ative of p**4/30 - p**3 + 14*p**2/5 - 3*p + 1. Factor o(c).
2*(c - 14)*(c - 1)/5
Let y(g) = 20*g - 48*g**3 - 2*g**3 - 8*g**2 - 27*g**2. Let p(n) = 25*n**3 + 18*n**2 - 10*n. Let i(q) = -5*p(q) - 3*y(q). Factor i(w).
5*w*(w + 1)*(5*w - 2)
Let a(k) be the second derivative of 0 + 0*k**2 + 4/5*k**5 - 2/7*k**7 - 4/15*k**6 - 2/3*k**3 + 21*k + 2/3*k**4. Let a(z) = 0. Calculate z.
-1, 0, 1/3, 1
Let t(w) be the second derivative of 4*w**5 - 1/2*w**6 + 0 + 50/3*w**3 - 10*w**2 - 145/12*w**4 + 15*w. Let t(n) = 0. What is n?
1/3, 1, 2
Suppose 5*p + 0*p + w + 28 = 0, 0 = 5*p + 3*w + 24. Let n = -2 - p. Factor -o**3 - 2*o**2 + o**2 + o**5 - 6*o**n + 7*o**4.
o**2*(o - 1)*(o + 1)**2
Let b = 15931/5 + -3185. Determine p so that -2*p + 2/5*p**3 - b*p**2 + 2/5*p**4 - 4/5 = 0.
-1, 2
Suppose 5*n = 14 + 21. Factor 2 - n*l**2 - l - 5*l**2 + 11*l**2.
-(l - 1)*(l + 2)
Factor 1/3*c**2 - 9 - 26/3*c.
(c - 27)*(c + 1)/3
Let y(b) be the second derivative of b**6/75 - 9*b**5/25 + 27*b**4/10 + 69*b. Factor y(s).
2*s**2*(s - 9)**2/5
Suppose 255*w + 180*w + 56*w**3 - 20*w + 297*w - 128 - 940*w**2 = 0. Calculate w.
2/7, 1/2, 16
Let g = -3864 + 11593/3. Let 4/3*j - j**3 + 0 + 0*j**2 - g*j**4 = 0. Calculate j.
-2, 0, 1
Suppose -h = -8*h + 28. Solve -5*c**2 - 10*c**3 - c + c - 5*c**h + 20*c**3 = 0 for c.
0, 1
Suppose 38 + 24 = 31*k. Let q(m) be the first derivative of -3 + 2/11*m**k + 7/22*m**4 + 0*m + 6/11*m**3. Solve q(d) = 0 for d.
-1, -2/7, 0
Suppose 46*w**3 - 2*w**5 - 63*w**4 - 28*w - 31*w**3 - 86*w**2 + 29*w**4 - 105*w**3 = 0. What is w?
-14, -1, 0
Let u(m) be the third derivative of -m**6/240 - m**5/3 - 39*m**4/4 - 108*m**3 - 34*m**2 - 3. Find v, given that u(v) = 0.
-18, -4
Let w = 33 - 34. Let f be w/((8/(-12))/2)*1. Solve 0*x**2 + 0*x + 0 + 1/3*x**f = 0 for x.
0
Let p = -35 + 33. Let i(g) = -2*g**3 - 4*g**2 + 2*g + 2. Let f(j) be the first derivative of j**4/4 - j**3/3 + j + 1. Let k(r) = p*f(r) + i(r). Factor k(b).
-2*b*(b + 1)*(2*b - 1)
Let x(m) = -m**3 - 13*m**2 - 18*m + 49. Let a be x(-11). Determine v, given that -4/5*v**3 - 4/5*v**2 + 6/5*v - 2/5 + 6/5*v**4 - 2/5*v**a = 0.
-1, 1
Suppose -4*d = 2*y - 70, 3*d - 46 = 4*y + y. Determine a, given that -4*a + 40 + 16*a + a + d*a + 5*a**2 = 0.
-4, -2
Factor 26/7*k - 20/7 - 6/7*k**2.
-2*(k - 1)*(3*k - 10)/7
Let z(p) be the second derivative of 1/30*p**6 + 1/84*p**7 - 1/12*p**4 + 0*p**3 + 0*p**2 - 5*p - 1/40*p**5 + 0. What is t in z(t) = 0?
-2, -1, 0, 1
Let g be 21*5/45 + 30/(-90). Determine l so that 0 + 2/3*l**g + 1/3*l**3 + 1/3*l = 0.
-1, 0
Let s(p) be the first derivative of -14*p**5/5 + 85*p**4 - 32*p**3 - 474. Factor s(q).
-2*q**2*(q - 24)*(7*q - 2)
Factor -23/6*g + 1/3 - 29/2*g**2.
-(3*g + 1)*(29*g - 2)/6
Let v(o) be the first derivative of -4 + 1/3*o**6 - 3*o**2 - 2*o + o**4 - 4/3*o**3 + 6/5*o**5. Solve v(l) = 0 for l.
-1, 1
Suppose -10821 = -2*k + 3*m - 3600, 4*k - 14469 = -3*m. Find t, given that -k - t**4 + 3615 = 0.
0
Let h(k) = -5*k**2 - 10*k + 12. Suppose 0 = -5*l - 7 - 3, -4*i - 5*l - 22 = 0. Let q(n) = -1. Let v(o) = i*q(o) + h(o). Suppose v(j) = 0. Calculate j.
-3, 1
Let a be (2 + 12)/(6/(-9)). Let w = -16 - a. Solve -6*z**2 + 3*z - z + w*z**2 = 0 for z.
0, 2
Let i(l) = 160*l**3 - 80*l**2 - 426*l - 216. Let h(g) = 64*g**3 - 32*g**2 - 171*g - 87. Let m(s) = 12*h(s) - 5*i(s). Factor m(q).
-2*(q - 2)*(4*q + 3)**2
Suppose -16 = -5*y + 14. Factor 5*c**2 - 125*c + 227 + y*c - 21*c + 753.
5*(c - 14)**2
Let x(g) = 7*g**4 - 20*g**3 - 7*g**2 + 23*g. Let y(o) = 8*o**4 - 20*o**3 - 8*o**2 + 24*o. Let d(u) = 4*x(u) - 3*y(u). Factor d(q).
4*q*(q - 5)*(q - 1)*(q + 1)
Let l(j) = j**2 - 16*j - 15. Let m be l(17). Factor 7*s**2 - 33*s**m - 5*s**4 - 5*s + 25*s**3 + 20*s - 9*s**2.
-5*s*(s - 3)*(s - 1)**2
Determine d so that 540*d + 26*d**2 + 460*d - 156*d + 21*d**2 - 45*d**2 + 89042 = 0.
-211
Suppose 0 = -5*m - 2*r + 24, 0 = m - 3*r + 6*r - 10. Factor -8*z**m + 2*z**3 - z - 8*z**2 - 6*z**3 - 8*z**3 - 2*z**5 - z.
-2*z*(z + 1)**4
Let c(x) be the first derivative of 2*x**3/39 + 2*x**2/13 + 2*x/13 + 74. Factor c(k).
2*(k + 1)**2/13
Let m(w) be the second derivative of -10/21*w**4 + 0*w**6 - 4/7*w**2 + 5/7*w**3 + 0 + 1/7*w**5 - 1/147*w**7 - 42*w. Factor m(b).
-2*(b - 1)**4*(b + 4)/7
Factor -3/5*m**2 - 21/5*m - 6.
-3*(m + 2)*(m + 5)/5
Let p be (0 - 8)*((-6)/(-4) + -2). Find c such that 259*c + 8*c**2 + 12*c**3 + p*c**4 - 259*c = 0.
-2, -1, 0
Suppose 3*o - 8*o = 0, -4*i - o = -48. Let f be ((-8)/i)/(30/(-9)). Determine k so that -k - f - 2*k**2 - k**4 - 1/5*k**5 - 2*k**3 = 0.
-1
Factor -4923*m**2 + 9843*m**2 + 102*m - 867 - 4923*m**2.
-3*(m - 17)**2
Find t, given that 5/2 - 9/2*t + 3/2*t**2 + 1/2*t**3 = 0.
-5, 1
Let o(x) be the first derivative of x**6/810 - x**5/120 + x**4/108 + 13*x**3/3 - 10. Let p(s) be the third derivative of o(s). Factor p(z).
(z - 2)*(4*z - 1)/9
Find o, given that -3*o**4 + 6*o - 678*o**2 - 676*o**2 + 1363*o**2 = 0.
-1, 0, 2
Suppose 0 = f - y - 1, -f - 1 = -3*f + 3*y. Suppose 69 = -f*w + 183. Find p, given that 15*p**4 + 156/5*p + 24/5 + w*p**3 + 342/5*p**2 = 0.
-2, -1, -2/5
Let k(g) be the second derivative of -g**4/24 - 5*g**3/6 + 13*g - 1. Factor k(u).
-u*(u + 10)/2
Let l(n) be the second derivative of -n**5/4 + 10*n**4/3 + 25*n**3/2 - 135*n**2 - 152*n. Find g such that l(g) = 0.
-3, 2, 9
Let t = -2/755 + 4544/5285. Let c be (-96)/432 + (-50)/(-63). What is x in -t*x - 2/7*x**2 - c = 0?
-2, -1
Find j, given that 0*j - 3*j**2 + 3*j**3 - 3/4*j**4 + 0 = 0.
0, 2
Suppose -2*v = -o - 208 + 206, 5*v = 5*o - 5. Factor -4/3*n**o + 8/3*n**3 - 16/3*n + 4*n**2 - 16/3.
-4*(n - 2)**2*(n + 1)**2/3
Suppose -16 = -7*k - 2. Let x(g) be the second derivative of 2*g + 0*g**4 - 1/126*g**7 + 1/30*g**5 + 0 - 1/18*g**3 + 0*g**k + 0*g**6. Factor x(y).
-y*(y - 1)**2*(y + 1)**2/3
Let m(l) be the second derivative of -l**6/12 - l**5/4 + 5*l**4/2 - 35*l**3/6 + 25*l**2/4 - 92*l. Factor m(a).
-5*(a - 1)**3*(a + 5)/2
Let x(r) be the third derivative of 2*r**7/105 + r**6/5 + r**5/15 - 4*r**4 + 32*r**3/3 - 416*r**2. Factor x(t).
4*(t - 1)**2*(t + 4)**2
Determine q, given that -18/7 + 2/7*q**3 - 34/7*q - 2*q**2 = 0.
-1, 9
Let s = -2/82315 - -68568401/246945. Let m = 278 - s. Determine i so that m*i**3 - 1 - 1/3*i**2 - 5/3*i = 0.
-1, 3
Let w = -2367 - -21307/9. Find i such that -2/9*i**2 + 0 + w*i = 0.
0, 2
Suppose -2*l = -164 - 46. Let z = l + -101. Suppose 2/3*k**3 - 2/3*k + 1/3 - 1/3*k**z + 0*k**2 = 0. What is k?
-1, 1
Suppose -15*k + 5*k - 70 = 0. Let w(l) = l**2 + 4*l - 18. Let b be w(k). Solve 0 - 1/4*m**4 + 1/4*m**2 + 1/4*m - 1/4*m**b = 0.
-1, 0, 1
Let q(h) be the third derivative of -h**7/280 - h**6/80 + 7*h**5/80 + 5*h**4/8 + 3*h**3/2 + 110*h**2. Find m such that q(m) = 0.
-2, -1, 3
Let n(u) be the first derivative of 0*u + 1/30*u**5 - 7/120*u**6 + 4 - 1/3*u**3 + 7/24*u**4 + 3*u**2. Let t(r) be the second derivative of n(r). Factor t(m).
-(m - 1)*(m + 1)*(7*m - 2)
Suppose 4/7*b**5 - 4/7*b**3 - 16/7 - 12/7*b**4 + 0*b + 4*b**2 = 0. What is b?
-1, 1, 2
Let r(k) = -127*k - 4189. Let h be r(-33). Find y, given that 1/9*y**h + 1/9 - 2/9*y = 0.
1
Let q(a) be the second derivative of -a**5/10 + 14*a**4/3 - 196*a**3/3 + 127*a. Let q(l) = 0. What is l?
0, 14
Let z = -56 - -61. Factor 9*s**2 + 11*s**2 + 0 - 22*s + 10 - z*s**3 - 3*s.
-5*(s - 2)*(s - 1)**2
Let v = 25 - 23. Factor -26*c**2 + c**v + 8*c + 5*c**4 + 7*c + 5*c**3.
5*c*(c - 1)**2*(c + 3)
Let m = 17/22 + -29/66. Let j = 15 - 13. Solve m + 17/3*h**4 - 2*h**j - 5/2*h**5 + 5/6*h - 7/3*h**3 = 0.
-2/5, -1/3, 1
Let f(v) be the second derivative of v**6/1080 - v**5/360 - v**4/36 + 13*v**3/6 - 14*v. Let t(i) be the second derivative of f(i). Factor t(r).
(r - 2)*(r + 1)/3
Let h(k) = -k**3 - k**2. Let w(t) = -t + 13. Let m be w(10). Let j(q) = -11*q**3 + 19*q**m - 34*q**2 + 2*q + 6*q. Let c(n) = 10*h(n) - j(n). Factor c(b).
-2*b*(3*b - 2)**2
Let v(w) be the first derivative of -8 + 2/3*w**4 + 0*w**2 + 0*w + 2/15*w**5 + 8/9*w**3. Factor v(c).
2*c**2*(c + 2)**2/3
Find h such that -6/7*h**2 + 0 + 2/7*h = 0.
0, 1/3
Let x = 137 + -89. Let h = x - 46. Factor -1/3*j**h + 0*j + 1/3.
-(j - 1)*(j + 1)/3
Let v(m) = m**4 + 6*m**3 - 4*m**2 - 6*m + 7. Let w(x) = -3*x**4 - 11*x**3 + 7*x**2 + 11*x - 14. Let p(j) = 5*v(j) + 2*w(j). Solve p(b) = 0 for b.
-1, 1, 7
Determine f so that -32*f**2 + 374 + 4*f**3 + 8