k. Let w(y) = 0. Calculate y.
-1, 0, 2
Let y be 10/2 + (-1001)/210. Let d(h) be the first derivative of 5/2*h**4 - 6/5*h**5 - 2/5*h + 3/2*h**2 - 8/3*h**3 + y*h**6 + 6. Suppose d(f) = 0. What is f?
2/7, 1
Let n(r) be the second derivative of r**7/28 - 2*r**6/5 - 63*r**5/20 - 17*r**4/2 - 47*r**3/4 - 9*r**2 + r - 28. Factor n(v).
3*(v - 12)*(v + 1)**4/2
Let b(j) be the first derivative of -2*j**3 + 5/2*j**2 + j + 18. Factor b(y).
-(y - 1)*(6*y + 1)
Factor 42*j**3 - 8*j**2 + 22*j - 19 - 44*j**3 + 7.
-2*(j - 1)**2*(j + 6)
Suppose -152*x + 68*x + 96 = -60*x. Find s, given that -1/3*s**4 + x + 2*s**3 - 4/3*s - 3*s**2 = 0.
-1, 2, 3
Let j(q) be the first derivative of -q**6/300 + q**5/150 - 9*q**2/2 - 9. Let o(y) be the second derivative of j(y). Factor o(c).
-2*c**2*(c - 1)/5
Let m = 16283/15 + -1071. Let b = m + -66/5. Factor 2/3*z**2 + 2/3 - b*z.
2*(z - 1)**2/3
Determine q so that -40*q**3 + 143 - 4*q**4 + 7*q**4 + 200*q + 30*q**2 + 2*q**4 - 18 = 0.
-1, 5
Let v(o) be the first derivative of -1/156*o**4 + 0*o**3 - 1 + 0*o - 2*o**2 + 1/390*o**5. Let a(t) be the second derivative of v(t). Let a(f) = 0. What is f?
0, 1
Let z(a) be the third derivative of a**8/2688 - a**7/840 + a**6/960 - 6*a**2 + 22. Factor z(p).
p**3*(p - 1)**2/8
Let f be (-3)/(-18) + (-149)/(-6). Let c be 46/40 - f/(-100). Solve 3/5*l**2 - l**4 - 7/5*l + c*l**3 + 2/5 = 0 for l.
-1, 2/5, 1
Let m = -626 - -626. Let i(s) be the third derivative of m*s + 0 - 1/240*s**6 - 1/60*s**5 + 0*s**3 - 1/48*s**4 + 9*s**2. Let i(j) = 0. Calculate j.
-1, 0
Factor -2/15*p**2 - 4/3 + 22/15*p.
-2*(p - 10)*(p - 1)/15
Let q(c) be the first derivative of c**3 + 3*c**2 + 3*c - 21. Let o(m) = 4*m**2 + 7*m + 3. Let z(u) = 4*o(u) - 5*q(u). What is b in z(b) = 0?
-1, 3
Factor -1/2*h**3 + 0 + 12*h - 7*h**2 + 1/2*h**4.
h*(h - 3)*(h - 2)*(h + 4)/2
Let h(u) be the second derivative of -u**5/20 + u**4/9 + 17*u**3/18 - u**2 + 3*u + 76. Factor h(c).
-(c - 3)*(c + 2)*(3*c - 1)/3
Let g(n) be the first derivative of 2*n**3/9 + n**2 - 8*n/3 + 120. Let g(r) = 0. What is r?
-4, 1
Suppose -y - 5 = 5*s, -3*y = -2*s + 19 - 55. Let i = y + -6. What is a in i*a - 64 + a + 3*a + 24*a - 4*a**2 = 0?
4
Let r = 2 + 2. Suppose w = -0*a - a + 3, r*a + 5*w - 13 = 0. Let 3 + 3*q + q - 2*q**2 + q**2 + 2*q**a = 0. What is q?
-3, -1
Let f(d) = d**2 - 4*d + 4. Let q be f(4). Suppose 77*o = 79*o - 6. Let 3/2*u**o - 3/4*u**q - 3*u + 9/4*u**2 - 3 = 0. Calculate u.
-1, 2
Let d = -2093 - -2095. Find t such that d*t**2 + 1/2*t + 0 = 0.
-1/4, 0
Let d(h) = -h**2 - h - 1. Let a(j) = 2*j**2 + 4*j + 4. Let q(y) = -a(y) - 4*d(y). Let q(z) = 0. What is z?
0
Let i = -3/392 - -811/3528. Suppose -1 = -d, 3*w + 2*d = -3*d + 11. Factor 0 - i*a**w - 2/9*a.
-2*a*(a + 1)/9
Factor -127308/7 - 3/7*r**2 - 1236/7*r.
-3*(r + 206)**2/7
Let v(u) be the second derivative of -1/6*u**4 + 0 - 9*u - 2*u**2 - u**3. Suppose v(o) = 0. What is o?
-2, -1
Factor 38985/2*v + 3/2*v**3 + 39675/2 - 687/2*v**2.
3*(v - 115)**2*(v + 1)/2
Let g(u) be the first derivative of -u**6/480 - u**5/160 + u**4/16 + 2*u**3/3 + 4. Let h(w) be the third derivative of g(w). Factor h(j).
-3*(j - 1)*(j + 2)/4
Let u(h) be the second derivative of -h**6/900 + 11*h**5/600 + h**4/20 + 2*h**3 - 4*h. Let g(b) be the second derivative of u(b). Let g(i) = 0. What is i?
-1/2, 6
Let x(k) be the third derivative of -k**7/42 + 2*k**6/3 - 23*k**5/6 - 30*k**4 - 135*k**3/2 + 4*k**2 - 1. Determine q so that x(q) = 0.
-1, 9
Find p, given that 6*p**2 - 2*p**3 - 14*p + 6*p + 4*p = 0.
0, 1, 2
Let r(t) be the third derivative of -t**7/105 + t**6/20 - t**5/15 - 13*t**2 - 2. Let r(y) = 0. What is y?
0, 1, 2
Let g = 3/7822 + 437915/305058. Let h = g - 4/39. Factor 2*k**3 - h + 4*k - 1/3*k**4 - 13/3*k**2.
-(k - 2)**2*(k - 1)**2/3
Let s(v) be the second derivative of -v**7/294 - 9*v**6/35 - 103*v**5/70 - 76*v**4/21 - 67*v**3/14 - 25*v**2/7 - 102*v. Factor s(g).
-(g + 1)**4*(g + 50)/7
Let t(h) = h**5 + 13*h**4 - 41*h**3 + 24*h**2 - 3*h - 3. Let u(r) = -12*r**4 + 40*r**3 - 24*r**2 + 4*r + 4. Let j(k) = 4*t(k) + 3*u(k). Let j(l) = 0. What is l?
-6, 0, 1
Let y(s) = s**3 - s**2 - 5*s - 3. Let a be y(-2). Let n be (-2)/a*(6 + -4). Factor 6/5 - 2/5*c**2 + n*c.
-2*(c - 3)*(c + 1)/5
Let a(n) be the second derivative of -n**6/75 - 17*n**5/100 - 2*n**4/3 - 8*n**3/15 + 110*n. Factor a(h).
-h*(h + 4)**2*(2*h + 1)/5
Suppose 5*q - 111 = -0*q + r, -4*r + 131 = 5*q. Suppose 8 + 46*l**3 - 12*l**2 + 16*l**4 - q*l + 3*l - 14*l**3 = 0. What is l?
-2, -1, 1/2
Suppose 0 = 4*t + 2*b - 26, -4*t = -b - 0*b - 17. Let g be 3/((-9)/6) + t. Factor p + 4*p**2 - 6*p**4 + 2*p**3 + 2*p**4 + g*p - 6*p.
-2*p*(p - 1)*(p + 1)*(2*p - 1)
Suppose -3*w = 3*t - 15, 2 + 4 = 2*t. Let a(i) be the third derivative of -1/60*i**5 + 4*i**w + 0*i + 0*i**3 + 1/8*i**4 + 0. Factor a(l).
-l*(l - 3)
Let d = -5 + 7. Let l be (-85)/(-35) + 6/(-14). Factor 3*w - 3*w - 2*w**d + l*w.
-2*w*(w - 1)
Let w(m) be the third derivative of m**7/1260 + 23*m**6/720 + m**5/3 - m**4 + 7*m**2 + 8*m. Determine q, given that w(q) = 0.
-12, 0, 1
Let p = -18 - -25. Suppose 2*u + 6*u = p*u. Determine b, given that 1/5*b - 1/5*b**5 + 0*b**3 + 2/5*b**4 + u - 2/5*b**2 = 0.
-1, 0, 1
Let r be 5 + (-140)/12 - -8. Factor 0*j + 0 - r*j**4 + 0*j**2 + 4/3*j**3.
-4*j**3*(j - 1)/3
Let s be (-6)/(-2) - (-8 - -11). Suppose 2*l + 0 - 6 = s. Factor 0 + q**4 - 3*q**l + 8*q**2 + 0 - 5*q**2 - q.
q*(q - 1)**3
Let c(i) be the third derivative of -i**7/315 + 7*i**6/540 - i**5/90 - i**4/36 + 2*i**3/27 + 101*i**2 + 2*i. Determine s, given that c(s) = 0.
-2/3, 1
Let d be (-70)/(-420)*2/5. Let f(x) be the first derivative of 1/4*x**4 + 0*x + 0*x**3 + 4 - 2/3*x**2 - d*x**5. Solve f(p) = 0 for p.
-1, 0, 2
Let u(b) be the second derivative of -3*b + 1/18*b**3 - 1/2*b**2 + 0 - 1/90*b**6 + 2/45*b**5 - 5/72*b**4. Let l(x) be the first derivative of u(x). Factor l(o).
-(o - 1)*(2*o - 1)**2/3
Let j be (-184)/(-56) + (-2)/7 + 1. Determine k so that 2*k - j - 5*k**2 + 5 - k - k**3 + 4*k**2 = 0.
-1, 1
Let c(a) = 10*a - 131. Let g be c(13). Let k be ((-4)/6)/((-102)/90 - g). Solve 1/3*w + 2/3*w**2 + 0*w**3 - 1/3*w**k - 2/3*w**4 + 0 = 0 for w.
-1, 0, 1
Let q(p) = 11*p - 22. Let o(b) = -5*b + 11. Let n(i) = 9*o(i) + 4*q(i). Let y be n(0). Factor 16*j - 2 - j**2 - 24*j + y*j.
-(j - 2)*(j - 1)
Suppose 3*m + i - 24 = -3, -2*m + i = -14. Let k = m + -7. Suppose 2*d**2 + k*d**2 + 4*d + 0*d + 2*d**2 = 0. What is d?
-1, 0
Let t(g) = -3*g + 17. Let l be t(5). Let -2*i**3 - l*i**3 - 3256*i - 12*i**2 + 3248*i = 0. What is i?
-2, -1, 0
Let o = -63 - -65. Let t = -35 + 109/3. Factor 0*y - t*y**o + 2/3*y**3 + 0.
2*y**2*(y - 2)/3
Let o(r) be the first derivative of 13*r**3/9 - 11*r**2/6 - 2*r/3 - 70. Factor o(t).
(t - 1)*(13*t + 2)/3
Let x(f) be the third derivative of f**8/240 - f**7/420 + 2*f**3 - f**2. Let g(u) be the first derivative of x(u). Factor g(r).
r**3*(7*r - 2)
Let f(u) be the first derivative of -u**3/3 + 4*u**2 - 306. Factor f(j).
-j*(j - 8)
Let b(h) be the first derivative of -9/4*h**4 + h**3 - 15 + 0*h + 3*h**2. Factor b(w).
-3*w*(w - 1)*(3*w + 2)
Factor -2 - 3*r**2 + 49 + 1 - 10*r**2 + 10*r**2.
-3*(r - 4)*(r + 4)
Let j = 369 - 369. Let u(x) be the third derivative of -7*x**2 + 0*x - 8/3*x**3 - 1/15*x**5 + 2/3*x**4 + j. Factor u(b).
-4*(b - 2)**2
Let z(p) = 178*p - 1246. Let f be z(7). Find j such that 0*j + f + 1/6*j**2 + 1/6*j**3 = 0.
-1, 0
Let a = 468310/9 - 52034. Solve a + 8/3*y - 13/9*y**2 = 0.
-2/13, 2
Let b = 124 + -122. Factor 3*z**3 + 6 - z**4 - 2*z**b + 26*z - 9*z + 17*z**2.
-(z - 6)*(z + 1)**3
Let z(n) be the first derivative of -n**5/35 + 97*n**4/28 - 800*n**3/7 + 1152*n**2/7 + 655. Determine r so that z(r) = 0.
0, 1, 48
Suppose 209 + 421 = 2*y. Suppose -821*m + 145*m**2 - y - 154*m - 5*m**3 - 810 = 0. What is m?
-1, 15
Let q(u) be the second derivative of -u**5/40 + 29*u**4/24 - 56*u**3/3 + 49*u**2 + 3*u. Factor q(k).
-(k - 14)**2*(k - 1)/2
Suppose -2*q**2 + 1/3*q**3 + 0 + 3*q = 0. Calculate q.
0, 3
Factor -48*i**3 + 63*i**4 + 330*i**2 - 96*i**4 - 484*i + 35*i**4.
2*i*(i - 11)**2*(i - 2)
Factor -22 + 2/3*c**2 - 16/3*c.
2*(c - 11)*(c + 3)/3
Let k(z) be the second derivative of 0 - 1/84*z**7 + 1/3*z**3 - 1/15*z**6 - 2*z**2 + 5/12*z**4 - 1/40*z**5 - 5*z. Factor k(s).
-(s - 1)**2*(s + 2)**3/2
Suppose 2*h = -2 + 8. Factor 202*u*