, given that u(s) = 0.
-1, 0, 1, 13
Suppose -o = -5*d + 2*d - 9, 69 = 5*o - 3*d. Let q be 9/6 - (5/2)/(-5). Factor -o*k**3 + 10*k**3 + 7*k**q - k**2 + 4*k + 7*k**3.
2*k*(k + 1)*(k + 2)
Determine r so that 7/2*r**4 - 1/4*r**5 - 11*r**3 + 10*r**2 + 0 + 0*r = 0.
0, 2, 10
Let p(s) = -s - 19. Let k be p(-24). Let c(o) = o**3 + 6*o**2 + o + 1. Let x be c(-5). Find r, given that 10*r**2 - 136 + 136 + 6*r**3 + k*r**5 - x*r**3 = 0.
-2, 0, 1
Suppose 5*n - 196*u = -191*u + 75, 0 = -4*n - 2*u - 18. Suppose 12/5 + 34/5*w + 22/5*w**n = 0. Calculate w.
-1, -6/11
Let w(s) be the first derivative of 1/6*s**3 + 53 - 1/2*s**2 - 4*s. What is i in w(i) = 0?
-2, 4
Let a(y) be the second derivative of -1/20*y**5 - 13/6*y**4 + 0*y**2 + 77*y + 0*y**3 - 2. Factor a(p).
-p**2*(p + 26)
Suppose -3*a + 42 = 0, 22065*a = 3*p + 22064*a + 8. Determine m so that 22/7 - 2/7*m**p + 20/7*m = 0.
-1, 11
Suppose -6*k + 190 + 74 = 0. Suppose 0 = -42*b + 64*b - k. Factor -1/7 + 1/7*c**5 - 2/7*c**b + 3/7*c**4 + 2/7*c**3 - 3/7*c.
(c - 1)*(c + 1)**4/7
Let y(w) = -w**4 + w**3 + w**2 + w + 1. Let f = 591 - 589. Let u(h) = -2*h**5 - h**4 + 37*h**3 + 41*h**2 + 19*h + 7. Let p(n) = f*u(n) - 14*y(n). Factor p(s).
-4*s*(s - 6)*(s + 1)**3
Let p(i) be the third derivative of -i - 1/20*i**5 + 5/2*i**4 + 45*i**2 + 0 - 19/2*i**3. Let p(a) = 0. Calculate a.
1, 19
Let s(m) be the second derivative of -1/2*m**3 - 1/4*m**4 + 16*m + 27/2*m**2 + 0 - 1/20*m**5. Let g(i) be the first derivative of s(i). Factor g(u).
-3*(u + 1)**2
Factor -31*d + 11*d**3 - 4*d**4 + 94*d - 9*d - 20*d**2 - 35*d**3 - 6*d.
-4*d*(d - 1)*(d + 3)*(d + 4)
Let u(r) be the third derivative of r**5/60 + 403*r**4/12 + 162409*r**3/6 + 83*r**2 + 7. Find c, given that u(c) = 0.
-403
Factor 1/9*s**2 - 16/3*s - 105.
(s - 63)*(s + 15)/9
Let l(y) = -3*y**2 - 182*y - 503. Let v(b) = -3*b**2 - 180*b - 501. Let m(r) = -3*l(r) + 4*v(r). Factor m(q).
-3*(q + 3)*(q + 55)
Let s(t) be the second derivative of 0*t**2 + 0*t**5 + 0*t**4 + 2 + 1/40*t**6 + 0*t**3 + 1/56*t**7 + 36*t. Factor s(l).
3*l**4*(l + 1)/4
Factor 2524/3 + 1258/3*c - 2/3*c**2.
-2*(c - 631)*(c + 2)/3
Suppose -5 = 2*t + q, -5*t - 37*q + 35*q - 8 = 0. Factor -5/4*p - 3/2 + 1/4*p**t.
(p - 6)*(p + 1)/4
Factor 6*r**3 + 69/2 - 267/2*r**2 - 105*r.
3*(r - 23)*(r + 1)*(4*r - 1)/2
Let k(b) = -7*b**2 - 2*b. Let p(a) be the second derivative of 85*a**4/12 + 25*a**3/6 - 92*a + 1. Let s(r) = 25*k(r) + 2*p(r). Factor s(d).
-5*d**2
Suppose -653 = 4*x + 439. Let b = -191 - x. Factor -4*q**2 - b*q + 41*q - 4 + 33*q.
-4*(q + 1)**2
Determine u so that 185 + 100 - 11 + 36*u**2 + 2240*u + 222 = 0.
-62, -2/9
Let q(i) be the third derivative of -i**9/15120 + i**8/1260 - i**7/315 - 6*i**5/5 + 2*i**2 + 3*i. Let f(l) be the third derivative of q(l). Factor f(z).
-4*z*(z - 2)**2
Let f(x) be the first derivative of -2*x**3/3 + 45*x**2/2 + 53*x + 26. Let v(g) = 5*g**2 - 90*g - 105. Let w(j) = 5*f(j) + 3*v(j). Find r, given that w(r) = 0.
-1, 10
Let r(v) = -32*v - 1053. Let i be r(-33). Let z be 3/((-30)/(-28))*5. Factor -4*f**2 + z - 4*f**i + 4 - 18.
-4*f**2*(f + 1)
Let s(m) be the first derivative of -7*m**3/4 - 943*m**2/8 + 45*m/2 + 8208. Let s(x) = 0. Calculate x.
-45, 2/21
Let b(j) be the third derivative of -j**6/2160 - 49*j**5/720 + 19*j**3/2 + 182*j**2. Let p(l) be the first derivative of b(l). Factor p(s).
-s*(s + 49)/6
Let g(d) be the first derivative of -2*d**3/21 - 8*d**2/7 + 18*d/7 - 1341. Find s such that g(s) = 0.
-9, 1
Suppose 6*k = 21 - 9. Find v, given that 262*v**2 + 240 + 75*v - 23*v**4 - 475*v - 2*v**4 - 62*v**k + 5*v**5 = 0.
-3, 2
Let r(j) = j**2 - 158*j - 283. Let n(t) = t**2 - 248*t - 424. Let h(d) = 5*n(d) - 8*r(d). Suppose h(g) = 0. Calculate g.
-4, 12
Suppose q = 2*z, 3*q - 2*z + z = 5. Factor -45*c - 9*c**q + 28*c**2 - 90 - 15*c**2 - 9*c**2.
-5*(c + 3)*(c + 6)
Let m be (-1 - (-45)/27)*1068. Let p = -710 + m. Factor 0*r**3 + 24/5*r + 9/5 - 3/5*r**4 + 18/5*r**p.
-3*(r - 3)*(r + 1)**3/5
Let k = -10884 - -10888. Let c(v) be the second derivative of 13*v + 5/3*v**3 - 5/2*v**2 - 5/12*v**k + 0. Factor c(h).
-5*(h - 1)**2
Let u(t) = -t. Let r be u(3). Let o be (r + -1 - -1)/(-21 - -16). Factor -3/5*a**3 + 0 + o*a**4 + 0*a + 3/5*a**5 - 3/5*a**2.
3*a**2*(a - 1)*(a + 1)**2/5
Let g = 590 + -569. Let m be 16/g*(0 + 7). Determine b, given that 4/3*b**2 - 8*b - 2/3*b**4 + m + 2*b**3 = 0.
-2, 1, 2
Let p(i) be the first derivative of i**6/864 + i**5/360 - i**4/288 - 14*i**3/3 - i**2/2 + 1. Let q(d) be the third derivative of p(d). What is u in q(u) = 0?
-1, 1/5
Let k(u) be the first derivative of 3*u**5/5 + 9*u**4 - 29*u**3 - 18*u**2 + 84*u + 386. Find t such that k(t) = 0.
-14, -1, 1, 2
Let o be (-3)/12 - (-8955)/3980. What is f in -18*f + 1/3*f**o + 243 = 0?
27
Let h(b) be the third derivative of b**5/15 - 28*b**4 + 664*b**3/3 - 431*b**2. Suppose h(s) = 0. What is s?
2, 166
Factor 160/7*i + 208 + 4/7*i**2.
4*(i + 14)*(i + 26)/7
Let u = -81 - -105. Factor -u + 131 - 375*d - 31 + 935*d**2 - 605*d**3 - 31.
-5*(d - 1)*(11*d - 3)**2
Let p(h) = 3*h**2 + 91*h + 90. Let u be p(-31). Factor 28 - 71 + 5*t**2 - u - 190*t.
5*(t - 39)*(t + 1)
Let g = 416 + -430. Let s be ((-2)/7)/(g/98). Let 6/11*x**s - 4/11*x + 0 - 2/11*x**3 = 0. What is x?
0, 1, 2
Let b(a) = -a**3 - a**2 - a. Let j(n) = 13*n**4 + 26*n**3 - 13*n**2 - 11*n. Let z(w) = -10*b(w) - 2*j(w). Let z(x) = 0. What is x?
-2, -8/13, 0, 1
Let m(k) be the first derivative of 4*k**5/5 - 75*k**4 + 6032*k**3/3 - 7200*k**2 - 20736*k + 1242. Factor m(q).
4*(q - 36)**2*(q - 4)*(q + 1)
Find r such that -3/2*r**2 + 0 + 3/2*r**4 - 5/3*r + 11/6*r**3 - 1/6*r**5 = 0.
-1, 0, 1, 10
Let h = 2011 - 2011. Let y(s) be the first derivative of -1/30*s**3 + 13 + 0*s**2 + h*s. Factor y(c).
-c**2/10
Let m(l) be the first derivative of 7*l**4/8 + 13*l**3/2 - 6*l**2 + 62*l - 76. Let o(z) be the first derivative of m(z). Factor o(p).
3*(p + 4)*(7*p - 2)/2
Let w = 5625 + -5622. Factor -48/5 - 4/5*s**w - 56/5*s**2 - 20*s.
-4*(s + 1)**2*(s + 12)/5
Find r, given that -905*r**3 - 14450 + 5/2*r**5 + 40*r**4 - 59755/2*r - 16370*r**2 = 0.
-17, -1, 20
Let i(t) = -t**2 - 21*t - 74. Let l be i(-7). Solve 45*n - 25*n - 38*n + 9*n**2 - l + 3*n**3 = 0 for n.
-4, -1, 2
Let i(r) be the first derivative of -r**4/4 + 8*r**3/3 + r**2 - 14*r - 11. Let x be i(8). Factor -204 - 9*f**3 + 500 + 13*f**3 + 432*f + 72*f**x + 568.
4*(f + 6)**3
Let b(a) = a**2 + 23*a - 312. Let w be b(-33). Suppose w*z - 21 - 15 = 0. Find s, given that 1/9*s**z + 2/3*s + 1 = 0.
-3
Let g = 186 + -187. Let r(j) = j**3 + 3*j**2 - 46*j - 45. Let f(q) = q**3 - q**2 - 2*q - 1. Let s(l) = g*r(l) - 3*f(l). Suppose s(b) = 0. Calculate b.
-3, -1, 4
Let w(t) = 2*t**4 - 9*t**2 - 7*t + 25. Let h(q) = q**4 - 4*q**2 - 4*q + 12. Let m(f) = 5*f + 208. Let s be m(-43). Let p(v) = s*h(v) + 4*w(v). Factor p(k).
(k - 2)**2*(k + 2)**2
Let b be (-2)/6*(1 - 1). Suppose 1/3*w + 1/3*w**2 + b = 0. What is w?
-1, 0
Factor -13*h**2 - 8*h**2 + 74133*h**3 + 360*h - 74134*h**3 - 1188.
-(h - 6)**2*(h + 33)
Let l be (((-10)/(-8))/5*0)/(-6 + 11 + -4). Let h = 73/42 + -5/21. Determine n, given that h*n**4 + 9/2*n**2 + l - 27/2*n + 15/2*n**3 = 0.
-3, 0, 1
Let i(j) be the third derivative of j**8/3192 - j**6/380 - j**5/285 - j**2 - 171. Factor i(r).
2*r**2*(r - 2)*(r + 1)**2/19
Let r = 1612/579 - -4042/1737. Let 4/3 - r*m + 14/9*m**2 = 0. What is m?
2/7, 3
Let g(m) = -m**3 - 13*m**2 - 14*m - 16. Let p be g(-12). Suppose -k - 2*h = 2, 3*k = 3*h + 4 + 26. Factor k*s**2 - s**3 + 4*s**3 + p*s**2 - 11*s**2.
3*s**2*(s + 1)
Let t = -1442022 + 1442034. Find q, given that 5/2*q + 1/2*q**2 - t = 0.
-8, 3
Suppose -4*g = -u - 19, -7*u = 5*g - 10*u - 36. Let d(r) be the first derivative of -r**2 + 17 - 3*r - 1/9*r**g. What is n in d(n) = 0?
-3
Find y, given that -852*y + 13376 - 527*y**2 + 73*y**3 + y**4 - 27099 - 175*y**3 + 13295 = 0.
-2, -1, 107
Let r(q) = -q**3 + 6*q**2 + 9*q - 9. Let y be r(7). Suppose -2 - 10 = -6*d. Factor 2*v**3 + 45*v**d - y*v**3 - 225*v - 1331 + 1706.
-3*(v - 5)**3
Let w(b) be the second derivative of -b**7/315 - b**6/36 + b**5/90 + 5*b**4/36 + 103*b**2/2 + 45*b - 2. Let k(s) be the first derivative of w(s). Factor k(t).
-2*t*(t - 1)*(t + 1)*(t + 5)/3
Let b = 11 + -1. Suppose -y = -5*x + 18, 7*y - 4*x = 4*y - b. Factor 22*k + 1 - 10 - 24*k**2 - 1 + 6 + 