7. Let r be h(5). Let l be (3 + (r - 1))/(-1). Factor -4/3*k + l + 2/3*k**2.
2*k*(k - 2)/3
Let v(y) = -y**5 - 65*y**4 + 95*y**3 + 731*y**2 + 874*y + 326. Let w(t) = t**5 - t**2 + t - 1. Let p(k) = -v(k) - 6*w(k). Factor p(c).
-5*(c - 8)**2*(c + 1)**3
Suppose 0 = 6*k - 13*k + 35. Suppose 3*s + a = -4*a + 69, 0 = 4*s - k*a - 57. Find o, given that 3*o**5 + 12*o**4 + 3*o + s*o**3 + 11*o**2 + 2*o**2 - o**2 = 0.
-1, 0
Let y(p) be the second derivative of -p**6/135 + 2*p**5/45 + p**4/27 - 4*p**3/9 - p**2 + 107*p - 1. Factor y(a).
-2*(a - 3)**2*(a + 1)**2/9
Suppose 7*s = 7 + 14. Let n(m) be the second derivative of 1/5*m**5 + 6*m + m**2 + 0 - 1/5*m**6 - m**s + 1/21*m**7 + 1/3*m**4. Factor n(g).
2*(g - 1)**4*(g + 1)
Let q(n) = 3*n**2 - n - 1. Let a(d) = 3*d**3 + 96*d**2 + 1599*d - 1713. Let l(c) = -a(c) - 15*q(c). Factor l(t).
-3*(t - 1)*(t + 24)**2
Find a such that 3*a**3 - 6*a + 5*a**2 + 8 - 8 - 2*a**2 = 0.
-2, 0, 1
Let g(q) be the second derivative of 1/3*q**3 + 0 + 27*q + 1/12*q**4 - 3/2*q**2. Let g(f) = 0. What is f?
-3, 1
Let u(f) = f - 2. Let v(t) = -t**2. Let x be 2232/(-63) - (-4)/(-7). Let d be (-24)/x - (-2)/6. Let b(m) = d*u(m) - 3*v(m). Factor b(k).
(k + 1)*(3*k - 2)
Let m(k) be the first derivative of -k**3 + 60*k**2 - 1200*k - 86. Factor m(t).
-3*(t - 20)**2
Let h(q) be the first derivative of q**3/8 + 3*q**2/2 - 64. Factor h(x).
3*x*(x + 8)/8
Factor -2*p**2 - 7*p - 16*p + 0*p**2 + 5*p.
-2*p*(p + 9)
Suppose 1/5*m**4 - 4/5*m**3 - 3/5*m**2 + 8/5 + 2*m = 0. Calculate m.
-1, 2, 4
Suppose -4*k + 43 = -5*p, 2*k - 5*k + 4*p + 33 = 0. Suppose 24*o**4 + 8*o**2 + 21*o**3 + 0*o**2 - 4*o - 22*o**4 - k*o**5 = 0. Calculate o.
-1, 0, 2/7, 2
Solve -178/13*z**2 - 60/13*z + 8/13*z**5 + 228/13*z**3 - 6*z**4 + 0 = 0.
-1/4, 0, 2, 3, 5
Let p(i) = -4*i**3 - 1 + 4*i**2 + 3*i**3 - 3*i**2. Let d(v) = 13*v**3 + 2*v**2 + 1. Let n(m) = -d(m) - p(m). Determine b, given that n(b) = 0.
-1/4, 0
Let i(m) be the first derivative of -m**2 + 20 + 0*m**3 + 0*m + 1/2*m**4. Let i(x) = 0. What is x?
-1, 0, 1
Let a(w) be the third derivative of 0*w + 0 + 1/30*w**5 + 7*w**2 - 1/4*w**4 - 4/3*w**3. Determine c, given that a(c) = 0.
-1, 4
Let d(b) = -b**3 + b - 3. Let n(i) = 5*i**3 + 15*i**2 + 70*i + 90. Let y(x) = -10*d(x) - n(x). Factor y(r).
5*(r - 6)*(r + 1)*(r + 2)
Let x = -15 - -19. Suppose -1 - 7 = -x*s. Determine y so that -2/7*y + 0 + 2/7*y**s = 0.
0, 1
Let w(r) be the second derivative of -r**7/84 + 13*r**6/12 - 165*r**5/4 + 3375*r**4/4 - 39375*r**3/4 + 253125*r**2/4 + 308*r. Determine i so that w(i) = 0.
5, 15
Suppose -15*m + 20 = -5*m. Factor -14 - m*d**2 + 2*d + 30 - 6*d.
-2*(d - 2)*(d + 4)
Let z(k) be the third derivative of -k**8/560 + k**7/525 + 7*k**6/60 + 8*k**5/75 - 89*k**4/40 - 3*k**3 + 79*k**2. Find s, given that z(s) = 0.
-3, -1/3, 2, 5
Let 19/2*l + 17 + 1/2*l**2 = 0. What is l?
-17, -2
Let m(f) = 8*f + 3. Let r be m(1). Factor -r*t - 3*t + 5*t**3 - 6*t.
5*t*(t - 2)*(t + 2)
Let x(f) = -21*f + 70. Let p be x(5). Let w = p - -37. Factor 0 - 9/5*m + 3/5*m**w.
3*m*(m - 3)/5
Let x(t) be the first derivative of t**4/20 - 91*t**3/15 + 1012*t**2/5 + 2116*t/5 - 546. Factor x(u).
(u - 46)**2*(u + 1)/5
Let z(v) be the second derivative of v**5/30 - v**4/18 - 4*v**3/9 + 4*v**2/3 + 20*v + 3. Factor z(j).
2*(j - 2)*(j - 1)*(j + 2)/3
Let c(m) = 3*m**5 + 12*m**4 - 26*m**3 + 60*m**2 - 28*m. Let s(d) = d**5 + 4*d**4 - 10*d**3 + 20*d**2 - 9*d. Let o(n) = -2*c(n) + 7*s(n). What is r in o(r) = 0?
-7, 0, 1
Let r = 54093/11 - 4915. Suppose 98/11*i**2 + 2/11 - r*i = 0. Calculate i.
1/7
Let n = 6397 + -6395. Let 8/7 + 8/7*h + 2/7*h**n = 0. What is h?
-2
Let y(a) be the first derivative of -2*a**5/45 + 4*a**4/9 + 40*a**3/27 - 13. Factor y(p).
-2*p**2*(p - 10)*(p + 2)/9
Let q(t) = 25*t**3 + t**2 - 1. Let h be q(1). Suppose -33*j**3 - 30*j + 9*j**3 + 5*j**4 + 38*j**3 - h + 20*j**2 + 16*j**3 = 0. Calculate j.
-5, -1, 1
Let k(q) = -q**3 - q**2 + 4. Let d be k(0). Factor -d - t + 11*t**3 - 2*t**4 + 17*t - 26*t**2 + 5*t**2.
-(t - 2)**2*(t - 1)*(2*t - 1)
Let o be 3/3*(-1 + 6). Factor -1 + 14*t**2 - o - 16*t - 15*t**2 - 9*t**2.
-2*(t + 1)*(5*t + 3)
Let x be (0 + 1)*(8/(-88) + 1253/1925). Find r, given that -8/5*r - x*r**3 + 36/25*r**2 + 2/25*r**4 + 16/25 = 0.
1, 2
Let b(q) be the third derivative of -1/2*q**4 - 1/20*q**5 + 0*q + 0 + 1/40*q**6 - 18*q**2 + 2*q**3. Factor b(k).
3*(k - 2)*(k - 1)*(k + 2)
Let f = 2716 - 2713. Suppose -2/7*r**f - 4/7 - 10/7*r - 8/7*r**2 = 0. What is r?
-2, -1
Let p be (-297)/(-7) + (-18)/42. Solve -3*y + 144*y**3 - 3*y - 3*y + 3 - 96*y**4 - p*y**2 = 0.
-1/4, 1/4, 1/2, 1
Let c(b) be the third derivative of b**5/240 + 5*b**4/48 - 3*b**2 + 2. Factor c(k).
k*(k + 10)/4
Let h(a) be the second derivative of -a**5/90 - a**4/54 + 9*a + 1. Factor h(g).
-2*g**2*(g + 1)/9
Let c(z) = 4*z**2 + 8*z + 6. Let q(y) = -5*y**2 - 9*y - 7. Let h = 7 - 13. Let u = -8 - h. Let x(k) = u*q(k) - 3*c(k). Let x(b) = 0. Calculate b.
-2, -1
Let z(w) = w**2 - 7*w + 4. Let l be z(7). Factor f**2 + 3*f**2 + l*f + 4 - 9*f**2 - 3*f**3.
-(f - 1)*(f + 2)*(3*f + 2)
Factor 0 - 16/13*z + 6/13*z**3 - 4/13*z**2.
2*z*(z - 2)*(3*z + 4)/13
Let s(q) be the third derivative of -q**7/280 + 3*q**6/80 - q**5/16 - 2*q**2 - 12*q. Suppose s(z) = 0. What is z?
0, 1, 5
Let h(o) = 195*o**2 - 1585*o + 100. Let q(w) = 65*w**2 - 528*w + 34. Let c(j) = -3*h(j) + 10*q(j). Factor c(t).
5*(t - 8)*(13*t - 1)
Let g(u) be the second derivative of -u**4/96 - 7*u**3/48 + u**2/2 + 764*u. Factor g(o).
-(o - 1)*(o + 8)/8
Factor -150/7*p + 3/7*p**2 + 1875/7.
3*(p - 25)**2/7
Let t be ((-10)/4)/((-6)/(-75) + (-1862)/1400). Determine u, given that -1/7 + 0*u + 1/7*u**t = 0.
-1, 1
Let q(u) be the first derivative of 2*u**7/105 - 2*u**5/15 + 2*u**3/3 - u**2 - 9. Let j(c) be the second derivative of q(c). Let j(d) = 0. What is d?
-1, 1
Let i(n) be the third derivative of n**9/393120 - n**8/65520 - n**7/8190 + n**6/585 - n**5/10 + 8*n**2. Let h(y) be the third derivative of i(y). Factor h(t).
2*(t - 2)**2*(t + 2)/13
Let z = 43 - 73. Let q be (2/z)/((-6)/72). Factor q*y - 1/5*y**2 - 4/5.
-(y - 2)**2/5
Let a(u) be the first derivative of -3*u**5/5 - 3*u**4 + u**3 + 6*u**2 + 53. Factor a(m).
-3*m*(m - 1)*(m + 1)*(m + 4)
Suppose -6*x + 34 + 14 = 12. Factor 2/9*g**4 + x*g + 2*g**3 + 6*g**2 + 0.
2*g*(g + 3)**3/9
Let i(s) be the first derivative of -2 + 9/2*s**2 + 1/4*s**4 + 0*s - 2*s**3. Factor i(y).
y*(y - 3)**2
Let a be -7 - (10/(990/(-1503)))/1. Determine f, given that -82/11*f**2 - 226/11*f**3 + a*f**4 + 162/11*f**5 - 8/11 + 64/11*f = 0.
-1, 2/9, 1
Let p(l) be the first derivative of -11/5*l**3 + 23 - 1/2*l**4 - 4*l**2 - 16/5*l - 1/25*l**5. Find o, given that p(o) = 0.
-4, -1
Suppose 0 = -221*w + 589*w. Factor -2/9*g**4 + 2/9 + 4/9*g - 4/9*g**3 + w*g**2.
-2*(g - 1)*(g + 1)**3/9
Suppose 5*k + 5 = 0, -4*j + 2*k - 10 = -0*k. Let v(y) = y**2 - y - 1. Let i(w) = 9*w**2 + 30*w + 12. Let m(f) = j*v(f) + i(f). What is o in m(o) = 0?
-5, -1/2
Find s such that -1/2*s**3 + 0 + 3/2*s - s**2 = 0.
-3, 0, 1
Let f(x) be the second derivative of -7*x**5/30 - 3*x**4/2 + 4*x**3/9 - 3*x - 1. Suppose f(z) = 0. What is z?
-4, 0, 1/7
Let u(k) be the second derivative of -k**4/14 + 5*k**3/2 - 51*k**2/14 + 121*k. Factor u(y).
-3*(y - 17)*(2*y - 1)/7
Let t = -44 - -49. Determine r so that 4*r**2 + 4 + 0 + 0*r - t*r - 3*r = 0.
1
Let r(s) be the third derivative of -s**6/360 - 7*s**5/90 - 4*s**4/9 + 64*s**3/9 + 125*s**2. Determine a so that r(a) = 0.
-8, 2
Suppose -40 = -3*l + 5. Find q such that -3 + 4*q + 7*q**2 - l*q**2 + 7*q**2 = 0.
1, 3
Let k(h) = -3*h + 17. Let z(v) = v. Let q(n) = -k(n) + z(n). Let b be q(5). Let 1/4*t**2 - 1/4 + 1/4*t**b - 1/4*t = 0. Calculate t.
-1, 1
Factor 14*x**4 + 1149*x - 39*x**4 - 643*x - 195*x**3 + 261*x**2 - 587*x.
-x*(x + 9)*(5*x - 3)**2
Suppose 25 = p + 4*p. Solve 12*q - 2*q**2 + q**3 - q**2 + 9*q**2 + 13 - p = 0.
-2
Let k be (1198/(-755) + 1)/(-1). Let h = k + 2/151. Find b, given that -h - 3/5*b**2 - 6/5*b = 0.
-1
Let k(f) be the second derivative of 7*f**7/30 + 7*f**6/20 + 3*f**5/20 + 5*f**2 - 15*f. Let r(p) be the first derivative of k(p). Factor r(y).
y**2*(7*y + 3)**2
Let d be (-1)/((-7)/6) - (0 + (-19)/35). Factor 1/5*h**2 + 8/5*h + d.
(h + 1)*(h + 7)/5
Let y(u) be the first derivative of -u**5/25 + u**4/5 - 2*u**3/5 + 2*u**2