.
-4*(s - 5)**2*(s + 1)
Let s(p) = -3*p**3 + 41*p**2 - 37*p + 17. Let b(r) = r**3 - 10*r**2 + 9*r - 4. Let z be (-1 - -2)/(12/(-48)). Let n(q) = z*s(q) - 18*b(q). Factor n(h).
-2*(h - 1)**2*(3*h - 2)
Determine j, given that -3/2*j - 3*j**2 + 3 + 3/2*j**3 = 0.
-1, 1, 2
Let p(u) be the second derivative of u**6/2340 - u**5/195 + u**4/39 + 9*u**3/2 + 5*u. Let i(v) be the second derivative of p(v). Factor i(r).
2*(r - 2)**2/13
Let j(l) be the second derivative of -l**6/30 - 29*l**5/20 - 9*l**4/4 + 29*l**3/6 + 14*l**2 + l + 226. Find h such that j(h) = 0.
-28, -1, 1
Let v(m) be the second derivative of -2/65*m**5 - 1/195*m**6 - 28*m + 4/13*m**3 + 1/39*m**4 - 9/13*m**2 + 0. Factor v(p).
-2*(p - 1)**2*(p + 3)**2/13
Suppose -67*s + 105 = -72*s. Let y = 24 + s. Factor 0*p - 6/5*p**2 - 4/5*p**y + 2/5.
-2*(p + 1)**2*(2*p - 1)/5
Factor -16*p + 8/3*p**2 + 0 + 5/3*p**3 - 1/3*p**4.
-p*(p - 4)**2*(p + 3)/3
Solve 17*n**3 - 46*n**3 + 18*n**3 + 30*n**2 + 16*n**3 = 0 for n.
-6, 0
Let d(r) be the third derivative of -r**9/756 + r**8/210 - r**7/210 - 2*r**3 - 7*r**2. Let i(p) be the first derivative of d(p). Factor i(z).
-4*z**3*(z - 1)**2
Factor -2*r**3 - 3528 - 198*r**2 - 174*r**2 + 496*r**2 - 216*r**2 - 1218*r.
-2*(r + 4)*(r + 21)**2
Let q(v) be the third derivative of v**7/840 - v**5/40 - 3*v**4/8 - 12*v**2. Let x(l) be the second derivative of q(l). Factor x(p).
3*(p - 1)*(p + 1)
Let x = 7058/3 - 2342. Let -2/3*d - 2/3 + 32/3*d**2 + x*d**3 = 0. What is d?
-1, -1/4, 1/4
Find f, given that 8 - 62*f**3 + 1477*f - 1455*f + 12*f**4 - 64*f**2 + 4 = 0.
-1, -1/3, 1/2, 6
Let d be ((-2601)/(-170) + -15)/(27/2). Let o(g) be the third derivative of d*g**5 + 0*g + 1/18*g**4 + 0 - 4/3*g**3 - g**2. Factor o(j).
4*(j - 2)*(j + 3)/3
Let w(b) be the third derivative of -b**8/47040 - b**7/11760 + 3*b**5/20 + 12*b**2. Let n(r) be the third derivative of w(r). Determine i, given that n(i) = 0.
-1, 0
Let c(r) be the first derivative of -r**6/120 + r**5/30 + r**4/8 + r**2 + 8. Let p(m) be the second derivative of c(m). What is s in p(s) = 0?
-1, 0, 3
Let f = 114151/2 - 57058. Suppose 1/2*y**5 + 0*y + 0 + f*y**3 + 25/2*y**2 + 11/2*y**4 = 0. What is y?
-5, -1, 0
Let y = 1/2215 + 17707/28795. What is j in y*j + 10/13*j**3 + 2*j**2 - 8/13 = 0?
-2, -1, 2/5
Let y(n) be the third derivative of -n**7/45 - 169*n**6/540 - 19*n**5/15 + 32*n**3/27 - 72*n**2 - 2*n. Let y(t) = 0. Calculate t.
-4, -1/3, 2/7
Find b such that 9/2*b + 0 + 17/4*b**3 - 1/8*b**4 + 71/8*b**2 = 0.
-1, 0, 36
Suppose -4*g = x - 127, 113 = 5*g + 3*x - 37. Solve -g*r**3 - 21*r**3 + 16*r**2 + 38*r**3 + 4*r**4 = 0 for r.
0, 2
Suppose 4*r = -0 - 4. Let d(s) = 8*s**2 + s + 1. Let t be d(r). Let 3 + 5*c + t*c - 2*c - 5*c + 3*c**2 = 0. What is c?
-1
Let x = -79/5 + 82/5. Let n = -442/15 + 451/15. Let -7/5*b**3 - 3/5*b**4 + x*b + 2/5 - n*b**2 = 0. Calculate b.
-1, 2/3
Let b = 29/10 - 43/20. Determine w so that -3/4*w + 3/4*w**3 - 3/4*w**4 + 0 + b*w**2 = 0.
-1, 0, 1
Let k(z) be the third derivative of 5*z**8/2016 - 5*z**7/252 + z**6/24 + z**5/18 - 5*z**4/18 + 91*z**2. Factor k(v).
5*v*(v - 2)**3*(v + 1)/6
Let z(r) be the third derivative of r**7/210 - 3*r**6/40 + r**5/3 - r**4/2 + 126*r**2 - 1. Factor z(p).
p*(p - 6)*(p - 2)*(p - 1)
Let d(w) = w**3 + 37*w**2 - 75*w + 119. Let f be d(-39). Factor f*o - 2/3*o**2 - 4/3.
-2*(o - 2)*(o - 1)/3
Suppose 5*m - 5*p = 365, 142 = 2*m - 4*p - 0*p. Suppose m*r - 10 = 70*r. Find f such that 1 + f - 3/4*f**r = 0.
-2/3, 2
Let l = -6870 - -6874. Factor -2*r**l - 2/7*r**5 + 0 - 30/7*r**3 - 18/7*r**2 + 0*r.
-2*r**2*(r + 1)*(r + 3)**2/7
Let 14*s**4 + 339*s**5 - 346*s**5 - 171*s**3 + 135*s**2 + 61*s + 47*s**4 - 7*s = 0. Calculate s.
-2/7, 0, 3
Let l(b) = -6*b**4 + 26*b**3 + 46*b**2 + 62*b. Let s(h) = -5*h**4 + 26*h**3 + 46*h**2 + 57*h. Let u(g) = 7*l(g) - 8*s(g). Factor u(j).
-2*j*(j + 1)**2*(j + 11)
Let v = 3997/34190 - 2/1315. Let w = v + 43/78. Let 1/3*u**5 - 2/3*u**3 + 2/3 - 7/3*u + 8/3*u**2 - w*u**4 = 0. Calculate u.
-2, 1
Suppose -5*q = 3 - 8. Let g be ((-9)/15)/(q/(-5)). Factor -g*j + 5*j + 2*j + 0*j - 4*j**3.
-4*j*(j - 1)*(j + 1)
Suppose -23*d = 13*d - 14*d. Factor d + 0*i + 2/7*i**3 - 2/7*i**2.
2*i**2*(i - 1)/7
Let i = 5118 - 5116. Solve -9/8*h**i + 9/8*h - 3/8 + 3/8*h**3 = 0 for h.
1
Suppose 0*o + o = 2*o. Suppose o = p - 2*p + 4. Factor 0*l**2 + 0 + l**p - 1/2*l**3 + 0*l + 3/2*l**5.
l**3*(l + 1)*(3*l - 1)/2
Find g, given that -9/2*g**3 - 21/2*g**4 + 63/2*g**2 + 9 + 69/2*g = 0.
-1, -3/7, 2
Let h(m) = -3*m**2 + 2*m. Let p(v) = 55*v - 160. Let c be p(3). Let t(b) = b**2 - 4 - b + 4. Let k(w) = c*t(w) + 2*h(w). Determine g so that k(g) = 0.
-1, 0
Let m(h) be the first derivative of 0*h + 1/2*h**3 + 35 - 9/4*h**2. Factor m(z).
3*z*(z - 3)/2
Let h = -58 + 52. Let f be 1/(-1) - h*(-3)/(-14). Suppose -2/7*w**2 + 0 - f*w = 0. What is w?
-1, 0
Suppose 51 = 20*c + 11. Let z(i) be the second derivative of 1/9*i**3 + 0 + 1/36*i**4 + 1/6*i**c - 11*i. Factor z(m).
(m + 1)**2/3
Let y = 48 + -42. Let l(n) = -n. Let f(q) = -q**2 + 6*q - 2. Let j(h) = y*l(h) + 2*f(h). Factor j(k).
-2*(k - 2)*(k - 1)
Let l = 5056/9 + -1646/3. Let b = 140/9 - l. Let -2*n**4 - 4*n**3 - b*n**2 + 0 - 4/9*n = 0. What is n?
-1, -2/3, -1/3, 0
Let -56/5*o**2 - 26/5*o**3 - 14/5 + 1/5*o**5 - 47/5*o - 2/5*o**4 = 0. What is o?
-2, -1, 7
Let m(i) be the third derivative of i**8/1512 - 31*i**7/945 + 17*i**6/36 - 5*i**5/6 - 5*i**2 - 12*i. Determine z, given that m(z) = 0.
0, 1, 15
Suppose 6/11*a**3 - 24/11*a + 0 - 24/11*a**2 + 6/11*a**4 = 0. Calculate a.
-2, -1, 0, 2
Let g(x) be the first derivative of -1/6*x**3 - 1/24*x**4 + 1/2*x + 1/12*x**2 - 1. Factor g(c).
-(c - 1)*(c + 1)*(c + 3)/6
Let h = -1/3248 - -1219/3248. Factor 0*z**2 - h*z**3 + 0 + 1/2*z + 1/8*z**4.
z*(z - 2)**2*(z + 1)/8
Let q(n) be the third derivative of 0*n - 1/630*n**7 + 0*n**4 + 0 + 1/45*n**5 - 1/1008*n**8 + 1/90*n**6 + 0*n**3 + 19*n**2. Solve q(w) = 0.
-2, -1, 0, 2
Let r(t) be the first derivative of -t**6/10 - 54*t**5/25 - 351*t**4/20 - 324*t**3/5 - 486*t**2/5 - 213. Factor r(o).
-3*o*(o + 3)**2*(o + 6)**2/5
Let k = -60 + 64. Solve 4*h**2 - 2*h - k*h**2 + 4*h**2 - h - h**3 = 0.
0, 1, 3
Let g = 123 + -118. Suppose -8*b + 11 = -g. Factor -1/6*a**4 + 0*a - 1/6 + 1/3*a**b + 0*a**3.
-(a - 1)**2*(a + 1)**2/6
Let f = -5 + 8. Factor -2*p**3 - p**4 - 5*p**2 + 0*p**4 - 2*p**f - 2*p.
-p*(p + 1)**2*(p + 2)
Let c(b) = -6 - 7*b**2 + 3*b**2 - 3*b - 3 + b**3 + 2. Let i be c(5). Factor 9*g**i + 22*g**2 - 5 + 3*g**4 - 19*g**2 - 9*g + 1 - 2.
3*(g - 1)*(g + 1)**2*(g + 2)
Let r(c) be the third derivative of 1/20*c**5 + 0*c + 0*c**3 - 1/70*c**7 + 1/56*c**8 + 0 - 3/40*c**6 + 1/8*c**4 + 6*c**2. Suppose r(b) = 0. What is b?
-1, -1/2, 0, 1
Let r = 661 + -1321/2. Factor -1/6*y**2 + 0 + r*y.
-y*(y - 3)/6
Let d(o) be the first derivative of -16/33*o**3 + 13/11*o**2 + 5 + 1/22*o**4 - 12/11*o. Factor d(y).
2*(y - 6)*(y - 1)**2/11
Let u be (-8)/(-6)*(13 - -5). Factor 2*g + u*g**3 - 6*g**2 - 5*g - 27*g**3.
-3*g*(g + 1)**2
Factor -52/5 - 2/5*r**2 - 6*r.
-2*(r + 2)*(r + 13)/5
Let d(r) be the third derivative of r**8/896 + r**7/70 + 11*r**6/160 + 3*r**5/20 + 9*r**4/64 - 63*r**2. Factor d(p).
3*p*(p + 1)**2*(p + 3)**2/8
Let s(d) be the second derivative of d**8/140 + 3*d**7/40 + d**6/24 - 5*d**3 - 23*d. Let p(t) be the second derivative of s(t). Factor p(b).
3*b**2*(b + 5)*(4*b + 1)
Let x = 55530 - 111039/2. Solve 3/4*q**2 + 0 + x*q = 0.
-14, 0
Let v(t) be the second derivative of t**4/3 - 22*t**3/3 + 2*t + 94. Factor v(g).
4*g*(g - 11)
Let j(z) be the first derivative of z**3/7 + 12*z**2/7 - 27*z/7 + 603. What is g in j(g) = 0?
-9, 1
Suppose -30 = -10*r + 5*r. Let p(y) be the second derivative of y + 0*y**5 + 0*y**2 + 0*y**3 + 0 + 1/120*y**r - 1/48*y**4. Determine m so that p(m) = 0.
-1, 0, 1
Let r(k) be the first derivative of -3*k**5/10 - 21*k**4/8 - 11*k**3/2 - 15*k**2/4 - 49. Factor r(a).
-3*a*(a + 1)**2*(a + 5)/2
Let c(m) = -3*m**2 + 25*m - 52. Let i be c(4). Let u(s) be the second derivative of i*s**2 - 2/5*s**5 + 4/3*s**3 + 0 - 1/3*s**4 + 2/15*s**6 + 3*s. Factor u(f).
4*f*(f - 2)*(f - 1)*(f + 1)
Suppose 3*j - 4*h - 15 = -h, 9 = -3*h. Let w(u) be the second derivative of 0*u**j - 1/90*u**5 - 6*u + 0 + 1/135*u**6 - 1/54*u**4 + 1/27*u**3. Factor w(a).
2*a*(a - 1)**2*(a + 1)/9
Let n(j) = -3*j**3 + j**