Let x be v(11). Factor -3/8*m**3 + 15/8*m**x + 0 + 0*m.
-3*m**2*(m - 5)/8
Suppose -3*p + 0*p - 18 = 0. Let z(v) = -v**4 + v**2 + v + 1. Let y(o) = 11*o**4 - 5*o**3 - 11*o**2 - o - 6. Let k(n) = p*z(n) - y(n). Factor k(j).
-5*j*(j - 1)**2*(j + 1)
Factor -1/2*d**3 + 9/4*d + 0 - 17/4*d**2.
-d*(d + 9)*(2*d - 1)/4
Let h = -52 + 54. Determine c so that h*c - 12*c**2 - 4*c**3 + 17*c - 20 + 17*c = 0.
-5, 1
Let z(g) = 4*g**2 + 8*g - 8. Let l(y) = y**2 + 3*y - 3. Suppose -15 = 3*b - 8*b. Let a(c) = b*z(c) - 8*l(c). Determine h, given that a(h) = 0.
0
Let g(s) be the second derivative of s**7/8820 + s**6/315 + 4*s**5/105 - s**4/4 - s. Let o(y) be the third derivative of g(y). Find p, given that o(p) = 0.
-4
Let a(x) be the third derivative of 1/56*x**4 + 0 - 2/7*x**3 + 0*x + 1/35*x**5 - 8*x**2 - 1/280*x**6. Factor a(g).
-3*(g - 4)*(g - 1)*(g + 1)/7
Suppose -n + 2*t + 13 = 0, n - t = -1 + 9. Let u(c) be the first derivative of 4/9*c**n + 2/3*c**2 - 8 - 8/3*c. Factor u(a).
4*(a - 1)*(a + 2)/3
Find b, given that -37*b**3 - 33*b**3 + b**2 - 33*b**3 - 33*b**3 + b**5 + 3*b**4 + 139*b**3 = 0.
-1, 0
Suppose -77 = -34*c + 25. Let p(m) be the third derivative of -1/300*m**5 + 0*m + 1/600*m**6 + 0 + 0*m**4 + 0*m**3 + c*m**2. Suppose p(r) = 0. What is r?
0, 1
Let b(k) = -95*k - 545. Let v(h) = 7*h + 39. Let q(p) = 4*b(p) + 55*v(p). Let d be q(7). Factor d + 2/5*g + 2/5*g**2.
2*g*(g + 1)/5
Factor 21*p + 6*p**2 - 6 + 6*p**4 - 11*p**2 - 3*p**5 + 3*p**3 + 3*p**3 - 19*p**2.
-3*(p - 1)**4*(p + 2)
Let m(o) = 43*o - 12 - 72*o**3 - 4*o + 60*o**3 - 25*o**2. Let k(d) = 18*d**3 + 37*d**2 - 59*d + 18. Let x(f) = -5*k(f) - 7*m(f). Factor x(w).
-2*(w - 1)*(w + 3)*(3*w - 1)
Let 62*s**2 + 0*s + 1/3*s**3 + 0 = 0. What is s?
-186, 0
Let c(w) be the first derivative of -w**6/300 + 2*w**5/75 + 29*w**2/2 - 20. Let y(p) be the second derivative of c(p). Factor y(a).
-2*a**2*(a - 4)/5
Let v(k) = -2*k**3 + k**2 - k + 2. Let w(b) = 10*b**3 + 621*b**2 + 32451*b + 562426. Let n(f) = 3*v(f) + w(f). Solve n(z) = 0 for z.
-52
Let j = -43 - -43. Let l be j + -2 + 264/96. Determine x so that 0*x + 3/4*x**2 - l = 0.
-1, 1
Let o(a) = 15*a - 2. Suppose -2*x + 3 = -1. Let t be o(x). Determine n, given that 0*n**2 + n + t*n**4 + 18*n**5 - 8*n**2 + n - 4*n**3 - 4*n**4 = 0.
-1, 0, 1/3
Let b = 127 - 101. Suppose b = x + 24. Solve -1/3 + 1/6*j**x - 1/6*j = 0 for j.
-1, 2
Let x(m) be the second derivative of -m**7/5460 - m**6/1170 - m**5/780 - 3*m**3 + 20*m. Let g(h) be the second derivative of x(h). What is z in g(z) = 0?
-1, 0
Suppose 84 - 84 = -157*o. Factor 1/2*j**2 - 3*j + o.
j*(j - 6)/2
Let b(t) be the third derivative of t**6/660 - t**5/110 - t**4/33 + 2*t**2 - 138. Factor b(n).
2*n*(n - 4)*(n + 1)/11
Find h such that -42*h**5 + 264*h - 239*h**4 - 401*h**3 + 436*h**4 + 260 + 51*h**5 - 7*h**2 - 704*h**2 + 382*h**4 = 0.
-65, -2/3, 1
Let n be 1/((-1)/10)*20/(-50). Let l(a) be the second derivative of 2/3*a**3 + 0 + 4*a**2 - 1/3*a**n + 3*a. Solve l(f) = 0.
-1, 2
Let r = 44/351 - -64/351. Let -4/13*n**3 + 8/13*n**2 + 2/13*n - 4/13*n**4 - r + 2/13*n**5 = 0. What is n?
-1, 1, 2
Let u(p) be the first derivative of -10 + 0*p + 1/3*p**6 + 0*p**2 + 0*p**3 - 4/5*p**5 + 1/2*p**4. Factor u(j).
2*j**3*(j - 1)**2
Let i(l) be the third derivative of 5/24*l**4 - 1/21*l**7 + 0*l**3 + 0*l - 2*l**2 + 1/6*l**5 - 5/336*l**8 + 0*l**6 + 0. Factor i(q).
-5*q*(q - 1)*(q + 1)**3
Let g be 4/(-10) - ((-12219)/60 - 6). Let f = -209 + g. Factor -f + 0*h + 1/4*h**2.
(h - 1)*(h + 1)/4
Let w(a) = -a**3 - a - 4. Let i be w(-2). Suppose -l + i*l = l. Factor 2/3*t + l + 2/3*t**3 + 4/3*t**2.
2*t*(t + 1)**2/3
Suppose 5*v + 5*g + 58 = 13, -4*g = 2*v + 20. Let h be (-2)/(-7)*((-48)/v + 1). Let 16/3*i**h + 2/3 + 4*i - 6*i**4 - 4*i**3 = 0. Calculate i.
-1, -1/3, 1
Let n be 181*5/450 + -2. Let q(m) be the second derivative of -n*m**5 + 0*m**2 + 0*m**3 + 0 - 1/54*m**4 + 4*m. Determine p, given that q(p) = 0.
-1, 0
Let h(m) = -4*m**2 + 276*m + 308. Let y(i) = i**2 - 55*i - 62. Let q(k) = -3*h(k) - 14*y(k). Solve q(c) = 0 for c.
-28, -1
Let l(i) be the first derivative of -i**4/2 + 2*i**3 + 18*i**2 + 581. Factor l(c).
-2*c*(c - 6)*(c + 3)
Let q(k) be the third derivative of k**8/1344 + k**7/60 + 73*k**6/480 + 43*k**5/60 + 11*k**4/6 + 8*k**3/3 + 22*k**2 + 2*k. Factor q(p).
(p + 1)**2*(p + 4)**3/4
Let -10/13*y**4 + 0 - 2/13*y**5 + 0*y - 16/13*y**3 - 8/13*y**2 = 0. Calculate y.
-2, -1, 0
Let q(t) be the third derivative of -t**5/30 + 11*t**4/12 - 694*t**2. Find m such that q(m) = 0.
0, 11
Suppose 62*v**2 + 54*v**2 - 8 - 117*v**2 + 9*v = 0. What is v?
1, 8
Let j(h) = -h**2 + 12*h - 31. Let l be j(5). Let -2*z**5 + 16*z**2 - 54*z**l - z + 66*z**4 - 24*z**3 + z = 0. Calculate z.
0, 2
Suppose 117 = -6*g + 141. Let q(k) be the second derivative of 8/3*k**2 + 1/36*k**g + k - 4/9*k**3 + 0. Let q(j) = 0. What is j?
4
Suppose -14*m + 5 + 37 = 0. Let v be 1*7 - 2/(-2). What is d in -9*d**2 + m*d**2 + 12*d + v + 10*d**2 = 0?
-2, -1
Let x(q) be the third derivative of q**6/480 - 77*q**5/240 + 95*q**4/6 - 361*q**3/6 + 12*q**2 - q. Factor x(y).
(y - 38)**2*(y - 1)/4
Let g = -109 - -112. Factor -37*u**2 + 5*u**g + 225*u + 65*u**2 + 32*u**2 + 250.
5*(u + 2)*(u + 5)**2
Let h(f) = -20*f**4 + 256*f**3 - 820*f**2 - 6848*f - 8128. Let y(l) = -7*l**4 + 85*l**3 - 273*l**2 - 2282*l - 2710. Let k(j) = 3*h(j) - 8*y(j). Factor k(v).
-4*(v - 13)**2*(v + 2)**2
Let k(x) be the first derivative of -x**6/600 + x**5/100 + 3*x**4/40 + 13*x**3/3 - 24. Let u(r) be the third derivative of k(r). Determine m so that u(m) = 0.
-1, 3
Let p(k) be the first derivative of -k**7/2520 - k**6/1080 + k**5/360 + k**4/72 - 2*k**3 + 9. Let h(n) be the third derivative of p(n). Factor h(s).
-(s - 1)*(s + 1)**2/3
Let g(a) be the first derivative of -5*a**6/6 + 8*a**5 + 5*a**4/4 - 40*a**3/3 + 173. What is p in g(p) = 0?
-1, 0, 1, 8
Solve 2800*k**4 - 1448*k**2 + 1220*k**3 - 125*k**5 + 160 + 625*k**5 - 112*k - 96*k = 0 for k.
-5, -1, -2/5, 2/5
Factor 0 - 11/2*x**4 + 39/2*x**3 - 49/2*x**2 + 1/2*x**5 + 10*x.
x*(x - 5)*(x - 4)*(x - 1)**2/2
Factor -1/2*i**5 + 0*i + 3*i**3 + 3/4*i**4 + 7/4*i**2 + 0.
-i**2*(i + 1)**2*(2*i - 7)/4
Let z(b) be the second derivative of -3*b**5/20 - 3*b**4 + b**3/2 + 18*b**2 + 14*b. Find y such that z(y) = 0.
-12, -1, 1
Let r(c) be the third derivative of -c**7/10080 + c**5/480 - 13*c**4/24 - 22*c**2. Let a(d) be the second derivative of r(d). Let a(l) = 0. What is l?
-1, 1
Suppose 4*x - 3*c = 7, -3*x + 15 = -0*x + c. Let a = 20/3 + -10/9. Solve -8 - 218/9*s**2 - a*s**x - 104/3*s + 260/9*s**3 = 0 for s.
-2/5, 3
Suppose -9/5*r**5 - 33/5*r**4 + 0 - 2/5*r - 37/5*r**3 - 3*r**2 = 0. Calculate r.
-2, -1, -1/3, 0
Let q(c) = -c + 14. Let m be q(18). Let v be (6/m)/((-13)/(65/30)). Factor 1/4*l**2 - 1 + v*l**3 - l.
(l - 2)*(l + 1)*(l + 2)/4
Let m(z) = -2*z**2 - z - 11. Let n(a) = 7*a**2 + 3*a + 43. Let d(t) = -22*m(t) - 6*n(t). Let k(s) = -s**2 - 2*s + 8. Let l(b) = -3*d(b) - 7*k(b). Factor l(u).
(u - 2)*(u + 4)
Let d(q) be the second derivative of -q**7/105 - 29*q**6/75 - 96*q**5/25 - 268*q**4/15 - 688*q**3/15 - 336*q**2/5 - 9*q - 14. Find s, given that d(s) = 0.
-21, -2
Let p(o) be the third derivative of o**6/12 + 43*o**5/30 + 11*o**4/6 - 16*o**3/3 + 44*o**2 + 1. What is f in p(f) = 0?
-8, -1, 2/5
Let k(g) be the third derivative of -g**7/7560 + g**6/540 - g**5/90 + 3*g**4/8 - 8*g**2. Let b(h) be the second derivative of k(h). Factor b(f).
-(f - 2)**2/3
Suppose 12 = 5*p - 78. Let z be (1068/p)/((-4)/(-6)). Factor -96*b - 138*b**2 - 328*b**3 - 327*b**4 - z*b**3 + 42*b**4 - 12 - 153*b**2 - 75*b**5.
-3*(b + 1)**3*(5*b + 2)**2
Let f(d) be the first derivative of -d**7/14 + d**6/5 - d**4/2 + d**3/2 - d - 6. Let k(v) be the first derivative of f(v). Solve k(i) = 0.
-1, 0, 1
Let d(i) be the second derivative of 31*i + 5/6*i**4 + 0*i**2 - 1/4*i**5 + 0 + 0*i**3. Solve d(l) = 0.
0, 2
Let n(r) = -r**2 + r + 1. Let h(p) = -6*p - 6*p + 4*p - 12. Let u(f) = h(f) - 4*n(f). Factor u(d).
4*(d - 4)*(d + 1)
Suppose 3*p + 3*w - 147 = 0, 0 = -3*p + 5*w - w + 126. Let -26*c + c**3 + p*c - 6*c**3 = 0. What is c?
-2, 0, 2
Factor 4 - 12 - 8 + 4*h**2.
4*(h - 2)*(h + 2)
Suppose 0 = -5*p + 5*r - 5, -5*p + 5 = -2*r + 1. Factor -9*n**p + 2 - 44*n + 11*n**2 + 38 + 2*n**2.
4*(n - 10)*(n - 1)
Let c(u) be the first de