. Factor z - s + 3/2*s**2 - 1/2*s**3.
-s*(s - 2)*(s - 1)/2
Let r = 1 - -12. Let p = -8 + r. Factor 3*w**2 - 2*w - p*w**4 - 4*w + 2*w**4 + 6*w**3.
-3*w*(w - 2)*(w - 1)*(w + 1)
Suppose -2*j - f - 4 = -2*f, 3*j - 20 = -5*f. Suppose j*x + x = 2. Factor -h + 4*h**x + 81 - 15*h - 65.
4*(h - 2)**2
Suppose -7*t = -6*t + 7. Let b(m) = 2*m**2 - 2*m - 13. Let u(q) = 3*q**2 - 3*q - 27. Let o(w) = t*b(w) + 3*u(w). Factor o(g).
-5*(g - 2)*(g + 1)
Let d(k) be the third derivative of k**6/420 + k**5/42 + k**4/14 - 3*k**2 + 21. Determine r, given that d(r) = 0.
-3, -2, 0
Let d(g) = -227*g - 1133. Let x be d(-5). Factor 624/5*u**x + 0 - 20*u**5 - 144/5*u - 436/5*u**3 - 104*u**4.
-4*u*(u + 3)**2*(5*u - 2)**2/5
Let w(z) be the second derivative of -z**4/4 - 53*z**3/2 - 78*z**2 + 423*z. Factor w(h).
-3*(h + 1)*(h + 52)
Let u**2 - 128*u + 5*u**3 - 6*u**2 + u**2 + 125*u + 2*u**4 = 0. What is u?
-3, -1/2, 0, 1
Let z(p) be the first derivative of p**6/240 - p**4/4 - 37*p**3/3 + 37. Let d(s) be the third derivative of z(s). Determine n so that d(n) = 0.
-2, 2
Let t(h) be the first derivative of h**5/25 - 2*h**4/5 + 7*h**3/15 - 423. Factor t(d).
d**2*(d - 7)*(d - 1)/5
Determine y, given that 5*y**4 - 13*y**2 + 3*y**3 + 3*y**5 - y**3 + 12 + 8*y - 4*y**5 - 5*y**3 = 0.
-1, 2, 3
Factor 8*o**2 + 1587 + 8*o**2 + o**2 - 14*o**2 + 138*o.
3*(o + 23)**2
Let n = 94 - 79. Let x be 4*(-3)/n*10/(-12). Let 0*c**3 - 2/3*c**4 + 0*c + x*c**2 + 0 = 0. Calculate c.
-1, 0, 1
Let o(n) be the third derivative of n**8/70560 - n**7/2520 + n**6/420 - n**5/60 + 12*n**2. Let u(x) be the third derivative of o(x). Factor u(c).
2*(c - 6)*(c - 1)/7
Let o be 10/((-32)/(-144) + -2 + (-94)/(-36)). What is w in -15/4*w**2 + o*w - 3 - 75/4*w**3 = 0?
-1, 2/5
Let j = 289 + -169. Let q be (-3)/((-9)/(-3)) + j/24. Factor 2/3*k**q - 8/3*k - 8/3*k**3 + 4*k**2 + 2/3.
2*(k - 1)**4/3
Suppose 0 = 2*o + 2*t + 4, -6 = -o + 4*t + 17. Suppose -o*x + x = 0. Factor x*b**4 - b - b - 6*b**3 + 3*b**2 - 9*b**2 - 2*b**4.
-2*b*(b + 1)**3
Suppose 5*m + 27 = y, -5*y + 3*m + 6 + 107 = 0. Let u = y - 20. Factor 35 - 2*k**2 + 30 - 61 + u*k.
-2*(k - 2)*(k + 1)
Factor 0*a**3 + 0*a**3 - 89*a**4 + a**3 - a + 88*a**4 + a**2.
-a*(a - 1)**2*(a + 1)
Let y(i) be the third derivative of -1/45*i**5 + 0 + 0*i + 7*i**2 - 1/60*i**6 + 0*i**4 + 0*i**3. Determine m, given that y(m) = 0.
-2/3, 0
Let j(c) be the second derivative of 2*c**6/45 - c**5/15 - c**4/9 + 2*c**3/9 + 57*c + 1. Let j(r) = 0. What is r?
-1, 0, 1
Suppose 4 = -4*j - 4*u, -2 = -3*j + 2*u + 10. Let s be (-3 + 4)/(11/44). Determine t so that 0*t**s + 4*t**4 - 2*t**4 - 2*t**3 - 2*t**j + 0*t**3 + 2*t**5 = 0.
-1, 0, 1
Suppose 0 = -16*t + 61*t - 135. Let p(u) be the third derivative of -1/20*u**4 + 0 + 0*u + 4*u**2 + 1/150*u**5 + 2/15*u**t. Factor p(i).
2*(i - 2)*(i - 1)/5
Let g(x) be the first derivative of 1/3*x**3 - 5 - 2/5*x**2 - 1/15*x**4 + 7*x. Let m(v) be the first derivative of g(v). Find w, given that m(w) = 0.
1/2, 2
Let k(s) be the first derivative of -s**5/25 - s**4/10 + s**2/5 + s/5 + 113. Suppose k(u) = 0. Calculate u.
-1, 1
Let n = -5835 - -5837. Factor -7/2*m + 1/4*m**n + 49/4.
(m - 7)**2/4
Let h(r) be the third derivative of -1/300*r**6 + 1/525*r**7 + 0*r - 2/15*r**3 + 1/12*r**4 - 2*r**2 + 0 - 1/50*r**5. Factor h(m).
2*(m - 1)**3*(m + 2)/5
Let a be (0/(-12))/((-2)/(-2) - -4). Let n be ((-3)/9)/((-10)/6). Factor 0 + n*g**3 - 1/5*g**2 + a*g.
g**2*(g - 1)/5
Let a(h) be the second derivative of h**6/10 + 3*h**5/5 + h**4 + h + 9. Solve a(x) = 0 for x.
-2, 0
Let b = 13586/477 - 256/9. Let q = 100/159 + b. Find s, given that -s**4 + 2/3*s**2 + 1/3 - q*s**3 + s - 1/3*s**5 = 0.
-1, 1
Let a be 1 + -4 + 1/(5/23). Determine y so that 32/5*y**2 + 2*y**5 - 4/5*y**4 - a*y + 0 - 6*y**3 = 0.
-2, 0, 2/5, 1
Suppose 6*i - 13 = -1. Factor -6 - t**2 - 13*t**2 + 3*t**2 + 8*t**i - 9*t.
-3*(t + 1)*(t + 2)
Let y(d) = -4 + 1187*d - 1197*d - 4*d**2 - d**2 + 2*d**2. Let a be y(-2). Factor 0*n**3 - 3/4*n**a + 9/4*n**2 - 3/2*n + 0.
-3*n*(n - 1)**2*(n + 2)/4
Determine d so that -1250/3 - 1/3*d**3 - 52/3*d**2 - 725/3*d = 0.
-25, -2
Let b be -1 + 8 - (-6 - -7). Let u(y) = -4*y**4 - 6*y**3 - 14*y**2 + 6*y + 6. Let l(c) = c**3 - c**2 + c + 1. Let h(t) = b*l(t) - u(t). Factor h(m).
4*m**2*(m + 1)*(m + 2)
Suppose 5*y + 5*n - 10 = 0, 5*y - 19 = -2*n - 0*n. Suppose 7*p + 31*p = 76. Factor 2/9*k**y + 0*k + 4/9*k**4 + 0*k**p + 2/9*k**3 + 0.
2*k**3*(k + 1)**2/9
Let d(t) = 3*t**3 - 43*t**2 - 52*t - 10. Let u(b) = -5*b**3 + 84*b**2 + 105*b + 21. Let z(a) = -11*d(a) - 6*u(a). Determine i, given that z(i) = 0.
-8, -2, -1/3
Let 128*h**2 + 152/3*h + 2*h**4 + 0 + 238/3*h**3 = 0. Calculate h.
-38, -1, -2/3, 0
Let d(k) be the first derivative of k**5/5 + 7*k**4/4 + 11*k**3/3 + 5*k**2/2 + 839. What is g in d(g) = 0?
-5, -1, 0
Let d(h) be the third derivative of h**8/84 - 8*h**7/105 + h**6/10 - 86*h**2. Factor d(f).
4*f**3*(f - 3)*(f - 1)
Factor -15876/5 + 504/5*d - 4/5*d**2.
-4*(d - 63)**2/5
What is s in -2/5*s**3 - 12/5 + 12/5*s**2 + 2/5*s = 0?
-1, 1, 6
Let r(w) be the third derivative of -w**5/240 + 25*w**4/48 - 625*w**3/24 - 145*w**2. Solve r(d) = 0.
25
Let u(a) be the second derivative of -a**7/21 + 31*a**6/15 + 71*a**5/5 - 29*a**4/3 - 143*a**3 + 315*a**2 - a + 197. Find r, given that u(r) = 0.
-3, 1, 35
Let w(h) be the third derivative of h**6/30 + 17*h**5/15 + 8*h**4/3 - 2*h**2 + 81*h. Factor w(g).
4*g*(g + 1)*(g + 16)
Let p(t) be the first derivative of 5/12*t**4 - 3/2*t**2 + 0*t + 4 + 11/180*t**6 + 4/15*t**5 + 2/9*t**3. Let h(b) be the second derivative of p(b). Factor h(o).
2*(o + 1)**2*(11*o + 2)/3
Suppose 4*v + 4 = -8, 0 = -4*i - 2*v + 74. Let z be (i/(-75))/(5/(-135)). Factor -4/5*s**2 - z - 24/5*s.
-4*(s + 3)**2/5
Let m(d) be the second derivative of d**5/10 - 7*d**4/3 + 43*d**3/3 - 30*d**2 - 720*d. What is j in m(j) = 0?
1, 3, 10
Let c(z) = -10*z**2 + 23*z - 4. Let y be c(2). Let h(t) be the second derivative of -3/10*t**y - 1/10*t**4 + 0 - 3/10*t**3 + t. Factor h(l).
-3*(l + 1)*(2*l + 1)/5
Suppose 2*c - 6*z + z = -3, 5*c + 2*z - 36 = 0. Suppose 10*s**2 + 16 + 20*s + 8 - c*s**2 = 0. Calculate s.
-3, -2
Factor 9*a + 1/4*a**2 + 81.
(a + 18)**2/4
Let w(l) be the second derivative of -l**5/50 - 11*l**4/30 + 46*l**3/15 + 56*l**2/5 - 450*l + 2. Find m, given that w(m) = 0.
-14, -1, 4
Let c(s) be the second derivative of -25/8*s**3 + 5/168*s**7 + 0 - 5/24*s**4 - 7*s + 45/8*s**2 - 7/24*s**6 + 7/8*s**5. Find i such that c(i) = 0.
-1, 1, 3
Let c(w) be the first derivative of -w**5/35 + 5*w**4/7 + 22*w**3/21 - 10*w**2/7 - 3*w + 726. Factor c(i).
-(i - 21)*(i - 1)*(i + 1)**2/7
Let f = -39 - -45. Let p be (3/(-9)*1)/((-3)/f). Factor p*z + 2/15*z**5 + 4/3*z**2 + 4/3*z**3 + 2/15 + 2/3*z**4.
2*(z + 1)**5/15
Let c(q) be the third derivative of q**9/453600 + q**8/12600 + q**7/1050 - q**5/4 - 14*q**2. Let a(k) be the third derivative of c(k). Factor a(s).
2*s*(s + 6)**2/15
Let r(s) be the third derivative of s**6/540 + s**5/60 + s**3/6 - 9*s**2. Let t(j) be the first derivative of r(j). Factor t(x).
2*x*(x + 3)/3
Let p(i) be the third derivative of -i**6/240 + i**5/30 + 5*i**4/48 + 3*i**2 + 5. Find k such that p(k) = 0.
-1, 0, 5
Let s(a) = 5*a**2 + 24*a + 16. Let k(n) be the first derivative of -5*n**3 - 71*n**2/2 - 49*n - 11. Let q(b) = -4*k(b) - 11*s(b). Factor q(y).
5*(y + 2)**2
Suppose -35*s + 35 = -34 - 71. Find l such that -2/3*l**3 + 0*l**2 + 1/3*l**s - 1/3 + 2/3*l = 0.
-1, 1
Let d(z) = 10*z**4 + 57*z**3 + 65*z**2 + 24*z + 2. Let u(o) = o**3 + 2*o + 1. Let h(g) = -d(g) + 2*u(g). Solve h(p) = 0.
-4, -1, -1/2, 0
Suppose -2*q + 7*s - 2*s + 35 = 0, 4*s - 137 = -5*q. Find x, given that -10*x**3 + q*x**2 - x**2 - 3*x**4 - 8*x + 5*x**4 - 8*x**2 = 0.
0, 1, 2
Let p(h) = -8*h**2 - 933*h + 54759. Let i(u) = -44*u**2 - 4664*u + 273796. Let d(n) = -3*i(n) + 16*p(n). Factor d(s).
4*(s - 117)**2
Let q(t) be the first derivative of -2*t - t**3 - 17 + 1/8*t**4 + 9/4*t**2. Factor q(l).
(l - 4)*(l - 1)**2/2
Let c(o) = -2*o + 8. Let l be c(9). Let a(h) = -h**3 + 5*h**2 - 2. Let k(g) = -3*g**3 + 11*g**2 - 5. Let p(x) = l*a(x) + 4*k(x). Let p(n) = 0. Calculate n.
-3, 0
Suppose -216/5*y**4 + 0 + 0*y + 16/5*y**5 + 21*y**3 - 13/5*y**2 = 0. What is y?
0, 1/4, 13
Let d(o) be the third derivative of -o**7/315 + o**6/180 + 2*o**5/45 - o**4/9 - 3