1. Let w(i) = -4*c(i) + m(i). Find y such that w(y) = 0.
-1, 0, 1
Let v be (234/104)/((-6)/(-20)). Let k = -69/10 + v. Factor -k*i**2 - 3/5*i - 1/5 - 1/5*i**3.
-(i + 1)**3/5
Suppose -5*l = 108 - 118. Let h(k) be the first derivative of -1/2*k**2 + 5 + 1/3*k**3 - l*k. Factor h(o).
(o - 2)*(o + 1)
Let s(y) be the first derivative of 2*y**3/27 - 37*y**2/9 + 262. Factor s(n).
2*n*(n - 37)/9
Suppose -5*o = -3*y - 15, -7*o - 9*y + 10 = -11*y. Determine l so that o + 0*l + 3/2*l**2 + 3/4*l**4 - 9/4*l**3 = 0.
0, 1, 2
Let s = 3957 + -3953. Solve -3/4*u**2 + 0 - 1/2*u + 3/4*u**s + 1/4*u**3 + 1/4*u**5 = 0.
-2, -1, 0, 1
Determine d, given that 7/4 + 1/4*d**2 + 2*d = 0.
-7, -1
Let p(s) = s**2 - 13*s - 2. Let l be p(15). Factor -4*m**2 - 3*m - m - 36*m**4 + 38*m**4 + 27*m**3 - l*m**4 + 7*m**5.
m*(m - 2)*(m - 1)**2*(7*m + 2)
Suppose 3*i + 11 + 22 = 0. Let j(a) = 3*a + 37. Let l be j(i). Determine k so that 2/3*k**3 - 4/3*k**l - 2/3 - 2/3*k + 2*k**2 = 0.
-1, -1/2, 1
Suppose 9*l = 6*l + 15. Factor 8*i - 3*i**2 - 4 - 4*i**2 - l*i**3 + 6*i**4 + i**5 - 5*i**4 + 6*i**2.
(i - 1)**3*(i + 2)**2
Factor -6 + 3/4*c**4 - 9*c - 3/2*c**2 + 9/4*c**3.
3*(c - 2)*(c + 1)*(c + 2)**2/4
Let c = 3437/278 - -158/139. Factor 117/2*g**2 + 18 + 60*g + c*g**3.
3*(g + 3)*(3*g + 2)**2/2
Let o = 8 + -6. Factor 15*s + 6*s**2 - 4*s**2 - 3*s**2 + 4*s**o + 12.
3*(s + 1)*(s + 4)
Let t(m) be the second derivative of m**6/10 - 33*m**5/20 - 3*m**4/4 + 35*m**3/2 - 33*m**2 - 105*m. Factor t(j).
3*(j - 11)*(j - 1)**2*(j + 2)
What is d in 40/7 + 212/7*d**2 - 242/7*d - 10/7*d**3 = 0?
1/5, 1, 20
Let g = 435 + -433. Let h(j) be the second derivative of -1/98*j**7 - 1/14*j**3 - 3/14*j**g + 9*j + 3/70*j**5 + 1/14*j**4 - 1/70*j**6 + 0. Factor h(q).
-3*(q - 1)**2*(q + 1)**3/7
Factor 2/3*r**3 - 14*r + 40/3*r**2 + 0.
2*r*(r - 1)*(r + 21)/3
Let j be 6/15 + 3082/20. Let o = 156 - j. Factor o - 2*t + 1/2*t**2.
(t - 3)*(t - 1)/2
What is z in -56/15*z - 8/5 - 2/15*z**4 - 16/15*z**3 - 46/15*z**2 = 0?
-3, -2, -1
Let w(b) = -12*b + 230. Let m be w(19). Factor -s - 1/2*s**2 + m + 1/4*s**3.
(s - 2)**2*(s + 2)/4
Let b = -9770/3 - -3258. What is d in 2/3*d**2 - 2/3*d**3 + b*d + 0 = 0?
-1, 0, 2
Let a(w) be the third derivative of -w**9/5670 - w**8/3360 + w**7/3780 + w**4/8 - 13*w**2. Let d(i) be the second derivative of a(i). Factor d(v).
-2*v**2*(v + 1)*(4*v - 1)/3
Let a(n) be the first derivative of n**6/6 + 2*n**5 + 6*n**4 - 10*n**3/3 - 25*n**2/2 + 29. Find o such that a(o) = 0.
-5, -1, 0, 1
Factor w**4 - 6912 + 76*w**3 - 1098*w**2 - 3*w**4 + 7914*w - 2730*w + 58*w**2 + 32*w**2.
-2*(w - 12)**3*(w - 2)
Let o = 238 - 259. Let z = o + 21. Find b such that -3*b**3 + z + 0*b + 3/2*b**2 + 3/2*b**4 = 0.
0, 1
Suppose 0 = -4*x + 6*x - 14. Factor 0*d**2 - 8*d - d**2 - 18 - x*d + 4*d**2.
3*(d - 6)*(d + 1)
Let u = 37 - 41. Let a(d) = -d**2 + 8*d - 27. Let o(l) = 5*l**2 - 39*l + 136. Let j(w) = u*o(w) - 22*a(w). Factor j(m).
2*(m - 5)**2
Factor -1/3*x**3 - 11/3*x**2 + 4*x + 0.
-x*(x - 1)*(x + 12)/3
Factor 156/11*u - 42/11*u**2 + 432/11 - 6/11*u**3.
-6*(u - 4)*(u + 2)*(u + 9)/11
Let j = 109 + -109. Suppose -3*c - t + 10 = 0, -c + 0*t + 3*t - 10 = j. Factor 2*m**3 - m**c - 7/8*m - 1/8.
(m - 1)*(4*m + 1)**2/8
Let l(f) be the first derivative of 15/4*f**4 - 3 + 9/5*f**5 - 2*f - 7/2*f**2 + 1/3*f**3. Factor l(m).
(m + 1)**2*(3*m - 2)*(3*m + 1)
Let x(o) be the first derivative of -8*o**3/9 + 73*o**2/3 - 12*o + 27. Factor x(q).
-2*(q - 18)*(4*q - 1)/3
Let j(g) be the first derivative of 3*g**4/16 + 5*g**3 + 69*g**2/2 + 84*g - 623. Factor j(n).
3*(n + 2)*(n + 4)*(n + 14)/4
Let v(l) = -10*l**2 - 214*l + 208. Let f(o) = -12*o**2 - 216*o + 208. Let q(z) = 4*f(z) - 5*v(z). Factor q(s).
2*(s - 1)*(s + 104)
Suppose 17*d - 15*d = 96. Let t be (-2)/(-7) + d/28. What is z in 2/3*z**4 + 2*z**t + 2*z**3 + 2/3*z + 0 = 0?
-1, 0
Solve 97 + 5*j**4 + 2*j**5 - 60*j**3 + 80*j + 2*j**2 + 3*j**5 - 97 + 18*j**2 = 0.
-4, -1, 0, 2
Let c = -5 - -9. Suppose 3*r - 7*q = -3*q + 21, c*q + 35 = 5*r. Let -4*o + o**2 + r*o - 16*o**2 = 0. Calculate o.
0, 1/5
Suppose 5*o = -2*h - 140, -2*o + 3*o - 5*h = -28. Let c be 14/4*o/(-49). Find m, given that -m - 2*m**3 - 3*m + 0*m**3 + 6*m**c = 0.
0, 1, 2
Factor 5/2*v + 1/2*v**2 - 3.
(v - 1)*(v + 6)/2
Find k, given that 1/8*k**4 + 0 + 5/8*k**2 + 0*k + 3/4*k**3 = 0.
-5, -1, 0
Let w be 16/(-28) + 25/7. Let g = w + 0. What is j in j**4 + 1 + j - 2*j**4 + 5*j - 4*j - 2*j**g = 0?
-1, 1
Find g, given that -80/3*g - 5/3*g**2 + 85/3 = 0.
-17, 1
Let w(g) be the third derivative of -5*g**8/84 - g**7/14 + g**6/24 - 355*g**2. Factor w(d).
-5*d**3*(d + 1)*(4*d - 1)
Let j = 52 + -52. Let f(l) = l**3 - 2*l**2 - l - 3. Let c be f(3). Factor j*a + c*a**2 - 11*a + 5*a.
3*a*(a - 2)
Solve 14/15*h**3 + 0 + 4/15*h + 8/3*h**4 - 22/15*h**2 = 0 for h.
-1, 0, 1/4, 2/5
Factor 1/4*t**3 + 1/4*t**4 + 0 + 0*t - 3/2*t**2.
t**2*(t - 2)*(t + 3)/4
Let b(v) be the third derivative of v**6/360 + v**5/48 + v**4/24 - 11*v**3/3 - 17*v**2. Let i(h) be the first derivative of b(h). Factor i(z).
(z + 2)*(2*z + 1)/2
Let -1/6*i**4 + 0 + 0*i + 0*i**2 + 7/2*i**3 = 0. What is i?
0, 21
Factor 46*f + 10*f + 3*f**2 + 67*f - 8*f**2 - 28*f.
-5*f*(f - 19)
Let a be 170/(-850)*(-110)/3 + (-8)/6. Factor -270*l - a - 6075/2*l**2.
-3*(45*l + 2)**2/2
Let b(d) be the third derivative of 2*d**7/525 - 9*d**5/25 + 5*d**4/3 - 16*d**3/5 - 3*d**2 - 12. Factor b(c).
4*(c - 4)*(c - 1)**2*(c + 6)/5
Let a(s) = 18*s + 832. Let o be a(-46). Determine w so that 0*w**2 + w - w**3 + 1/2*w**o - 1/2 = 0.
-1, 1
Factor -58*k**2 + 119*k**2 - 51*k**2 + 15*k.
5*k*(2*k + 3)
Suppose -4*x + 5*x - 201 = -4*f, 0 = x - 1. Factor y**4 + f*y**3 + 198*y + 147*y**2 + 145*y - 29*y**3.
y*(y + 7)**3
Let u(g) be the first derivative of g**7/105 - g**6/75 - g**5/25 + 21*g - 23. Let s(i) be the first derivative of u(i). Suppose s(p) = 0. Calculate p.
-1, 0, 2
Let l be (-5)/(-3) + 32/24. Let s(j) be the second derivative of -2/33*j**l - 1/66*j**4 + 2*j + 3/11*j**2 + 0. Factor s(z).
-2*(z - 1)*(z + 3)/11
Let m(f) = 2*f**2 + f - 2. Let y be m(-2). Factor 4*p - 4*p**5 - y*p**2 + 0*p**5 + 8*p**4 - 4*p**2.
-4*p*(p - 1)**3*(p + 1)
Let q(g) = -g**2 + 17*g + 25. Let z be q(18). Suppose -6*n + z = -11. Find k, given that -35*k**3 + 36*k**3 - n*k + 2 - 4 = 0.
-1, 2
Let -125/8*z**3 - 75*z**2 - 64 - 120*z = 0. Calculate z.
-8/5
Let s(l) be the third derivative of -9*l**8/2240 - l**7/140 - l**6/180 + l**5/4 + 5*l**2. Let b(p) be the third derivative of s(p). Factor b(h).
-(9*h + 2)**2
Let m(g) be the second derivative of g**6/6 - 11*g**5/20 + g**4/4 + 7*g**3/6 - 2*g**2 - 10*g + 1. Factor m(x).
(x - 1)**3*(5*x + 4)
Let d(h) be the first derivative of -h**3/3 + 5*h**2/2 + 69*h + 25. Let o be d(11). Factor 3/5*q + 3/5*q**4 + 3/5*q**5 - 6/5*q**2 + 3/5 - 6/5*q**o.
3*(q - 1)**2*(q + 1)**3/5
Let b be 502/2640 + 10/(-55). Let k(l) be the third derivative of b*l**6 + 0*l**7 + 0*l**5 - 1/48*l**4 + 0 - l**2 + 0*l + 0*l**3 - 1/672*l**8. Factor k(f).
-f*(f - 1)**2*(f + 1)**2/2
Let t be ((-9)/(180/(-2)))/1. Let y(s) be the second derivative of 0*s**2 + t*s**6 - 1/4*s**4 - 1/2*s**3 + 3/20*s**5 + 6*s + 0. Factor y(n).
3*n*(n - 1)*(n + 1)**2
Let t(r) be the third derivative of -r**5/30 - 7*r**4/6 - 13*r**3/3 + 281*r**2. Determine f, given that t(f) = 0.
-13, -1
Let f(x) be the second derivative of 3*x**5/20 - 399*x**4/2 + 106134*x**3 - 28231644*x**2 - 121*x. Find v, given that f(v) = 0.
266
Let y be 0*(-3)/(-2)*(-5)/15. Let t(s) be the second derivative of 0 + y*s**3 + 2/21*s**7 + 1/3*s**4 + 3/5*s**5 + 2/5*s**6 - 3*s + 0*s**2. Factor t(w).
4*w**2*(w + 1)**3
Find q such that -2*q**2 + 18 - 18*q + 4*q**3 + 11*q**2 - 7*q**2 - 2*q**3 - 4*q**2 = 0.
-3, 1, 3
Let q = 566 - 566. Let l(b) be the second derivative of -2*b + 2/9*b**3 + q + 0*b**2 + 1/18*b**4. Factor l(v).
2*v*(v + 2)/3
Factor -12/7 - 6/7*r**2 - 3*r + 3/7*r**3.
3*(r - 4)*(r + 1)**2/7
Let q(v) = 36*v**2 - 9348*v + 1469514. Let w(t) = 7*t**2 - 1870*t + 293903. Let m(b) = 4*q(b) - 21*w(b). Factor m(y).
-3*(y - 313)**2
Find w, given that 298*w**2 - 178*w**2 + 28*w - 144*w**2 - 4 = 0.
1/6, 1
Let i(t) = -4*t**3 + 144*t**2 + 1736*t + 6912. Let g(j) = j + 12. Let o be g(-13). Let l(a) = a**3 - a. Let w(s) = o*i(s) - 8*l(s). Factor w(z).
-4*(z + 12)**3
Let u(p) be the first derivative of 2*p**6/3 + 4*p**5 +