 2*s - 15 = -2*a. Suppose s*h - 8 = o + 2*h, 3*h = 3*o. Factor -4/7*p**2 + 2/7*p**o - 24/7*p + 18/7 + 8/7*p**3.
2*(p - 1)**2*(p + 3)**2/7
Let t be 2/(-5) - 1362/(-30). Let f = t - 45. Factor 0*v + f + 2/7*v**4 - 4/7*v**3 + 2/7*v**2.
2*v**2*(v - 1)**2/7
What is p in 2/5*p**3 - 16/5*p**2 - 32/5 + 8*p = 0?
2, 4
Let 564*j - 103*j - 60085 - 11990 + 469*j - 3*j**2 = 0. What is j?
155
Let x(p) be the first derivative of -3 - 1/6*p**3 - 13/4*p**2 + 0*p. Determine d, given that x(d) = 0.
-13, 0
Let l be ((-27)/6)/3*(4 + -8). Let z(n) = -4*n**2 - 6*n. Let y(s) = -2*s**2. Let p(k) = l*y(k) - 2*z(k). Factor p(f).
-4*f*(f - 3)
Let i be 37002/110 + -3*(-4)/(-66). Let n = i + -335. Solve 6/5*h - 2/5 - n*h**2 + 2/5*h**3 = 0.
1
Let s(t) be the third derivative of t**8/144 + t**7/126 - t**6/180 + 2*t**2 - 40*t. Solve s(j) = 0 for j.
-1, 0, 2/7
Let p(s) be the second derivative of s**7/168 + s**6/60 - 3*s**5/20 - 3*s**4/8 + 9*s**3/8 + 75*s. Find a, given that p(a) = 0.
-3, 0, 1, 3
Let q = -33/23 + -686/115. Let p = -34/5 - q. Factor -p*f**3 + 9/5*f**2 - 6/5*f + 0.
-3*f*(f - 2)*(f - 1)/5
Let q(p) be the first derivative of 1/15*p**3 + 1 - 1/20*p**4 - 1/5*p + 1/10*p**2. Factor q(f).
-(f - 1)**2*(f + 1)/5
Suppose -211*c + 220*c = 99. Let l(u) be the third derivative of -c*u**2 + 0*u + 0 - 3/10*u**5 + 7/12*u**4 + 2/3*u**3. What is f in l(f) = 0?
-2/9, 1
Let w(t) be the first derivative of t**5/5 - 2*t**3/3 + t - 140. Suppose w(b) = 0. Calculate b.
-1, 1
Let w be 130/13 - (-351)/(-36). Factor -w*g + 0 - 1/4*g**2.
-g*(g + 1)/4
Suppose -3 = 4*z - 23. Determine n so that -z*n**4 + 8*n**2 - 2*n**2 - 5*n**3 - 6*n**2 = 0.
-1, 0
Let h(u) = 3*u**2 + 28*u - 31. Let o(f) = -4*f - 56. Let q be o(-15). Let j(z) = -21*z**2 - 195*z + 216. Let m(g) = q*j(g) + 27*h(g). Let m(v) = 0. Calculate v.
-9, 1
Let q(h) be the first derivative of -h**6/50 + 3*h**5/100 + h**4/10 - 8*h + 7. Let b(j) be the first derivative of q(j). Factor b(w).
-3*w**2*(w - 2)*(w + 1)/5
Let w(t) = t + 70. Let j be w(0). Let n = j + -40. Let 5*g**4 + 21*g**3 - 54*g**2 - 8*g**4 + n*g - 24 + 30*g = 0. What is g?
1, 2
Let d(a) be the first derivative of -a**6/15 + a**5/8 - a**4/24 + 15*a + 5. Let f(j) be the first derivative of d(j). Factor f(o).
-o**2*(o - 1)*(4*o - 1)/2
Factor 4*y**3 - 6518 + 23100*y + 612*y**2 - 5019 - 2294 - 9885.
4*(y - 1)*(y + 77)**2
Suppose 359*q - 15 = 354*q. Let j(c) be the first derivative of -1/2*c**4 - 5 - 10/3*c**q - 8*c - 8*c**2. Solve j(n) = 0.
-2, -1
Let n be 1786/57 + ((-16)/10 - 10/25). Factor n*z + 76/3*z**2 + 16/3 - 200/3*z**4 + 250/3*z**5 - 230/3*z**3.
2*(z - 1)**2*(5*z + 2)**3/3
Let z(u) = -80*u**3 + 55*u. Let k(w) = -3*w**3 + 2*w. Suppose -2*t - 4*l + 94 = -16, -t + 55 = -5*l. Let g(n) = t*k(n) - 2*z(n). What is b in g(b) = 0?
0
Suppose 19 = -2*r - 3*a + 13, -4*r - 2 = a. Factor -1/9*z**4 + 0*z**3 + 1/9*z**2 + 0 + r*z.
-z**2*(z - 1)*(z + 1)/9
Find r such that -7/2*r**5 + 0 + 1/3*r - 61/6*r**4 - 5/2*r**2 - 19/2*r**3 = 0.
-1, 0, 2/21
Let s(o) be the second derivative of o**5/25 + o**4/5 - 4*o**3/3 - 48*o**2/5 + 514*o. Determine r, given that s(r) = 0.
-4, -2, 3
Determine j so that 1750 - 1642 + 2*j**2 + 2*j**2 - 112*j = 0.
1, 27
Factor 2/7*n + 0 + 1/7*n**2 - 1/7*n**3.
-n*(n - 2)*(n + 1)/7
Let w = -22791/280 - -2862/35. Factor 1/8*i**5 + w*i - 1/2*i**3 + 0*i**4 + 1/4*i**2 - 1/4.
(i - 1)**3*(i + 1)*(i + 2)/8
Suppose 14 = -6*g + 44. Suppose -u + 2*u = 2*c - 6, -g*c + 20 = 0. Solve -2/19*j**u + 6/19 + 4/19*j = 0 for j.
-1, 3
Let d = 86/7 + -416/35. Let x(h) be the first derivative of 1/3*h**6 + 4/3*h**3 - 2*h - d*h**5 - h**4 - 5 + h**2. Suppose x(b) = 0. What is b?
-1, 1
Let f(m) = -m**3 - 3*m**2 + 4*m + 2. Let c be f(-4). Let l be (8 + 1)*1/3. Factor -2*u**3 + 16*u**5 + 4*u**c + l*u**4 - u**3 - 3*u**2 - 17*u**5.
-u**2*(u - 1)**3
Let f(a) = a**2 - 6*a - 4. Let y be f(7). Factor -15*p**y - 10*p**3 + 960 - 960 - 20*p**4 - 5*p**2.
-5*p**2*(p + 1)*(4*p + 1)
Let l(j) be the first derivative of j**6/72 + j**5/4 + 15*j**4/8 - 19*j**3/3 - 26. Let d(s) be the third derivative of l(s). Factor d(g).
5*(g + 3)**2
Let p = 3238/7245 + -2/805. Factor 16/9*m**3 + 0*m + 0 + 16/9*m**2 + p*m**4.
4*m**2*(m + 2)**2/9
Let w(g) be the first derivative of g**5/60 + g**4/12 - g**3/2 - 5*g**2/2 + 9. Let q(n) be the second derivative of w(n). Find c, given that q(c) = 0.
-3, 1
Let n(j) be the third derivative of j**6/220 - 2*j**5/55 + j**4/11 - 31*j**2. Factor n(i).
6*i*(i - 2)**2/11
Suppose 52*p - 29*p = 161. Let c(n) be the second derivative of 0 - 6*n + 0*n**4 + 2/105*n**6 + 1/70*n**5 + 0*n**3 + 1/147*n**p + 0*n**2. Factor c(s).
2*s**3*(s + 1)**2/7
Factor -323*h**2 - 735*h + 18*h**3 - 191 + 6 - 3*h**3 - 212*h**2.
5*(h - 37)*(h + 1)*(3*h + 1)
Let s(f) = 8 - 350*f - f**2 - f**3 + 352*f - 7. Let d(n) = 9*n**4 - 54*n**3 + 28*n**2 + n + 3. Let k(m) = -4*d(m) + 12*s(m). Suppose k(c) = 0. What is c?
0, 1/3, 5
Let t(r) = -r**4 + 0*r**3 + 34*r**2 - 35*r**2 + r**3. Let b(u) = -9*u**4 + 56*u**3 - 133*u**2 + 84*u + 36. Let y(q) = -b(q) + 2*t(q). Let y(d) = 0. What is d?
-2/7, 2, 3
Let f(q) = 7*q**2 + 73*q + 62. Let o(t) = -6*t**2 - 72*t - 63. Let s(n) = 3*f(n) + 4*o(n). Determine c, given that s(c) = 0.
-22, -1
Let m be 27/(-2)*(-240)/360. Let k(y) be the second derivative of 1/2*y**6 + 0*y**3 - m*y - 3/4*y**5 + 0*y**2 - 5/42*y**7 + 5/12*y**4 + 0. Factor k(w).
-5*w**2*(w - 1)**3
Let p(r) = 18*r**4 - r**3 - 12*r**2 - 5. Let s(z) = -760*z**3 + 3 + 760*z**3 + 6*z**2 - 9*z**4. Let u(g) = -3*p(g) - 5*s(g). Suppose u(d) = 0. Calculate d.
-2/3, 0, 1
Let n be 0/1 + 224/5. Let o = 45 - n. Solve 2/5*u + 1/5*u**2 + o = 0.
-1
Suppose 207 = 2*v + v. Find u, given that -44*u + 31*u + 29*u - u**2 - v + 5 = 0.
8
Let m(u) be the first derivative of -u**5/30 + 7*u**4/24 - 2*u**3/3 - 110. Factor m(y