erivative of 1/40*t**5 + 2*t + 0*t**2 + 1/24*t**3 + 1/16*t**d + 0. Factor r(a).
a*(a + 1)*(2*a + 1)/4
Let a(c) = -c**3 - 53*c**2 - 35*c + 305. Let b(k) = -k**3 - 26*k**2 - 17*k + 152. Let p(z) = -2*a(z) + 5*b(z). Factor p(j).
-3*(j - 2)*(j + 5)**2
Let d be 10/(-8) + 1 + (-355)/20. Let v be (2/d)/((-15)/90). Find c, given that -14/15*c - v*c**3 + 6/5*c**2 + 4/15 + 2/15*c**4 = 0.
1, 2
Let g(s) be the second derivative of -s**6/360 + s**5/60 - s**4/24 + 7*s**3/2 - 12*s. Let r(v) be the second derivative of g(v). Factor r(l).
-(l - 1)**2
Let v(r) be the second derivative of -3*r**5/100 - 2*r**4/5 - 8*r**3/5 + 84*r. Suppose v(j) = 0. What is j?
-4, 0
Let d be (280/(-32) - -9)/((-2)/(-8)). Let v be 6/90*d - 2/(-6). Factor -v*n - 2/5*n**2 + 4/5.
-2*(n - 1)*(n + 2)/5
Let t(a) be the first derivative of 6 + 1/12*a**4 + 5/6*a**2 + 4/9*a**3 + 2/3*a. Factor t(i).
(i + 1)**2*(i + 2)/3
Let o = -85 - -88. Suppose 90*a - 114*a - 28*a**2 + o + 1 = 0. Calculate a.
-1, 1/7
Let p(j) be the first derivative of j**6/22 - 41*j**5/55 + 47*j**4/22 - 2*j**3 - j**2/22 + j - 161. What is f in p(f) = 0?
-1/3, 1, 11
Let v be (-78)/10*(-28)/(-21). Let a = v + 213/20. Factor 0*t + 1/4*t**2 - a.
(t - 1)*(t + 1)/4
Suppose -30*u = -39*u + 189. Factor u + 13 - 10 - b**2 + 5*b**2 + 20*b.
4*(b + 2)*(b + 3)
Let i(r) be the first derivative of 4*r**5/5 - 2*r**4 - 491. Factor i(a).
4*a**3*(a - 2)
Suppose -4*u + 4 = -4*p - 20, -4*u + 3*p + 22 = 0. Factor 7*i - u*i**3 + 2 + i**2 - 5*i**2 + 2 - 3*i.
-4*(i - 1)*(i + 1)**2
Suppose 0 = -8*c - 3*c - 572. Let h = c - -54. Solve 1/5*g**h + 0 + 1/5*g = 0.
-1, 0
Let f be -1*(-9 - -3)*37/111. Suppose 3/4*d**f + 3/4*d - 3/2 = 0. Calculate d.
-2, 1
Suppose -1045*y = -1077*y + 96. Determine s so that 6/7*s**y + 0 - 3/7*s**4 + 12/7*s**2 - 24/7*s = 0.
-2, 0, 2
Determine f so that 69*f**2 - 8*f**3 - 30*f**2 - 73*f**2 - 8*f = 0.
-4, -1/4, 0
Let u(f) = -3*f**2 - 3*f + 12. Let w(b) = -13 - 10*b**2 - 12 + 15*b**2 + 5*b. Let g(r) = 5*u(r) + 2*w(r). Suppose g(x) = 0. What is x?
-2, 1
Factor -88*w - 48 + 22/3*w**3 - 97/3*w**2 - 1/3*w**4.
-(w - 12)**2*(w + 1)**2/3
Let i(j) be the first derivative of -j**6/45 + 2*j**5/75 + j**4/15 - 4*j**3/45 - j**2/15 + 2*j/15 + 177. Factor i(q).
-2*(q - 1)**3*(q + 1)**2/15
Suppose -36 - 120*i**2 + 4*i**3 + 38*i**3 + 112*i - 4*i**4 + 4*i**3 + 2*i**3 = 0. Calculate i.
1, 9
Suppose -10/7*o**2 + 24/7*o + 0 - 2/7*o**4 - 12/7*o**3 = 0. What is o?
-4, -3, 0, 1
Solve 3/4*o**2 + 3/8*o**3 - 3/8*o - 3/4 = 0 for o.
-2, -1, 1
Let l(j) be the second derivative of -1/9*j**4 + 0*j**2 + 0*j**6 + 1/10*j**5 - 7*j - 1/63*j**7 + 0*j**3 + 0. Solve l(f) = 0.
-2, 0, 1
Suppose 1/5*r**3 - 9/5 - 11/5*r**2 + 19/5*r = 0. What is r?
1, 9
Let q = 40 + -33. Let g be (29/q + -5)/(-3). Factor -g*p**2 - 2/7 + 4/7*p.
-2*(p - 1)**2/7
Suppose -x = -s + 5, -20*s + 25*s + 4*x = 16. Let q(v) be the first derivative of 0*v + 0*v**2 + 1/21*v**6 + 0*v**s - 2 + 0*v**3 + 2/35*v**5. Factor q(u).
2*u**4*(u + 1)/7
Let u(a) = -36*a**3 - 219*a**2 - 377*a - 67. Let f(c) = 18*c**3 + 110*c**2 + 188*c + 34. Let p(z) = 10*f(z) + 4*u(z). Factor p(k).
4*(k + 3)**2*(9*k + 2)
Let x = -5423 - -5423. What is n in 3/5*n**2 - 2/5*n + x + 1/5*n**5 + 1/5*n**3 - 3/5*n**4 = 0?
-1, 0, 1, 2
Factor -89*v - 3160 - 15*v + 3192 + 44*v**2.
4*(v - 2)*(11*v - 4)
Let b be (-5 + 15)/(3/12). Suppose -6 = -2*d, -2*n - 3*n = 5*d - b. Factor 2*z**2 + 7 + 2*z**2 - z - n*z**2 - 5.
-(z - 1)*(z + 2)
Let z(q) be the first derivative of q**9/8064 + q**8/2240 + 4*q**3/3 + 10. Let u(p) be the third derivative of z(p). Factor u(g).
3*g**4*(g + 2)/8
Let b be (-3)/(-10) + (-38)/(-76). Let k(q) be the first derivative of 8/5*q + 2/15*q**3 - 3 - b*q**2. Factor k(z).
2*(z - 2)**2/5
Suppose 2*m + 18 = -4*m. Let p(q) = q**2 - q - 1. Let h(j) = j**3 + 8*j**2 - 3*j - 5. Let b(v) = m*h(v) + 15*p(v). Factor b(w).
-3*w*(w + 1)*(w + 2)
Let x be ((-2)/8)/((-1)/8). Let i(p) = -8*p**3 + 10*p**2 + 12*p - 2. Let m(f) = -f**3 + f**2 + f + 1. Let g(j) = x*m(j) - i(j). Factor g(y).
2*(y - 2)*(y + 1)*(3*y - 1)
Let q(g) be the second derivative of -g**7/4200 - g**6/900 - 10*g**3/3 - 9*g. Let s(o) be the second derivative of q(o). Factor s(x).
-x**2*(x + 2)/5
Let b = 70/39 - -446/273. Solve -b*a + 100/7*a**5 + 0 + 128/7*a**2 - 30/7*a**4 - 174/7*a**3 = 0.
-3/2, 0, 2/5, 1
Factor 28 + 33/5*h + 1/5*h**2.
(h + 5)*(h + 28)/5
Let z(p) = p**4 + p**3 + p. Let u(m) = 4*m**4 + 9*m**3 + 8*m**2 - 3*m - 9. Let s(w) = 5*u(w) - 15*z(w). What is x in s(x) = 0?
-3, -1, 1
Let n(o) = 4*o**4 + 40*o**3 - 44*o**2 + 4*o + 4. Let q(h) = -12*h**4 - 120*h**3 + 132*h**2 - 11*h - 11. Let g(z) = 11*n(z) + 4*q(z). Factor g(i).
-4*i**2*(i - 1)*(i + 11)
Let i = 1354 - 1354. Let r(h) be the third derivative of 0*h**3 - 1/540*h**6 + 0*h**5 + 4*h**2 - 1/945*h**7 + 0*h**4 + 0*h + i. Factor r(q).
-2*q**3*(q + 1)/9
Let v(s) be the second derivative of s**7/280 + s**6/60 - 3*s**5/40 - 2*s**3/3 - 3*s. Let w(b) be the second derivative of v(b). Let w(p) = 0. Calculate p.
-3, 0, 1
Let j(f) be the first derivative of -f**5 + 35*f**4/4 - 80*f**3/3 + 30*f**2 - 314. Let j(h) = 0. What is h?
0, 2, 3
Suppose 3 = -3*d + 12. Factor 28*j - 6*j**2 + 4*j**d - 6*j**2 - 20*j.
4*j*(j - 2)*(j - 1)
Let o(u) be the third derivative of -u**7/70 + 3*u**6/70 + 207*u**5/140 - 19*u**4/7 - 30*u**3/7 + 583*u**2. Suppose o(z) = 0. Calculate z.
-5, -2/7, 1, 6
Let q be -4*(-8 + 16/4). Determine p so that 34*p**2 - 10 + 85*p**3 - 10*p**3 + 20*p**4 + q*p**2 + 15*p + 30*p**2 = 0.
-2, -1, 1/4
Let v = -2236 + 2236. Let b(j) be the third derivative of 0 + v*j + 0*j**4 - 10*j**2 + 1/30*j**5 - 1/3*j**3. Find f such that b(f) = 0.
-1, 1
Factor 17/2*x**2 + 1/2*x**4 + 5*x + 0 + 4*x**3.
x*(x + 1)*(x + 2)*(x + 5)/2
Let f = 61 + -58. Factor 4*d**5 - f*d**4 - 4*d**3 + 8*d**4 + 3*d**4 - 8*d**5.
-4*d**3*(d - 1)**2
Suppose 8*j = 12*j. Let -5*x - 4*x**5 + j*x + 10*x**3 + 4*x**5 - 5*x**5 = 0. What is x?
-1, 0, 1
Suppose 18 = 5*o - 4*l, 0 = -4*o + 19*l - 17*l + 18. Let j(x) be the third derivative of -1/36*x**5 + 0 - o*x**2 + 2/9*x**3 + 0*x - 1/9*x**4. Factor j(d).
-(d + 2)*(5*d - 2)/3
Let u(b) be the first derivative of b**6/120 - b**5/20 + 35*b**3/3 + 13. Let d(x) be the third derivative of u(x). Find z, given that d(z) = 0.
0, 2
Find k, given that 76/3*k**2 + 46/3*k**3 - 8/3*k**4 - 440/3*k + 400/3 - 2/3*k**5 = 0.
-5, 2
Suppose -c + 87 = 3*c - 3*m, -97 = -4*c + 5*m. Suppose 40*v**2 - 7*v**3 + c*v**3 + 14*v**3 + 5*v**4 + 20*v = 0. Calculate v.
-2, -1, 0
Suppose 2*r - 2*n = n + 3, -5 = 2*r + 5*n. Suppose r = 4*y + x + 5 - 21, -4*y = -4*x - 16. Find v such that 0*v**y + 0 + 0*v - 2/3*v**5 + 4/3*v**2 + 2*v**3 = 0.
-1, 0, 2
Let z(x) = -x**2 - 749*x - 2238. Let d be z(-3). Determine p, given that 1/2*p**2 + 11/2*p + d = 0.
-11, 0
Let i(d) be the first derivative of -3*d**5/10 - 3*d**4/4 + 31*d**3/2 + 69*d**2 + 90*d - 366. Find v, given that i(v) = 0.
-5, -2, -1, 6
Let h(d) be the first derivative of 32*d**5/5 - 44*d**4 + 274*d**3/3 - 53*d**2 + 12*d + 6. Factor h(z).
2*(z - 3)*(z - 2)*(4*z - 1)**2
Find c, given that -12 - 20 - 24 + 3*c**2 + 2 - 21*c = 0.
-2, 9
What is b in -2 - 168*b**3 - 105 + 108*b + 29 - 116 - 4*b**5 + 44*b**4 + 216*b**2 - 130 = 0?
-1, 3
Let h(v) be the first derivative of 10 + 0*v**2 + 1/30*v**4 + 1/25*v**5 + 1/75*v**6 + 0*v**3 - 4*v. Let d(f) be the first derivative of h(f). Factor d(c).
2*c**2*(c + 1)**2/5
Determine b so that -1/2*b**4 + 16*b**3 + 51*b**2 + 52*b + 35/2 = 0.
-1, 35
Let r be (12/42)/(2/14). Factor 4*g**2 + g**3 - 4*g**2 - 8*g + 5*g**3 - 8*g**4 + r*g**5 + 8*g**2.
2*g*(g - 2)**2*(g - 1)*(g + 1)
Let s be (-2)/(-14) + 1/(-7). Suppose 3*q = -s*q + 6. Factor n**3 - 7*n**q + 10*n**2 + 0*n**3.
n**2*(n + 3)
Factor 6/7*r**2 + 8 + 88/7*r.
2*(r + 14)*(3*r + 2)/7
Let i(j) be the first derivative of -3*j**4/28 + 2*j**3 - 75*j**2/14 + 36*j/7 - 12. Let i(t) = 0. What is t?
1, 12
Let c(h) be the third derivative of -h**6/240 - h**5/120 + 25*h**4/48 + 25*h**3/12 + 12*h**2 + 5*h. Factor c(j).
-(j - 5)*(j + 1)*(j + 5)/2
Let m(r) = 11*r**3 + 10*r**2 - 6*r. Let n(q) = -13*q**3 - 11*q**2 + 6*q. Let i(b) = -6*m(b) - 5*n(b). Factor i(c).
-c*(c - 1)*(c + 6)
Suppose 8/5*a + 24/5*a**4 - 4/5*a**3 - 4*a**2 + 0 = 0. What is a?
-1, 0, 1/2, 2/3
Let i(t) = 5 + 16*t**2 - 6*t + 3 - 15*t**2. Let w be i(2). Find h, given that 1