**3 + 6*c**2 - 4*c + 2. Let d(v) = 2*f(v) - r(v). Solve d(i) = 0.
-2, 0
Let z = -6/281 - -371/4215. Let c(o) be the second derivative of 0 + 0*o**3 + 7*o - z*o**4 + 2/5*o**2. Determine h, given that c(h) = 0.
-1, 1
Let p(o) = o + 15. Let l be p(-11). Find q, given that 3 + 0 + 4 + 9 - 12*q**2 + 16*q - 8*q**3 + 4*q**l = 0.
-1, 2
Suppose 50 = -5*w + 7*w. Find r such that 10*r - w*r**2 - 12*r**3 + 15*r**5 - 13*r**3 + 235*r**4 - 210*r**4 = 0.
-2, -1, 0, 1/3, 1
Let i(r) be the second derivative of -1/14*r**7 + 3/10*r**5 + 1/5*r**6 + 0 + 14*r + 7/2*r**3 - 2*r**4 - 3*r**2. Determine w so that i(w) = 0.
-2, 1
Let v be (1 - 18/10)*((-559)/104)/43. What is a in 1/5*a**2 + v*a + 1/10*a**3 + 0 = 0?
-1, 0
Suppose -24*p**2 + 6347*p**3 + 10*p - 400 + 170*p - 6346*p**3 = 0. Calculate p.
4, 10
Let w(x) be the third derivative of 0*x**3 + 33*x**2 + 14/135*x**7 + 182/135*x**6 + 16/27*x**4 - 44/27*x**5 + 0*x + 0. Solve w(q) = 0.
-8, 0, 2/7
Let c(n) be the third derivative of 0*n + 1/210*n**7 + 0 + 2/3*n**3 + 13/60*n**5 + 1/20*n**6 + 1/2*n**4 - 11*n**2. Factor c(g).
(g + 1)**2*(g + 2)**2
Let r be (-4)/(-8)*-4*-1. Let v = 994/5 - 198. Factor 0*q + 2/5*q**r + 0 - v*q**3 - 6/5*q**4.
-2*q**2*(q + 1)*(3*q - 1)/5
Solve 48*h + 84*h**2 - h**4 + 18*h**3 + 18*h**3 + 467*h**5 - 2*h**4 - 937*h**5 + 467*h**5 = 0.
-2, -1, 0, 4
Let x = -13 - 10. Let a(p) = p**3 + 22*p**2 - 24*p - 19. Let n be a(x). Factor 0 + 3/4*k**2 - 3/4*k**n - 3/4*k**3 + 3/4*k.
-3*k*(k - 1)*(k + 1)**2/4
Factor -465*q**3 + 252*q**3 + 248*q**3 + 10*q**2 + 25*q**4.
5*q**2*(q + 1)*(5*q + 2)
Let l = -20 + 20. Suppose -6*g + g - 4*j + 45 = l, 15 = 3*j. Factor g*x**2 - 2*x**4 - 2*x**4 - 2 + 2*x**4 + 8*x + 8*x**3 - 17*x**2.
-2*(x - 1)**4
Factor -5/2*j**5 + 0*j**4 + 0 - 5*j**2 + 0*j + 15/2*j**3.
-5*j**2*(j - 1)**2*(j + 2)/2
Find f such that -17/5*f**2 + 2/5 - 14/5*f**3 - 1/5*f = 0.
-1, -1/2, 2/7
Let a(w) = -5*w**2 + 58*w - 53. Let y(v) = 27*v**2 - 291*v + 264. Let n(r) = 21*a(r) + 4*y(r). Factor n(m).
3*(m - 1)*(m + 19)
Solve -4*i**2 + 4/3*i**3 + 4 - 4/3*i = 0 for i.
-1, 1, 3
Let j(w) be the second derivative of -5*w**7/42 + 3*w**6 - 30*w**5 + 460*w**4/3 - 440*w**3 + 720*w**2 + 306*w. Solve j(n) = 0 for n.
2, 6
Let z = -175/12 - -179/12. Factor -z*f**2 - 2/3 - f.
-(f + 1)*(f + 2)/3
Let p(x) be the second derivative of -x**4/48 + x**3/3 + 9*x**2/8 - 86*x. Factor p(d).
-(d - 9)*(d + 1)/4
Let i(o) be the third derivative of 1/36*o**4 + o**2 + 1/20*o**5 + 0*o**3 + 7/360*o**6 + 0 - 5*o. Let i(f) = 0. What is f?
-1, -2/7, 0
Let t(y) = 8*y**3 + 20*y**2 - 18*y - 30. Let j(m) = 14*m**3 + 40*m**2 - 35*m - 61. Let l(f) = 6*j(f) - 11*t(f). Factor l(c).
-4*(c - 3)**2*(c + 1)
Let t(p) be the second derivative of -p**5/160 - 7*p**4/32 - 49*p**3/16 - 343*p**2/16 + 78*p. Solve t(s) = 0.
-7
Factor 9 - 2 + 2 - 8*l - l**2 + 0.
-(l - 1)*(l + 9)
Let h(i) = 3*i**4 + 4*i**3 + 2*i**2 + i. Let g(o) = o**3 + o**2. Let z(t) = 5*g(t) - h(t). Solve z(r) = 0.
-1, 0, 1/3, 1
Let x be (-44)/(-4) - 4697/429. Let m(q) be the third derivative of -1/130*q**5 + 0 + 7*q**2 + 3/260*q**6 + 4/39*q**3 - x*q**4 + 0*q. Factor m(k).
2*(k + 1)*(3*k - 2)**2/13
Suppose 14*n + 2 = 16*n. Let l be (n - 4)/((-6)/4). Factor 0 + 3/2*d**4 + 2*d - 7/2*d**3 + 0*d**l.
d*(d - 2)*(d - 1)*(3*d + 2)/2
Let -12*f**4 - 47*f**4 + 35*f**2 - 5*f - 21*f**4 - 16*f**3 - 24*f**3 = 0. What is f?
-1, 0, 1/4
Let g(o) be the second derivative of o**4/66 - 7*o**3/33 + 6*o**2/11 + 18*o - 1. Factor g(b).
2*(b - 6)*(b - 1)/11
Let v(y) be the third derivative of y**9/15120 + y**5/10 - 7*y**2. Let k(g) be the third derivative of v(g). Factor k(u).
4*u**3
Factor 4/5*a**3 - 1/5*a**4 - 1/5 + 4/5*a - 6/5*a**2.
-(a - 1)**4/5
Let v(n) be the first derivative of 4*n**3/15 - 28*n**2/5 - 128*n/5 - 94. Factor v(b).
4*(b - 16)*(b + 2)/5
Let p(m) = 6*m**5 - 6*m**3 + 5*m**2. Let k(v) be the first derivative of 7*v**6/6 - 7*v**4/4 + 2*v**3 + 1. Let b(h) = 5*k(h) - 6*p(h). Factor b(a).
-a**3*(a - 1)*(a + 1)
Let j(o) be the third derivative of -o**5/270 - 29*o**4/27 - 3364*o**3/27 + 306*o**2. Solve j(m) = 0.
-58
Solve -8*d + 38*d**3 + 81*d**3 + 59*d - 5*d**4 + 170*d**2 + 69*d - 74*d**3 = 0 for d.
-2, -1, 0, 12
Let w(y) be the second derivative of 5/12*y**4 + 5/42*y**7 + 0*y**2 + 0 - 1/4*y**5 + 0*y**3 - 1/6*y**6 + 20*y. Factor w(p).
5*p**2*(p - 1)**2*(p + 1)
Solve 25*v**3 - 97*v**3 + v**4 + 3*v**4 = 0 for v.
0, 18
Factor 1 - 9*x**2 - 69*x - 9*x**3 - 51*x**2 + 28 + 1.
-3*(x + 2)*(x + 5)*(3*x - 1)
Let v(h) be the first derivative of 5*h**3/12 + 3*h**2/8 - 104. Factor v(i).
i*(5*i + 3)/4
Let k(y) be the second derivative of y**7/840 + 7*y**4/6 + 8*y. Let d(o) be the third derivative of k(o). Factor d(x).
3*x**2
Let f(k) = -96*k**3 + 43*k**2 + 13*k - 155. Let r(w) = -26*w**3 + 11*w**2 + 3*w - 39. Let t(y) = 6*f(y) - 22*r(y). Find p, given that t(p) = 0.
-2, 3
Let d = 34 + -41. Let c(p) = -7*p**3 - 3*p**2 + 3*p - 13. Let x(o) = -10*o**3 - 4*o**2 + 5*o - 19. Let y(v) = d*c(v) + 5*x(v). Factor y(u).
-(u - 2)*(u - 1)*(u + 2)
Let o(m) be the second derivative of -m**4/6 - 71*m**3/6 + 18*m**2 - 206*m. Solve o(q) = 0 for q.
-36, 1/2
Let z(g) be the third derivative of g**5/15 - 6*g**4 + 136*g**3/3 + 2*g**2 - 15. Determine f, given that z(f) = 0.
2, 34
Let m(g) be the second derivative of -g**5/25 - 11*g**4/15 - 14*g**3/3 - 10*g**2 - 192*g. Factor m(p).
-4*(p + 1)*(p + 5)**2/5
Let r(j) be the second derivative of 2 + 4/7*j**2 + 55/21*j**4 + 41/21*j**3 - 26*j + 5/14*j**5. Factor r(c).
2*(c + 4)*(5*c + 1)**2/7
Let i be -2*3/(-69) + 352/184. Factor -7/2*s**i - s - 2*s**3 + 1/2.
-(s + 1)**2*(4*s - 1)/2
Suppose 5*x + d - 17 = 0, 9*d - 8*d = 3*x - 7. Let w(k) be the second derivative of -3*k + 1/2*k**2 + 0 - 1/6*k**x + 1/80*k**5 - 1/48*k**4. Factor w(p).
(p - 2)*(p - 1)*(p + 2)/4
Let s = -154 + 157. Let p(d) be the second derivative of 0*d**2 + 1/50*d**5 + 4*d + 0*d**s + 0*d**4 + 0. Factor p(a).
2*a**3/5
Let h be (-46)/14 - (-4)/14. Let p be 2 - (h - -3)/(-2). Solve -2*z**2 + p*z**2 - 2*z**2 + 4 + 2*z = 0 for z.
-1, 2
Let l(n) = -n + 8. Let i be l(8). Let m be (-3)/(-1) - (0 - i). Factor -3*q**2 - 3*q**3 - 3*q**4 + m*q**5 + 2*q**4 + 4*q**4.
3*q**2*(q - 1)*(q + 1)**2
Let f be (-1)/6 + 345/1800. Let a(n) be the third derivative of 1/5*n**3 + 0 - 1/100*n**5 + 5*n**2 + 0*n - f*n**4. Suppose a(x) = 0. Calculate x.
-2, 1
Let 6 + 3/2*p**2 - 15/2*p = 0. What is p?
1, 4
Let b be 11/(-3) - 14/(-21). Let l be 12/8 - b/6. Factor -8*g**2 - 3*g + 11*g**l - 4 - 2.
3*(g - 2)*(g + 1)
Let j be 105/20*(-20)/(-70). Let d(z) be the first derivative of -1 - j*z**2 + 1/2*z**3 + 3/2*z. Determine a, given that d(a) = 0.
1
Suppose -252 = -32*s - 156. Let k(t) be the first derivative of 1 - 1/4*t**s - 3/2*t**2 - 9/4*t. Suppose k(w) = 0. What is w?
-3, -1
Let t(a) be the second derivative of a**5/30 + 11*a**4/6 + 35*a**3 + 225*a**2 + 108*a - 1. What is v in t(v) = 0?
-15, -3
Let j = 11 + -18. Let f(v) = -v**2 + 6*v - 12. Let r(x) = 39*x - 54. Let l(b) = -8*b + 11. Let p(s) = 24*l(s) + 5*r(s). Let i(a) = j*p(a) + 3*f(a). Factor i(y).
-3*(y - 1)*(y + 2)
Let o(p) be the third derivative of p**7/945 + p**6/108 + 2*p**5/135 + 6*p**2 - p. Suppose o(i) = 0. Calculate i.
-4, -1, 0
Let b = -1815 + 1817. Factor 0*j - 2/3*j**3 + 0 + 2/3*j**b.
-2*j**2*(j - 1)/3
Let y = -1248/5 - -3764/15. Factor y*t**3 + 0*t + 2*t**4 + 0 - 2/3*t**2.
2*t**2*(t + 1)*(3*t - 1)/3
Let w = 64 - 34. Factor 10*u**4 + 14*u**4 + 40*u - 19*u**4 + w*u**3 + 60*u**2.
5*u*(u + 2)**3
Let o(p) be the first derivative of -p**5/5 - 29*p**4/12 - 7*p**3 + 15*p**2/2 + 50*p/3 + 54. Suppose o(g) = 0. Calculate g.
-5, -2/3, 1
Suppose -3*k + 6 = 0, -30*m + 3*k = -28*m. Factor 0 - 1/6*i**4 - 5/6*i**m - 2/3*i - 4/3*i**2.
-i*(i + 1)*(i + 2)**2/6
Suppose -2*a + d = 3*d + 2, -3*a + d = -1. Let m(g) be the second derivative of a*g**2 - g**3 - 7/10*g**6 + 0 - 3/4*g**4 + 9/5*g**5 - 7*g. Factor m(q).
-3*q*(q - 1)**2*(7*q + 2)
Suppose 0 = 5*o - 4*p - 26, 5*p + 28 = o + 3*o. Factor -g**2 + 5*g**4 + 15*g - 10 + 4*g**3 - 19*g**3 + 6*g**o.
5*(g - 2)*(g - 1)**2*(g + 1)
Let k(c) = c**3 + 3*c**2 - 7*c - 10. Let s be k(-4). Suppose -d**2 + 5*d**4 - 4*d**2 - 2*d**4 + s*d**4 = 0. What is d?
-1, 0, 1
Let k(p) = p**3 - 10*p**2 + 9*p + 5. Let n be k(9). Let -m**2 + 4*m**3 + 10*m**n + 10*m**5 + m**4 - 21*m**5 - 3*m**3 = 0. Calculate 