. Calculate s.
0
Let x(n) = -6*n + 1. Let z be x(-4). Let l(a) = -a**2 - 9*a - 6. Let g be l(-8). Factor 5*p**2 + 50*p - z + 95 + 0*p**g + 55.
5*(p + 5)**2
Let g(b) = 33*b**3 - 87*b**2 + 15*b. Let x = 8 + -17. Suppose -19*m = -15*m + 16. Let l(n) = -17*n**3 + 44*n**2 - 8*n. Let t(f) = m*g(f) + x*l(f). Factor t(j).
3*j*(j - 2)*(7*j - 2)
Let g(c) = c**5 + 5*c**4 + 5*c**3 - 17*c**2 + 6*c. Let h(m) = -2*m**5 - 10*m**4 - 11*m**3 + 34*m**2 - 11*m. Let l(w) = -13*g(w) - 6*h(w). Factor l(k).
-k*(k - 1)**2*(k + 3)*(k + 4)
Factor -14*b + 4817*b**2 - 4801*b**2 + b**3 + b**5 + 4 + b**5 - 4*b**4 - 5*b**3.
2*(b - 1)**4*(b + 2)
Suppose -4*t = 50 - 62. Suppose -4*f + 2 = 5*p, 5*p - f = 2*p + 8. Solve 6/7 - t*z + 15/7*z**p = 0.
2/5, 1
Let x = 54 - 52. Factor 4*s**3 + 20*s**x - 6*s - 11*s + 5*s - 12*s.
4*s*(s - 1)*(s + 6)
Suppose 2*w = -i + 3*w - 19, 2*i + 35 = 3*w. Let b be (-33)/i*8/6. Let l + 1 + 1/4*l**b = 0. Calculate l.
-2
Let c = 720/13 - 4936/91. Solve -c*x + 2/7*x**2 + 6/7 = 0 for x.
1, 3
Solve -192/5*j**4 - 4251/5*j**2 - 432/5 + 336*j**3 + 504*j = 0.
3/8, 4
Determine j so that 20/3*j + 5/3*j**5 + 0 - 65/3*j**2 + 25*j**3 - 35/3*j**4 = 0.
0, 1, 4
Let y(z) be the third derivative of -1/27*z**3 + 6*z**2 + 0*z - 1/540*z**6 + 1/270*z**5 + 1/108*z**4 + 0. Factor y(i).
-2*(i - 1)**2*(i + 1)/9
Let i(s) = s**3 + 17*s**2 + 17*s - 5. Let f be i(-16). Let m be (-5)/(-35) + (-39)/f. Factor -x**2 + 6*x**3 - 3*x**m + 0*x**2.
2*x**2*(3*x - 2)
Let u(q) be the first derivative of -18*q**5/5 + 25*q**4/2 + 4*q**3 - 12. Determine j, given that u(j) = 0.
-2/9, 0, 3
Let s = 3949 - 19739/5. Let r = 35/4 - 163/20. Find b such that -3/5*b**2 + s + r*b = 0.
-1, 2
Let x = 2 - 3. Let t(b) be the third derivative of -b**6/60 - b**5/20 + b**3/6 - b**2 - 10*b. Let p(q) = q**3 + q**2 - 1. Let r(o) = x*p(o) - t(o). Factor r(v).
v**2*(v + 2)
Let h(f) = f**2 + f + 1. Suppose -3*j - 5 = 5*v, 5*j = 3*v + 2*v + 45. Let w(s) = s**2 + s - 14. Let y(l) = v*h(l) - w(l). Factor y(t).
-5*(t - 1)*(t + 2)
Let y(p) = -6*p - 2. Let v be y(-1). Factor 2*a**4 - 6*a - 36*a**3 + 13*a**4 + 27*a**2 + 2*a**v - 2*a**4.
3*a*(a - 1)**2*(5*a - 2)
Let n(b) be the first derivative of 2*b**3/3 - 15*b**2 + 92. Factor n(o).
2*o*(o - 15)
Let s(w) be the third derivative of -w**5/270 - w**4/108 + 50*w**2. Find k such that s(k) = 0.
-1, 0
Suppose 21*x - 217 = -175. Let -1/2*q**x + q + 3/2 = 0. Calculate q.
-1, 3
Let p(i) be the third derivative of -i**9/30240 - i**8/3360 - i**5/5 - 26*i**2. Let d(y) be the third derivative of p(y). Find o such that d(o) = 0.
-3, 0
Let s(c) = 357*c**2 - 378*c + 108. Let o(m) = 1072*m**2 - 1137*m + 324. Let h(i) = -6*o(i) + 17*s(i). Determine t so that h(t) = 0.
6/11
Suppose 0 = -9*v + 44 - 8. Let k(o) = -10*o + 24. Let u(s) = s**2 + 1. Let t(a) = v*u(a) + 4*k(a). Factor t(z).
4*(z - 5)**2
Let q(g) be the first derivative of g**8/280 + 23*g**7/560 + g**6/8 - 9*g**5/80 - 4*g**3/3 + 9. Let s(h) be the third derivative of q(h). Factor s(x).
3*x*(x + 3)**2*(4*x - 1)/2
Let c(t) = 13*t**3 - 11*t**2 + 4*t - 13. Let f(z) = 7*z**3 - 5*z**2 + z - 7. Let w(b) = -4*c(b) + 7*f(b). Factor w(p).
-3*(p - 1)**3
Let a(f) be the first derivative of f**3 - 9*f**2 + 15*f + 580. Determine h, given that a(h) = 0.
1, 5
Suppose -5*q + 5 + 5 = 0. Suppose -5*u = -2*g + 24, 2*g + 6 = -3*u - 2. Find l, given that -38*l + 38*l + 2*l**q - g = 0.
-1, 1
Let b = -40294/375 + 19/375. Let g = b + 108. Factor 9/5*v**4 + 9/5*v - g - 3/5*v**5 - 6/5*v**3 - 6/5*v**2.
-3*(v - 1)**4*(v + 1)/5
Factor 3552*x**2 - 3*x**5 + x**5 - 3548*x**2 + 2*x - 4*x**4.
-2*x*(x - 1)*(x + 1)**3
Let p(c) = c**3 - c**2 + c. Let v(l) = 5*l**2 + 20*l. Let h(b) = -5*p(b) + v(b). Factor h(k).
-5*k*(k - 3)*(k + 1)
Factor -4/7*w**3 - 96/7*w**2 - 280 - 108*w.
-4*(w + 7)**2*(w + 10)/7
Let h = -56 + 116. Let v(r) = 4*r**2 + 2*r. Let i be v(-1). Factor 3*s**3 - 60 + 3*s**i + h.
3*s**2*(s + 1)
Find f such that 0 + 3/8*f**3 - 51/4*f**2 + 867/8*f = 0.
0, 17
Let d = -95492/11 + 8684. Determine p, given that -128/11 - 2/11*p**2 + d*p = 0.
8
Let x = 1 + 2. Suppose -x*y = -7 - 5. Factor -7*j**y + 2 + 5*j - 5*j**3 - 1 + 9*j**2 - 3.
-(j - 1)*(j + 1)**2*(7*j - 2)
Let p(o) = -o**3 + 8*o**2 - o + 10. Suppose 0*g - 32 = -4*g. Let n be p(g). Factor 15*q**3 - 58*q**2 + 10*q**n + 12*q + 23*q**4 - 2*q**4.
3*q*(q - 1)*(q + 2)*(7*q - 2)
Let r(z) be the third derivative of z**5/210 - z**4/21 + 4*z**3/21 + 4*z**2. Let r(s) = 0. What is s?
2
Let f = -1286 - -1286. Solve 8/5*b**2 - 8/5*b + f - 2/5*b**3 = 0.
0, 2
Let q be (-13)/(819/27) + (-2)/(-2). Factor -3/7*i + q - 1/7*i**2.
-(i - 1)*(i + 4)/7
Let f(q) be the first derivative of 0*q**3 + 1 - 3/4*q**4 + 0*q**5 + 1/2*q**6 + 0*q + 0*q**2. Factor f(d).
3*d**3*(d - 1)*(d + 1)
Let c(j) = -j**3 - 4*j**2 + 1. Let d be c(4). Let r = d - -129. Let 1/4*u**r + 0*u - 1/4 = 0. What is u?
-1, 1
Let 50*d**3 - 1892*d + 1900*d + 55*d**2 - 15*d**2 = 0. What is d?
-2/5, 0
Let y(c) be the second derivative of -c**8/40320 + c**7/2520 - c**6/540 + 23*c**4/6 - 51*c. Let q(h) be the third derivative of y(h). Let q(r) = 0. Calculate r.
0, 2, 4
Let o(m) be the second derivative of -m**4/96 + m**3/6 - m**2 - 14*m - 1. Factor o(u).
-(u - 4)**2/8
Let s(x) = -21*x**3 + 33*x**2 + 58*x + 24. Let q(m) = -125*m**3 + 197*m**2 + 350*m + 144. Let k(b) = 6*q(b) - 34*s(b). Suppose k(l) = 0. Calculate l.
-2/3, 3
Factor -8/5 + 32*n - 78/5*n**2.
-2*(n - 2)*(39*n - 2)/5
Let n(v) be the third derivative of -11*v**5/120 - 41*v**4/16 - 11*v**3/6 + 287*v**2. Factor n(k).
-(k + 11)*(11*k + 2)/2
Let b(l) be the first derivative of l**3/21 + l**2/14 - 6*l/7 + 71. Factor b(n).
(n - 2)*(n + 3)/7
Let j be (-2)/11 + (399/77 - 6). Let v be ((-3)/(-2))/(j + 124/16). Suppose 2/9 + 0*w**3 + 0*w + v*w**4 - 4/9*w**2 = 0. Calculate w.
-1, 1
Let v = 24 + -48. Let y(b) = b**4 - b**3 - b + 1. Let o(d) = 7*d**4 - 9*d**3 + 5*d**2 - 11*d + 8. Let t(g) = v*y(g) + 3*o(g). Factor t(r).
-3*r*(r - 1)**2*(r + 3)
Suppose 2*a - 7*a = -5*n - 15, 3*n + 2*a = -34. Let v be (-5)/10*(n - -2). Factor v - 2 + 0*c + c**2 - 2*c.
(c - 1)**2
Let r(g) be the first derivative of -4*g**5/5 + 48*g**4 - 2104*g**3/3 - 2400*g**2 - 2500*g - 333. Solve r(t) = 0 for t.
-1, 25
Let h(r) be the second derivative of 1/70*r**5 + 1/21*r**3 + 1/21*r**4 + 10*r + 0*r**2 + 0. Find o, given that h(o) = 0.
-1, 0
Let w(u) = -83*u + 498. Let s be w(6). Factor 0*p + s - 2/7*p**2.
-2*p**2/7
Let p(b) be the second derivative of -3*b**5/20 - 63*b**4/4 - 540*b**3 - 4050*b**2 + b - 89. Factor p(c).
-3*(c + 3)*(c + 30)**2
Let d(o) be the third derivative of o**9/105840 - o**8/20160 - o**7/2520 - o**6/1680 - o**5/60 - 15*o**2. Let c(n) be the third derivative of d(n). Factor c(f).
(f - 3)*(f + 1)*(4*f + 1)/7
Let 276*h**3 + 208 + 408*h + 93*h**4 - 4*h**3 - 74*h**3 + 3260 + 363*h**3 - 2589*h**2 + 3*h**5 = 0. What is h?
-17, -1, 2
Solve 28227 - 331*q + 3*q**2 - 336*q + 85*q = 0 for q.
97
Let i(v) = -v**3 - 12*v**2 - 11*v + 2. Let t = 5 + -16. Let k be i(t). Let -2*x + k*x + 4*x**3 - 2*x**2 - 2*x + 0*x**2 = 0. Calculate x.
-1/2, 0, 1
Let l(i) = 4*i**2 - 4*i - 1. Let n be l(3). Let w = n - 11. Let -5*m**2 - w*m + 4*m**3 - m**4 + 0*m**4 + 14*m = 0. What is m?
0, 1, 2
Let w(l) = -4*l**4 + 5*l**3 + 57*l**2 - 26*l - 20. Let v(q) = -q**4 - 2*q**2 + q. Let i(r) = 6*v(r) + w(r). Suppose i(f) = 0. What is f?
-2, -1/2, 1, 2
Let j(r) = 4*r**2 + 20*r - 48. Let w(f) = f**2 - f - 1. Let h(t) = j(t) - 8*w(t). Suppose h(l) = 0. Calculate l.
2, 5
Let n be (32/12 - 1)*3. Suppose 24 = -2*m + n*m. Determine b, given that 2 - 2*b**2 + 0*b + 8*b - 1 - m*b**3 + 1 = 0.
-1, -1/4, 1
Let w(l) = 2*l - 5. Let t = -9 + 14. Let k be w(t). Let -k - 3*x**2 - 5*x - x - 1 - 3*x = 0. Calculate x.
-2, -1
Let c be 330/(-231)*(-14)/48. Let q(z) be the second derivative of -1/84*z**7 - z - 1/4*z**5 + 1/4*z**2 + 5/12*z**4 + 0 + 1/12*z**6 - c*z**3. Factor q(f).
-(f - 1)**5/2
Let s(u) be the first derivative of 1/3*u**4 - 2 - 1/3*u**2 + 2/3*u - 4/9*u**3 - 1/9*u**6 + 2/15*u**5. Find g such that s(g) = 0.
-1, 1
Let g be -5 + -45 + (0 - -2). Let o be 33/(-132)*g/7. Solve 4/7 - o*l**4 + 8/7*l**3 - 12/7*l + 4/7*l**5 + 8/7*l**2 = 0 for l.
-1, 1
Let j = 105037/9 - 11709. Let t = -38 - j. Suppose -4/9*g**2 + 2/9*g + 0 + t*g**3 = 0. What is g?
0, 1
Let g(r) = 14*r**4 - 12*r**3 - 2*r**2 - 2. Let k