4*-2 - (-17)/7. Let z be (m/16)/(10/20). Factor -z*c + 1/4*c**3 - 1/4*c**4 + 3/4*c**2 - 1/2.
-(c - 2)*(c - 1)*(c + 1)**2/4
Let t = -265 + 190. Let z = t + 77. Find k, given that -4 - 1/4*k**z - 2*k = 0.
-4
Let j(u) be the second derivative of u**4/12 - 2*u**3/3 + u**2/2 - 7*u. Let b(o) = o - 1. Let c(r) = -3*b(r) - 3*j(r). Suppose c(w) = 0. Calculate w.
0, 3
Let f(y) = -5*y**5 + 3*y**4 - 4*y**3 - 10*y**2 + 6*y + 16. Let m(c) = -c**5 + c**2 + c. Let x(a) = 5*f(a) - 30*m(a). Factor x(d).
5*(d - 2)*(d - 1)*(d + 2)**3
Let d(h) = -41*h**2 + 43*h**2 - 1 + 4 - 3*h. Let l be d(2). Factor 5 + l*u + 2*u**2 + 3*u + 1.
2*(u + 1)*(u + 3)
Let w(s) = 2*s**2 - 12*s. Let r(i) = -5*i**2 + 25*i. Let v(p) = 7*p**2 - p + 1. Let y be v(-1). Let m(d) = y*w(d) + 4*r(d). Factor m(h).
-2*h*(h + 4)
Let k = -1/239634 + -402824743/2635974. Let y = 153 + k. What is l in -y*l**3 - 4/11*l**2 + 4/11 + 2/11*l = 0?
-2, -1, 1
Let w = 0 - -2. Suppose 6*k + 12 + 3*k**w - 3 - 6 = 0. What is k?
-1
Let a(l) be the third derivative of l**10/60480 - l**9/6720 - l**8/5040 - 29*l**5/60 - l**2 + 9*l. Let p(z) be the third derivative of a(z). Factor p(b).
b**2*(b - 4)*(5*b + 2)/2
Let f be -4 + (-4)/4 + 8. Factor 37*z**2 - 25*z**2 + f*z**3 + z**3.
4*z**2*(z + 3)
Let r(o) be the first derivative of -o**6/27 + 2*o**5/9 - 4*o**4/9 + 8*o**3/27 - 188. Determine b, given that r(b) = 0.
0, 1, 2
Let h = -1428 - -1431. Suppose -2/3*x**h - 2 - 10/3*x**2 - 14/3*x = 0. What is x?
-3, -1
Let l(y) be the third derivative of -y**8/420 + 2*y**7/75 + y**6/200 - y**5/15 - 7*y**4/120 + 228*y**2. Determine j, given that l(j) = 0.
-1/2, 0, 1, 7
Let f = 81566/91701 - 6/10189. Factor -f*c + 16/9 + 2/9*c**3 - 4/9*c**2.
2*(c - 2)**2*(c + 2)/9
Let u(g) = -8*g**2 + 117*g - 374. Let y(a) = 33*a**2 - 465*a + 1497. Let s(r) = 21*u(r) + 5*y(r). Factor s(n).
-3*(n - 41)*(n - 3)
Let s = 264113/484187 + -1/44017. Solve 18/11 + s*a**3 - 6/11*a - 18/11*a**2 = 0 for a.
-1, 1, 3
Let k(p) be the third derivative of -p**6/30 - 2*p**5/3 + 11*p**4/6 + 57*p**2 - 1. Solve k(w) = 0.
-11, 0, 1
Let q = 1455 - 1455. Determine p, given that -4/5*p - 4/5*p**4 - 12/5*p**2 - 12/5*p**3 + q = 0.
-1, 0
Let c(z) = -5*z**2 + 1470*z - 54755. Let s(k) = 8*k**2 - 2206*k + 82133. Let l(h) = 7*c(h) + 5*s(h). Find j, given that l(j) = 0.
74
Factor 4/3*o**2 - 224/3*o + 220/3.
4*(o - 55)*(o - 1)/3
Let m be 5/40 - (-126)/16. Factor -2*q**3 + q**3 + 12 + 25*q**2 + m + 40*q + 6*q**3.
5*(q + 1)*(q + 2)**2
Let l(f) be the second derivative of -1/18*f**4 - 15*f + 0 + 2*f**2 + 1/9*f**3. Factor l(k).
-2*(k - 3)*(k + 2)/3
Let f(b) be the third derivative of -1/3*b**5 + 3*b**2 + 0*b + 8/3*b**3 + 1/60*b**6 + 1/168*b**8 + 4/105*b**7 - 1/3*b**4 + 0. Factor f(n).
2*(n - 1)**2*(n + 2)**3
Suppose -3*c = 10*c. Find w such that -2/3*w**2 + 2/3*w**4 - 2/9*w**3 + c + 2/9*w = 0.
-1, 0, 1/3, 1
Let c(x) = -2*x**2 - 5*x + 60. Let j(p) = -p**2 - 3*p + 30. Let w(o) = 4*c(o) - 9*j(o). Factor w(s).
(s - 3)*(s + 10)
Suppose 8*q + 21 = 15*q. Let v = 6 + -2. Find i, given that 27/2*i**5 - 12*i**q + 9*i**2 - 3/2*i - 9*i**v + 0 = 0.
-1, 0, 1/3, 1
Let t(z) = -6*z**4 - 84*z**3 - 550*z**2 - 1118*z - 648. Let d(a) = a**4 + a**2 + a. Let h(u) = -2*d(u) - t(u). Find p, given that h(p) = 0.
-9, -2, -1
Let d be -2*(-584)/288 + -4. Let x(l) be the second derivative of d*l**4 - 2/9*l**3 + 0 + 0*l**2 - 6*l. Let x(b) = 0. What is b?
0, 2
Suppose 325 = 4*d - 19. Solve 5*x + 0*x**4 - 81*x**5 + d*x**5 + 0*x**4 - 10*x**3 = 0.
-1, 0, 1
Let z(c) be the third derivative of c**7/210 - 7*c**6/120 - c**5/12 + 25*c**4/8 - 90*c**2. Let z(g) = 0. What is g?
-3, 0, 5
Let q(k) be the second derivative of 3*k**8/140 + 2*k**7/21 + 13*k**6/90 + k**5/15 + k**3/6 + 5*k. Let t(j) be the second derivative of q(j). Factor t(a).
4*a*(a + 1)**2*(9*a + 2)
Let g(u) be the first derivative of 25*u**4/24 - 215*u**3/6 + 42*u**2 - 50*u/3 - 43. Solve g(w) = 0 for w.
2/5, 25
Let t(j) be the second derivative of -27*j - 4/15*j**5 + 1/6*j**4 + 0*j**2 + 2/9*j**3 + 1/15*j**6 + 0. What is p in t(p) = 0?
-1/3, 0, 1, 2
Let g(p) be the second derivative of 0*p**2 + 1/90*p**5 + 0*p**3 + 0 - 1/54*p**4 - 8*p. What is n in g(n) = 0?
0, 1
Let o be (-8)/16*(-78)/(-9). Let h = 17/3 + o. Factor 2/9*r**4 + 8/3*r**2 - 16/9*r + 0 - h*r**3.
2*r*(r - 2)**3/9
Let f(h) be the first derivative of h**3/18 - h**2/12 - h/3 - 113. Let f(x) = 0. Calculate x.
-1, 2
Let r(k) be the second derivative of -k**6/420 - k**5/35 - 3*k**4/28 - 2*k**2 + 8*k. Let b(t) be the first derivative of r(t). Factor b(w).
-2*w*(w + 3)**2/7
Factor 0 - 9/2*o**2 + 21/4*o - 3/4*o**3.
-3*o*(o - 1)*(o + 7)/4
Suppose 30 = 3*l + 6. Let q be (-1)/(-7) - (-936)/112. Factor l*z**2 + q*z**3 + 5/2*z**4 + 2*z + 0.
z*(z + 1)*(z + 2)*(5*z + 2)/2
Let d(b) = -b**2 + 99*b - 6. Let a(o) = -o**2 + o - 3. Let r(g) = -2*a(g) + d(g). Solve r(z) = 0 for z.
-97, 0
Let w(n) be the first derivative of -n**4/14 - 40*n**3/21 - 53*n**2/7 - 68*n/7 + 78. Determine r so that w(r) = 0.
-17, -2, -1
Suppose 0 = 18*z - 5*z - 0*z - 39. Factor -z*k**2 + 12/7*k + 0 + 6/7*k**3 + 3/7*k**4.
3*k*(k - 1)**2*(k + 4)/7
Let x(y) be the second derivative of y**5/60 - y**4/12 + y**3/6 - 8*y**2 - 10*y. Let w(u) be the first derivative of x(u). Factor w(h).
(h - 1)**2
Let q = -41227/9 + 4581. Solve 10/9*n**2 - 2/9*n**4 + 0 - q*n**3 - 2/3*n = 0.
-3, 0, 1
Let h(l) = -5*l**5 - 4*l**4 + 2*l**3 + 3*l. Let p(w) = w**5 + w**4 - w. Let s(i) = h(i) + 4*p(i). Suppose s(a) = 0. What is a?
-1, 0, 1
Suppose 36 = 10*r + 2*r. Let v(u) be the third derivative of 0*u - 1/84*u**4 + 6*u**2 + 0 + 1/21*u**r - 1/105*u**5. Factor v(h).
-2*(h + 1)*(2*h - 1)/7
Let j = -2443 - -2446. What is c in -3/5*c**2 + c**j - c + 4/5 - 1/5*c**4 = 0?
-1, 1, 4
Suppose w = -2*w + 9. Let r be ((-9)/(-5))/w*30. Determine t, given that r*t**2 + 26*t**3 + 3*t - 7*t + 4*t**5 - 26*t**5 - 18*t**4 = 0.
-1, 0, 2/11, 1
Let b(x) be the second derivative of -x**6/105 - x**5/70 + x**4/42 + x**3/21 + 37*x. Solve b(l) = 0.
-1, 0, 1
Suppose -6*a - o = -a + 66, 2*a - o = -32. Let d be a/(-7) + 0 + -2. Suppose 2/3*y**5 + 2*y**4 + d*y + 4/3*y**3 + 0*y**2 + 0 = 0. Calculate y.
-2, -1, 0
Find b such that -48/5*b - 14*b**5 + 694/5*b**2 - 342/5*b**4 - 162/5*b**3 - 72/5 = 0.
-3, -2/7, 2/5, 1
Let k(p) = -p**2 + 4*p. Let j be k(4). Suppose j = -4*l - 4*f + 12, 5*f + 6 = l + l. Factor -16*a**4 + 4*a**l + 14*a**4 - 8*a**3 + 4*a + 2*a**2.
-2*a*(a - 1)*(a + 1)*(a + 2)
Suppose -53/3*k**2 + 0 + 1/3*k**4 - 10/3*k**3 - 14*k = 0. What is k?
-3, -1, 0, 14
Let d = 1/2291 + 4573/20619. Factor 4/9*x + 2/3*x**2 + d*x**3 + 0.
2*x*(x + 1)*(x + 2)/9
Let k = 36 + -35. Suppose 0 = -2*t + d + 2, -t - 5*d = -13 + k. Determine p, given that -2/3*p**3 + 0*p**t + 1/3*p**5 + 1/3*p + 0 + 0*p**4 = 0.
-1, 0, 1
Let s(h) be the second derivative of -h**9/5040 + h**7/280 + h**6/120 - 8*h**4/3 - 34*h. Let z(g) be the third derivative of s(g). Let z(c) = 0. What is c?
-1, 0, 2
Let b(y) be the second derivative of y**5/100 + 13*y**4/60 - 23*y**3/15 + 16*y**2/5 - 176*y. Solve b(t) = 0.
-16, 1, 2
Let k(v) be the second derivative of 10*v**2 + 1/2*v**5 + 0 - 20/3*v**3 - 1/6*v**6 + 5/4*v**4 + 37*v. Let k(s) = 0. What is s?
-2, 1, 2
Let j(o) = -15*o**2 + 3*o - 3. Let m be j(-3). Let b = m - -150. Solve -1/2*i**b + 1/2*i - 1/2 + 1/2*i**2 = 0 for i.
-1, 1
Let w = -1 + 6. Suppose -3*m - 10 = -u + 2, 4*u + w*m = 14. Factor 0 - 15*p + 3*p**3 - 6 + u*p.
3*(p - 2)*(p + 1)**2
Find c such that 2*c**3 + 4*c**2 + 34*c**2 + 58*c**2 + 110*c**2 + 204*c = 0.
-102, -1, 0
Let z(a) = 3*a**3 + 13*a**2 - 32*a - 32. Let t(y) = -2*y**2 + y + 1. Let v(o) = 5*t(o) + z(o). Let v(k) = 0. What is k?
-3, -1, 3
Let t(w) be the third derivative of w**6/540 - w**4/9 + 5*w**3/3 - 12*w**2. Let r(a) be the first derivative of t(a). Let r(i) = 0. Calculate i.
-2, 2
Let j(k) be the first derivative of k**6/9 - k**4/3 + k**2/3 + 15. Determine y so that j(y) = 0.
-1, 0, 1
Suppose -5*b + 13 = -w, 16*b = -3*w + 15*b + 9. Factor 6/11 - 8/11*r + 2/11*r**w.
2*(r - 3)*(r - 1)/11
Let z(n) be the second derivative of 1/54*n**4 + 0*n**2 + 0 + 7*n - 2/27*n**3. Determine x so that z(x) = 0.
0, 2
Suppose 0 = 8*h - 4*h - 12, 0 = -4*m - 4*h + 32. Factor 0 + 0*f + 2/17*f**4 - 2/17*f**m - 2/17*f**2 + 2/17*f**3.
-2*f**2*(f - 1)**2*(f + 1)/17
Let p(d) be the first derivative of d**3/3