 + 15 = c*a. Factor 1/4*z**a + 1/4*z**2 + 0 + 0*z - 1/4*z**5 - 1/4*z**4.
-z**2*(z - 1)*(z + 1)**2/4
Let q be 4*(64/56 - 1/7). Suppose -2/5*o**2 + 1/5 + 1/5*o**5 + 1/5*o + 1/5*o**q - 2/5*o**3 = 0. Calculate o.
-1, 1
Let d(p) be the third derivative of p**5/80 - 15*p**4/32 + 25*p**3/4 - 144*p**2 - p. Solve d(w) = 0 for w.
5, 10
Let i(m) = -3*m**3 + 10*m**2 - 19*m + 8. Let k(b) = -b**3 + b**2 - b - 1. Let t(r) = -3*i(r) + 6*k(r). Factor t(l).
3*(l - 5)*(l - 2)*(l - 1)
Let g(j) = 3*j**5 - 7*j**4 - 6*j**2 - 6*j. Let c(u) = -u**3 + u**2 + u. Let l(a) = -6*c(a) - g(a). Suppose l(t) = 0. Calculate t.
-2/3, 0, 3
Suppose -56*t**2 + 27 + 5 + 0 + 52*t**2 + 8*t = 0. What is t?
-2, 4
Let p(f) = 3*f**2 - 4 + 10 - 3*f - 6. Let g(w) be the third derivative of w**5/20 - w**4/8 - w**2. Let z(a) = 3*g(a) - 4*p(a). Determine o, given that z(o) = 0.
0, 1
Suppose 4*j + 32 - 133 = -x, -2*j + 52 = 2*x. Suppose -44*i = -49*i + j. Find r, given that 8*r + 1/2*r**i + 19/2*r**3 - 2 - 25/2*r**2 - 7/2*r**4 = 0.
1, 2
Let t(b) be the third derivative of b**7/1365 - b**6/260 + b**5/390 + b**4/52 - 2*b**3/39 - 356*b**2. Solve t(d) = 0 for d.
-1, 1, 2
Let w = 1/20232 + 20225/141624. Factor w*l**3 + 5/7*l - 4/7*l**2 - 2/7.
(l - 2)*(l - 1)**2/7
Let i(f) = f + 2. Let n(y) = 8*y**2 + y - 1. Let j be n(1). Let o be i(j). Find b, given that 6*b**3 + o*b**4 - 9*b + 3*b**5 + 8*b - 2*b**4 + 0*b = 0.
-1, 0, 1/3
Let q(f) be the first derivative of 6 + 8/7*f**3 + 5/7*f**4 + 4/35*f**5 - 8/7*f**2 - 32/7*f. Determine k, given that q(k) = 0.
-2, 1
Let b(w) be the third derivative of -40/3*w**3 + 5/336*w**8 + 2/3*w**5 + 6*w**2 - 1/42*w**7 + 0 - 1/3*w**6 + 10/3*w**4 + 0*w. Suppose b(p) = 0. What is p?
-2, 1, 2
Let c = -194 - -166. Let j = -186/7 - c. Solve -4/7*t**2 + 0 + 0*t - 2/7*t**5 - j*t**3 - 8/7*t**4 = 0.
-2, -1, 0
Suppose 5*w = 5*y + 30, -2*w + 3*y = -2*y - 6. Suppose -w*d = -4*d - 16. Find z, given that -4*z**4 + 0*z**3 + 2*z**4 + 4*z + 2*z**2 - d*z**3 = 0.
-2, -1, 0, 1
Factor -3*i**3 - 120*i - 108 - 5*i**2 - 36*i**2 + 6*i**2 - 4*i**2.
-3*(i + 2)**2*(i + 9)
Let x(i) = 2 + 3 + 6*i**3 - 6 - i + 0*i. Let a(o) = o**2 + o - 1. Suppose -2*h + 0 + 4 = 0. Let v(p) = h*a(p) - 2*x(p). Factor v(r).
-2*r*(2*r + 1)*(3*r - 2)
Let o = -420 + 47. Let p = 4107/11 + o. Factor -6/11*q + 2/11*q**3 + 0 + p*q**2.
2*q*(q - 1)*(q + 3)/11
Let j = 19/75 + 2/25. Let k = 54/11 - 140/33. Factor 0 + 1/3*t + j*t**3 + k*t**2.
t*(t + 1)**2/3
Suppose 2*q - 136*q + 167 = -235. Factor -2*m + 8/5*m**2 + 4/5 - 2/5*m**q.
-2*(m - 2)*(m - 1)**2/5
What is y in 21*y**2 + 25*y**2 - 39 - 100*y**2 + 25*y**2 + 26*y**2 + 42*y = 0?
1, 13
Factor o**4 + 1300*o + 159*o**3 - 241*o**3 + 134*o**3 + 726*o**2 + 625.
(o + 1)**2*(o + 25)**2
Factor -3/2 - 24*x**2 + 51/2*x.
-3*(x - 1)*(16*x - 1)/2
Let c(s) be the second derivative of s**4/42 - 38*s**3/21 + 37*s**2/7 - 2*s - 2. Factor c(m).
2*(m - 37)*(m - 1)/7
Let c(l) be the second derivative of -7*l**4/3 + 220*l**3/3 + 64*l**2 + l + 92. Let c(v) = 0. Calculate v.
-2/7, 16
Let z be (-2*10/144)/(3/(-9)). Let c(g) be the third derivative of 4*g**2 + 0*g + 1/12*g**6 + 2/3*g**3 - z*g**4 - 1/15*g**5 + 0. Factor c(f).
2*(f - 1)*(f + 1)*(5*f - 2)
Suppose -3*t = 8*t - 33. Find k, given that 53*k - 14*k**3 - 5*k**4 + 7*k + 10*k**2 - 45 - 6*k**t = 0.
-3, 1
Let a(b) be the third derivative of 5*b**8/2016 + b**7/21 + 35*b**6/144 - b**5/6 - 5*b**4/4 - 221*b**2. Let a(j) = 0. What is j?
-6, -1, 0, 1
Let m = -70 + 83. Suppose -m*p = -p + 3*p. Factor 0 + p*f + 1/2*f**3 + f**2.
f**2*(f + 2)/2
Suppose -3*f + 7 + 53 = 0. Factor -54*q + f*q + 45*q**2 - 5*q**3 - 41*q + 4 + 31.
-5*(q - 7)*(q - 1)**2
Let y(d) = d**4 + 8*d**3 - 12*d**2 - 3. Suppose j - 4 = -0. Let z(r) = 8*r**3 - 12*r**2 - 4. Let v(m) = j*y(m) - 3*z(m). Suppose v(f) = 0. What is f?
-3, 0, 1
Let y(q) = q. Let j = 73 - 77. Let o(w) = -36*w**2 - 73*w - 15. Let z(p) = j*y(p) - o(p). Find n, given that z(n) = 0.
-5/3, -1/4
Let f(k) be the second derivative of -k**6/40 - k**5/20 + k**4 + 6*k**3 + 7*k**2/2 - k + 3. Let d(v) be the first derivative of f(v). Solve d(h) = 0.
-2, 3
Let n(g) = 3*g**4 - 2*g**3 - 17*g**2 - 24*g - 8. Let d(a) = -2*a**4 + 3*a**3 + 16*a**2 + 25*a + 9. Let x(m) = 4*d(m) + 5*n(m). Suppose x(u) = 0. Calculate u.
-1, -2/7, 2
Let t(j) = -22*j**3 - 2542*j**2 - 21*j - 14. Let m(p) = 7*p**3 + 847*p**2 + 6*p + 4. Let r(o) = 7*m(o) + 2*t(o). Let r(f) = 0. Calculate f.
-169, 0
Factor -30*j + 152 + 44*j + 54*j - 4*j**2.
-4*(j - 19)*(j + 2)
Let b be 12/9 - 2/(-3). Let 114*z**2 - 149*z**b + 9*z**3 - 4*z**3 = 0. What is z?
0, 7
Let u(j) = -6*j**5 + 2*j**4 + 6*j**3 - 2*j**2 - 8*j - 16. Let k(t) = -t**5 + t**3 - t - 2. Let s(w) = 8*k(w) - u(w). Factor s(b).
-2*b**2*(b - 1)*(b + 1)**2
Let o(q) = -2*q**2 + 52*q + 313. Let u be o(31). Let b(h) = -h**2 - 5*h + 6. Let v be b(-6). Factor -1/4*i**u + v*i - 1/2*i**2 + 0.
-i**2*(i + 2)/4
Let g(k) be the first derivative of -k**3/3 - 5*k**2 + 6*k - 5. Let h(t) = -10*t + 5. Let q(l) = 5*g(l) - 6*h(l). Factor q(c).
-5*c*(c - 2)
Factor 5 - 1/2*x**3 + 4*x**2 + 19/2*x.
-(x - 10)*(x + 1)**2/2
Let f(h) = -2*h + 2. Let n be f(-2). Let x be ((-8)/10)/(n/(-15)). Factor 2 - 5*p + 2*p**x + p + 0*p**2.
2*(p - 1)**2
Let o = 1514 - 1510. Suppose 0*p - 3/4*p**3 - 3/4*p**2 + 3/4*p**5 + 3/4*p**o + 0 = 0. What is p?
-1, 0, 1
Suppose -1102*m = -1103*m + 4. Let l(o) be the second derivative of 1/30*o**5 + 0*o**2 + 0*o**4 - 1/9*o**3 + m*o + 0. Suppose l(z) = 0. Calculate z.
-1, 0, 1
Factor 270*p + 7290 + 5/2*p**2.
5*(p + 54)**2/2
Suppose 37 = 2*k - p, -4*p + 90 = 4*k + 22. Factor -1 + 1 + 12*t**2 - 3*t - 230*t**4 - 3*t**5 - k*t**3 + 242*t**4.
-3*t*(t - 1)**4
Let x(m) be the second derivative of -m**5/10 + m**4/2 + 4*m**3/3 - 12*m**2 - 95*m. Suppose x(i) = 0. Calculate i.
-2, 2, 3
Let t(r) = -6*r**4 - 26*r**3 + 2*r**2 + 50*r - 40. Let m(c) = 17*c**4 + 76*c**3 - 7*c**2 - 150*c + 119. Let j(n) = 4*m(n) + 11*t(n). Let j(o) = 0. Calculate o.
-9, -2, 1
Let a(o) = -3*o**2 - 2 + o**3 - o**2 + 3*o**2 + 1. Let l(d) = -3*d**3 + 5*d**2 - 2*d - 2. Let g(u) = 4*a(u) - 2*l(u). Factor g(v).
2*v*(v - 1)*(5*v - 2)
Let l = 143/140 - -5/28. Let g(i) = -i**3 + 4*i**2. Let u be g(4). Factor 3/5*n**3 + 0*n + u - l*n**2.
3*n**2*(n - 2)/5
Let k = 133 + -136. Let t be 0/k*2/(-1 + 3). Determine h so that 4/7*h + 4/7*h**2 + t = 0.
-1, 0
Suppose 0 = 111*p - 112*p + 41. Let n = 41 - p. Factor 4/5*c**2 + n*c + 0.
4*c**2/5
Suppose 21 = 27*p - 28*p + 3*m, -2*m = -16. Find i, given that 0*i**2 + i**p + 5/2*i**4 + 0*i + 0 = 0.
-2/5, 0
Let a(k) be the first derivative of 1/18*k**4 - 1/9*k**3 + 7 - 2/3*k**2 + 8*k. Let x(j) be the first derivative of a(j). Factor x(b).
2*(b - 2)*(b + 1)/3
Let y(u) be the second derivative of 0 + 1/12*u**4 + u**2 - u - 1/2*u**3. Factor y(k).
(k - 2)*(k - 1)
Let s(v) = -v**3 - 3*v**2 + v + 3. Let m be s(-3). Factor m*r**3 + r + r**3 - 4*r**3 + 2*r.
-3*r*(r - 1)*(r + 1)
Let l(r) be the third derivative of -r**6/10 - 7*r**5/6 + 4*r**4 - 7*r**3/3 + 137*r**2. Factor l(n).
-2*(n - 1)*(n + 7)*(6*n - 1)
Let v(h) = -6*h**3 - h**2. Let r be v(-1). Suppose 25 = r*q - 0*q. Determine d, given that 3*d**2 + 0*d + d - q*d + 2 - d**2 = 0.
1
Let n(k) be the third derivative of k**7/5040 + k**6/1080 - k**3/2 + 33*k**2. Let i(j) be the first derivative of n(j). Suppose i(s) = 0. Calculate s.
-2, 0
Let n(g) be the first derivative of 5/2*g**2 - 20*g**3 + 45*g**4 + 0*g + 8. Solve n(p) = 0.
0, 1/6
Let f = 3/29390 - -23509/29390. Let -f*d**2 - 52/5 - 56/5*d = 0. What is d?
-13, -1
Let f(w) be the third derivative of 1/70*w**7 + 16*w**2 + 2401/2*w**3 - 343/2*w**4 - 7/10*w**6 + 0*w + 147/10*w**5 + 0. Factor f(a).
3*(a - 7)**4
Let c = -2027 - -2030. Let b(q) be the second derivative of -9*q + 5/12*q**4 + 0 - 5/2*q**2 + 0*q**c. Factor b(h).
5*(h - 1)*(h + 1)
Let z be ((-5)/20*4)/(-300). Let g(p) be the third derivative of z*p**6 - 1/90*p**4 + 0*p**3 - 1/450*p**5 - p**2 + 0 + 0*p. Solve g(k) = 0 for k.
-2/3, 0, 1
Let x(g) be the third derivative of g**6/1080 - g**5/45 + 2*g**4/9 + 3*g**3/2 + 33*g**2. Let l(c) be the first derivative of x(c). Factor l(b).
(b - 4)**2/3
Let d(j) be the first derivative of 6*j - 4/3*j**6 - 12*j**3 + 25 - 2*j**4 + 8*j**2 + 6*j**5. Determine m, given that d(m) = 0.
-1, -1/4, 1, 3
Let k(y) be the second derivative of 0 + 1/2*y**5 - 1/6*