).
i**2/2
Let i be 3 + 0/1 + (-85)/30. Let z = 5/42 + i. Factor -1/7*h**3 - 2/7 + z*h**2 + 1/7*h.
-(h - 2)*(h - 1)*(h + 1)/7
Let g = -58 - -61. Let b be (0 + 2/8)/(73/219). What is z in -3/4*z**4 + b*z + 3/2*z**2 + 3/4*z**5 - 3/4 - 3/2*z**g = 0?
-1, 1
Let d(g) = -g**2 - 21*g - 35. Let w be d(-19). Factor 58*l**3 + 106*l**4 + 147*l**5 + 122*l**w + 272*l**4 + 24*l**2.
3*l**2*(l + 2)*(7*l + 2)**2
Let m be (2/(-4) - 12/(-48))*-8. Let s(a) be the first derivative of 5/4*a**5 - 4 + 55/16*a**4 - 7/2*a**2 - 1/2*a**3 + m*a. Determine l, given that s(l) = 0.
-2, -1, 2/5
Let w(n) = -6*n**4 - 4*n**3 + 2*n**2 + 4*n. Let l(m) = 17*m**4 + 12*m**3 - 6*m**2 - 12*m. Let d(u) = -4*l(u) - 11*w(u). Suppose d(k) = 0. What is k?
-2, -1, 0, 1
Let w(o) be the second derivative of o**7/168 + o**6/120 - 11*o**5/80 + 7*o**4/48 + 5*o**3/12 - o**2 - 158*o - 2. Let w(u) = 0. What is u?
-4, -1, 1, 2
Let -183/5*d**3 - 384/5 - 48/5*d**4 + 96*d - 3/5*d**5 + 138/5*d**2 = 0. Calculate d.
-8, -2, 1
Factor 2971*k - 6*k**4 - 2936*k - 45*k**2 - 10 + 10*k**3 + 15*k**3 + k**4.
-5*(k - 2)*(k - 1)**3
Let l be (-232)/(-176) + 16/88. Solve -9/8*d**4 - l + 0*d - 3/8*d**5 + 21/8*d**2 + 3/8*d**3 = 0 for d.
-2, -1, 1
Let q(l) be the third derivative of 3*l**8/112 + 2*l**7/35 - l**6/5 - 3*l**5/10 + 5*l**4/8 + l**3 + 5*l**2 + 6. Suppose q(w) = 0. Calculate w.
-2, -1, -1/3, 1
Let 23 - 20*p**4 - 23 - 45 - 335*p**2 - 111*p**3 - 255*p - 34*p**3 = 0. What is p?
-3, -1, -1/4
Let w(j) be the second derivative of 7 + 2*j + 0*j**2 - 1/2*j**3 - 3/20*j**5 + 1/2*j**4. Factor w(q).
-3*q*(q - 1)**2
Let i(b) be the second derivative of -b**8/840 + b**7/105 + b**6/90 - b**5/5 - 3*b**4/4 + b**3 + 6*b. Let q(n) be the second derivative of i(n). Factor q(a).
-2*(a - 3)**2*(a + 1)**2
Let f(v) = 9*v**2 - 21*v + 3. Let l(s) = -2 - 6*s**2 - 1250*s + 1261*s + s**2. Let x(j) = -6*f(j) - 11*l(j). Solve x(y) = 0.
-4, -1
Let v(i) = 7*i**2 + 9*i + 12. Let c(o) = 9*o**2 + 10*o + 13. Let x(h) = 3*c(h) - 4*v(h). Factor x(r).
-(r + 3)**2
Let c(a) = -13*a**2 + 10*a + 5. Let m(x) = -3*x**2 + 3*x + 2. Let g(l) = 2*c(l) - 9*m(l). Factor g(i).
(i - 8)*(i + 1)
Let a be 2 - (-3 + (3 - (-1)/(-3)))*6. What is g in 0 + 8/5*g + 36/5*g**3 - 12*g**2 + 104/5*g**a = 0?
-1, 0, 2/13, 1/2
Let n(d) be the third derivative of -d**5/90 - 7*d**4/18 - 8*d**3/3 + 16*d**2 + 4*d. Suppose n(g) = 0. Calculate g.
-12, -2
Let j(q) be the second derivative of -1/240*q**5 + 0 + 1/96*q**4 + 0*q**3 + 5*q + 1/2*q**2. Let f(w) be the first derivative of j(w). What is s in f(s) = 0?
0, 1
Let a(j) be the third derivative of 10*j**2 - 1/12*j**5 + 0*j**3 - 1/30*j**6 - 1/210*j**7 - 1/12*j**4 + 0 + 0*j. Let a(r) = 0. What is r?
-2, -1, 0
Let n(p) = 25*p**2 - 6*p - 10. Let o be n(-2). Let t = -102 + o. Factor 1/3*x**4 + t*x + 1/3 + 0*x**3 - 2/3*x**2.
(x - 1)**2*(x + 1)**2/3
Let a(d) be the third derivative of d**6/40 + 2*d**5/15 + d**4/6 - 35*d**2. Factor a(l).
l*(l + 2)*(3*l + 2)
Suppose 3*k + 6 = 2*a, 2*k + 3*a - 7*a + 4 = 0. Let g be (-1 - k)/((-6)/(-18)). Factor -12*u - 5*u**g - 48*u**2 + 16*u**3 + 16*u**3.
3*u*(u - 2)*(9*u + 2)
Let z(j) be the third derivative of -1/20*j**5 + 0*j**4 + 0*j + 1/112*j**8 + 13*j**2 + 0 - 1/40*j**6 + 1/70*j**7 + 0*j**3. Let z(n) = 0. Calculate n.
-1, 0, 1
Let j be (-36)/(-24) - (13/44 + (-18)/33). Factor j*t**2 + 0 + 3/2*t**3 - 1/4*t**4 + 0*t.
-t**2*(t - 7)*(t + 1)/4
Suppose -2*n + 5 = -y, 24*n - 19*n - 17 = -2*y. Let m(t) be the first derivative of 0*t + 0*t**2 + 9 - t**6 + 14/5*t**5 + 2/3*t**n - 5/2*t**4. Factor m(k).
-2*k**2*(k - 1)**2*(3*k - 1)
Let c be (-10)/4 + 110/22. Let n(f) be the second derivative of -2*f**3 - 4/5*f**2 - 5/4*f**5 + 0 - 7*f - c*f**4. Find s, given that n(s) = 0.
-2/5
Let w(l) be the first derivative of 3*l**5/40 + 33*l**4/32 + 29*l**3/8 - 33*l**2/16 - 45*l/4 - 240. Solve w(a) = 0.
-6, -5, -1, 1
Let p = 386 - 757/2. Let g = 23/3 - p. Factor -1/3*h**4 + 1/6*h**5 + 0 + 0*h**3 + 1/3*h**2 - g*h.
h*(h - 1)**3*(h + 1)/6
Factor -1/2*f**4 - 2*f + f**3 + 3/2*f**2 - 2.
-(f - 2)**2*(f + 1)**2/2
Solve 2*q**5 + 6*q**2 - 91*q**2 + 3*q**5 - 5*q**3 + 5*q**4 + 45*q**4 + 35*q**4 = 0 for q.
-17, -1, 0, 1
Let z(g) be the first derivative of -1/6*g**4 - 5*g**2 - 14/3*g + 6 - 2*g**3. Factor z(f).
-2*(f + 1)**2*(f + 7)/3
Let c(f) be the second derivative of f**8/1120 + 8*f**7/315 + 19*f**6/72 + 5*f**5/6 + 11*f**4/6 - 10*f. Let p(k) be the third derivative of c(k). Factor p(r).
2*(r + 5)**2*(3*r + 2)
Suppose -19*z - 5 + 62 = 0. Factor 0 + 0*m + 3/4*m**4 + 3/2*m**z + 3/4*m**2.
3*m**2*(m + 1)**2/4
Let u = -433/12 - 19151/156. Let o = u - -159. Factor -o + 2/13*g**3 + 6/13*g - 6/13*g**2.
2*(g - 1)**3/13
Let d(w) be the second derivative of -1/21*w**3 - 5*w - 1/7*w**2 + 0 - 1/105*w**6 - 1/147*w**7 + 1/21*w**4 + 1/35*w**5. Factor d(u).
-2*(u - 1)**2*(u + 1)**3/7
Factor 2/5*j**3 + 0*j**4 + 0 - 1/5*j + 0*j**2 - 1/5*j**5.
-j*(j - 1)**2*(j + 1)**2/5
Let 419*r**2 + 2*r - 417*r**2 + r**3 - 5*r**3 = 0. What is r?
-1/2, 0, 1
Suppose -2*i = 4*f, i - 526 = 2*f - 534. Find m such that -2/9*m + 0*m**f + 2/9*m**3 + 0 = 0.
-1, 0, 1
Factor -20*z**4 + 26 + 148*z**3 - 26 - 256*z**2 + 80*z.
-4*z*(z - 5)*(z - 2)*(5*z - 2)
Find o such that 110/3*o**3 + 424/3*o - 204*o**2 + 50/3*o**4 - 80/3 = 0.
-5, 2/5, 2
Let o(i) be the third derivative of -27/2*i**4 - 3*i**2 - 81/2*i**3 + 0 - 27/10*i**5 - 3/10*i**6 - 1/70*i**7 + 0*i. Solve o(t) = 0 for t.
-3
Let x(d) = 11*d**3 + 3*d**2 - 3*d + 1. Let y(l) = 13*l**3 + 3*l**2 - 3*l + 1. Let h(w) = 7*x(w) - 6*y(w). Factor h(q).
-(q - 1)**3
What is v in 19/4*v**2 - 7/4*v**3 + 7/4*v - 1/4*v**4 - 9/2 = 0?
-9, -1, 1, 2
Let k be 3 - (-4)/26*-13. Let u be (-2 - 0)*(-1 + 0). Factor -d**4 + 74*d - k - 74*d + 2*d**u.
-(d - 1)**2*(d + 1)**2
Let u(h) be the second derivative of h**6/24 + 11*h**5/40 + 13*h**4/48 - 7*h**3/6 - 3*h**2/2 - 255*h. Solve u(w) = 0 for w.
-3, -2, -2/5, 1
Let q = -157775/4 + 39444. Determine f so that q*f**5 - 3*f - 3/4*f**4 + 11/4*f**2 + 1 - 1/4*f**3 = 0.
-2, 1, 2
Find d, given that 5*d**3 - 4*d**4 - 6*d**4 + 1062*d**5 - 1057*d**5 = 0.
0, 1
Let k = 45824 + -91643/2. Factor 0 - 11*v**3 + k*v**4 + 0*v + 4*v**2.
v**2*(v - 4)*(5*v - 2)/2
Let v = 153 + -163. Let m be v/(-40)*13 - (-1)/(-4). Factor -7/2*w - 1/2*w**4 - 5/2*w**m - 1 - 9/2*w**2.
-(w + 1)**3*(w + 2)/2
Suppose 2*h - 6*h = 0. Suppose -4*o + 20 = 4*f, 5*o - f + 12 - 37 = h. Let -7*y + 6 + o*y**2 + 4*y - 2*y**2 - 6*y = 0. Calculate y.
1, 2
Let c(i) be the first derivative of 11 - 2/15*i**3 - 1/5*i**2 + 0*i. Factor c(v).
-2*v*(v + 1)/5
Solve 1/4*k**4 + 43/4*k - 9/2 + 5/4*k**3 - 31/4*k**2 = 0.
-9, 1, 2
Suppose -l = 0, 5*l - 14 + 2 = -3*n. Let z = 3 + -1. What is v in 4*v**4 + 2*v**2 + z*v**4 - 4*v**n - 4*v**4 = 0?
-1, 0, 1
Let n(i) be the third derivative of i**5/180 - 3*i**4/8 - 5*i**2 - 8*i. Factor n(u).
u*(u - 27)/3
Let w(i) be the first derivative of 2*i**5/5 - 2*i**3/3 + 95. Find t, given that w(t) = 0.
-1, 0, 1
Let i = 87 + -85. Let a be 3/(1 + (-2)/(-4)). Find w, given that -4 + 5*w**2 + 6*w - 3*w**2 - 2*w**a - i*w**2 = 0.
1, 2
Suppose 0 = -2*w - 7*w. Suppose 4*y = 4*s - 4 + 12, -3*s - 4*y + 29 = w. Factor 3/4*q**2 - 3*q + 3/4*q**3 - s.
3*(q - 2)*(q + 1)*(q + 2)/4
Let u(v) be the third derivative of -1/3*v**3 + 0 - 1/6*v**4 + 0*v + 4*v**2 - 1/30*v**5. Solve u(a) = 0 for a.
-1
Let l = -227/2 - -114. Let c(r) be the first derivative of 3/4*r**2 - l*r**3 + 0*r + 3/10*r**5 + 2 - 3/8*r**4. Suppose c(o) = 0. What is o?
-1, 0, 1
Factor 17*k**2 - 50*k**2 - 96*k**2 + 1108*k + 756*k + 1452 - 544*k + 3*k**3.
3*(k - 22)**2*(k + 1)
Let c = 117 + -117. Let f(m) be the first derivative of 1/4*m**4 - 2/3*m**3 + c*m + 13 + 1/2*m**2. Determine u, given that f(u) = 0.
0, 1
Let y be -5 + -12 + 69/4. Let a = 45/212 - -2/53. Factor 3/4*u - 3/4*u**2 + a*u**3 - y.
(u - 1)**3/4
Suppose -42/11*t**4 + 0*t - 534/11*t**3 + 0 + 156/11*t**2 = 0. What is t?
-13, 0, 2/7
Let g(d) be the second derivative of d**6/360 - 2*d**5/15 + 8*d**4/3 + 17*d**3/3 + 8*d. Let w(c) be the second derivative of g(c). Factor w(r).
(r - 8)**2
Let w(n) = n**2 + 17*n + 34. Let k be w(-15). Factor 31*p**5 - 8*p**4 + 3*p - 30*p**5 - 10*p**2 + 5*p**k - 3*p**4 + 12*p**3.
p*(p - 3)*(p - 1)**3
Let t be 20/3*(20 + 5892/(-300)). Factor -2/5*z**3 - 18/5*z + t*z**2 + 0.
-2*z*(z - 3)**2/5
Let q(d) = -d**2 + 2. Suppo