= -7. Factor -2 - 15*z**2 + 14 + 1 - 5*z + 2 + k*z**3.
5*(z - 3)*(z - 1)*(z + 1)
Let q(d) = -d**4 - d**3 - d**2 + 5*d. Let i(w) = w**4 - w**3 + w**2 - w - 1. Let t = 43 - 45. Let x(r) = t*i(r) - q(r). What is u in x(u) = 0?
-1, 1, 2
Suppose -o + 0*o + 4 = 0. Suppose q - 3 = -4, -n = -q - o. Solve 4*d**5 + 12*d + 32*d**n + 0*d**5 + 20*d**4 + d**2 + 2 - 2*d**4 + 27*d**2 = 0 for d.
-1, -1/2
Let q(z) = -6*z**2 + 9*z - 13. Let t(s) = -5*s**2 + 9*s - 14. Let n(c) = 4*q(c) - 5*t(c). Let l be n(6). Factor 7*a**2 - 7*a**4 + 5*a**4 + l*a**2 - 3*a**2 - 2.
-2*(a - 1)**2*(a + 1)**2
Let s(j) be the second derivative of -j**4/3 - 26*j**3/3 - 60*j**2 + 235*j. Suppose s(f) = 0. Calculate f.
-10, -3
Let s(r) be the first derivative of r**5/15 - 59*r**4/12 + 133*r**3 - 9025*r**2/6 + 13718*r/3 - 44. Find y, given that s(y) = 0.
2, 19
Let g(u) be the first derivative of -u**6/24 + 5*u**4/6 + 7*u**2 - 4. Let z(m) be the second derivative of g(m). Factor z(x).
-5*x*(x - 2)*(x + 2)
Let j(h) = 11*h**4 + 47*h**3 + 71*h**2 + 35*h + 10. Let k(a) = 6*a**4 + 24*a**3 + 36*a**2 + 18*a + 6. Let r(q) = -3*j(q) + 5*k(q). Find m, given that r(m) = 0.
-5, -1, 0
Let h(s) be the first derivative of s**7/105 + s**6/15 + s**5/6 + s**4/6 - s**2 - 3. Let u(k) be the second derivative of h(k). Factor u(x).
2*x*(x + 1)**2*(x + 2)
Let l(r) = -r**3 - 2*r**2 + r + 3. Suppose -4*o = -o. Let c be l(o). Find p, given that 8*p**4 - 2*p**2 - 4*p**2 + 4*p + c*p - 5*p = 0.
-1, 0, 1/2
Let a = 2035 + -2029. Let w(u) be the third derivative of 0 - 1/10*u**a + 0*u + 1/15*u**5 + 1/84*u**8 - 2/105*u**7 + 0*u**3 + 1/3*u**4 + 4*u**2. Factor w(x).
4*x*(x - 2)*(x - 1)*(x + 1)**2
Suppose 0 = -9*f + 7*f + 8. Factor -3*x - 3*x**3 + 4*x - 8 + f*x**2 - 2 + 8.
-(x - 1)**2*(3*x + 2)
Let x(o) = 17*o**5 + 32*o**4 + 39*o**3 + 23*o**2 - o - 18. Let j(z) = -8*z**5 - 16*z**4 - 20*z**3 - 12*z**2 + 8. Let r(g) = 9*j(g) + 4*x(g). Factor r(p).
-4*p*(p + 1)**4
Let l(j) = -4*j**4 + 2*j**3 + 6*j**2 + 2*j + 2. Let n(g) = 9*g**4 - 4*g**3 - 13*g**2 - 5*g - 5. Let t(r) = 5*l(r) + 2*n(r). Factor t(i).
-2*i**2*(i - 2)*(i + 1)
Let h = -4/389 - -2378/4279. Suppose 43*c - 51*c = 0. Factor -h*x - 2/11*x**2 + c.
-2*x*(x + 3)/11
Find y such that -68/7*y**3 + 578/7*y**2 + 0 + 2/7*y**4 + 0*y = 0.
0, 17
Let v = 12 + 3. Let a(w) = -7*w**2 - 4*w + 3. Let f(t) = -27*t**2 - 15*t + 12. Let u(r) = v*a(r) - 4*f(r). Factor u(n).
3*(n - 1)*(n + 1)
Factor -y**2 - 4482*y + 9001*y - 4480*y + 40.
-(y - 40)*(y + 1)
Let g = -9917/18 + 551. Let a(l) be the first derivative of 1/36*l**6 - 1/30*l**5 + 0*l - 5 + g*l**3 + 0*l**2 - 1/24*l**4. Find c, given that a(c) = 0.
-1, 0, 1
Let k(t) be the second derivative of t**6/50 + 21*t**5/100 - 27*t**4/20 + 29*t**3/10 - 3*t**2 + 63*t. Determine f so that k(f) = 0.
-10, 1
Let q(l) = l**2 + l + 1. Let v(w) = 5*w**2 + 3*w + 3. Let s be (-2)/6 + 136/(-24). Let m = 3 + s. Let b(d) = m*q(d) + v(d). Factor b(r).
2*r**2
Let c(j) be the second derivative of j**5/100 - 3*j**4/20 - 7*j**3/10 - 11*j**2/10 - 104*j. Factor c(k).
(k - 11)*(k + 1)**2/5
Factor -4/7*k**2 - 976/7 + 496/7*k.
-4*(k - 122)*(k - 2)/7
Let j(a) = -a**2 + 11*a - 21. Let b be j(9). Let s(n) = -5*n**2 + 2*n. Let y(w) = -2*w**2 + w. Let p(x) = b*s(x) + 7*y(x). Determine o, given that p(o) = 0.
-1, 0
Suppose -5*f + 4*z = 8*z - 27, 4*f - 6 = 2*z. Let a(x) be the third derivative of 0*x + 2/5*x**5 + 1/2*x**f + 0 + 3/4*x**4 + 3*x**2. Factor a(k).
3*(2*k + 1)*(4*k + 1)
Suppose 2 = -d, -5*d = -5*b + 8 + 12. Factor -2*k + 3*k**b - k + 24*k**3 - 9*k**3 - 12*k**3 - 3.
3*(k - 1)*(k + 1)**2
Suppose -141*s - 9 = -192 - 240. Factor 3/2 + 5/2*f**s + 11/2*f + 13/2*f**2.
(f + 1)**2*(5*f + 3)/2
Let l = -68 + 72. Find u, given that -12*u - 4 + l*u + 126*u**2 - 130*u**2 = 0.
-1
Let n(d) be the second derivative of d**7/252 - d**6/60 - d**5/20 + 7*d**4/18 - 2*d**3/3 - 52*d. Let n(u) = 0. What is u?
-3, 0, 2
Let g(s) = 4*s**2 - 10*s - 4. Let o(y) = y**3 - 6*y**2 - 4*y + 27. Let n be o(6). Let p be g(n). Factor 5/2*w**p + 2*w**3 + 1/2*w**4 + 0 + w.
w*(w + 1)**2*(w + 2)/2
Let r = 243 + -238. Let c(h) be the third derivative of -1/75*h**r + 0*h**6 + 0*h**3 + 2/525*h**7 + 0*h + 1/60*h**4 + 0 - 6*h**2 - 1/840*h**8. Factor c(g).
-2*g*(g - 1)**3*(g + 1)/5
Let a(j) be the first derivative of -j**8/3360 - j**7/240 - j**6/40 - j**5/12 - j**4/6 + 14*j**3/3 + 3. Let c(q) be the third derivative of a(q). Factor c(z).
-(z + 1)*(z + 2)**3/2
Let h(o) = 3*o**2 + 13*o - 12. Let l be h(-6). Solve 15*z**3 - 15*z**4 + 5*z**5 - l*z**2 + 31*z**2 - 18*z**2 = 0.
0, 1
Let b be 2/13 + 2 + 10/(-65). Let x(o) be the second derivative of 0 + 0*o**b + 5/24*o**3 + 1/16*o**5 - o + 5/24*o**4. Factor x(i).
5*i*(i + 1)**2/4
Let m = 77 - 75. Solve 2*j**2 + 18 - 11*j**2 + 4*j + 7*j**m - 2 = 0 for j.
-2, 4
Suppose 0 = -14*q + 8*q + 4*q. Let n(w) be the second derivative of -1/80*w**5 + 5/48*w**4 + 1/2*w**2 + 6*w - 1/3*w**3 + q. Factor n(l).
-(l - 2)**2*(l - 1)/4
Let p(w) be the first derivative of 4*w**3/27 - 2*w**2/9 - 8*w/9 + 105. Factor p(x).
4*(x - 2)*(x + 1)/9
Let n(a) be the first derivative of 5*a**6/6 - a**5 - 15*a**4/4 + 5*a**3/3 + 5*a**2 - 217. Factor n(q).
5*q*(q - 2)*(q - 1)*(q + 1)**2
Let h(s) = -2*s - 2*s**2 - 405 + 407 - 20*s. Let g be h(-11). Let -5/4*n**g + 5/4 + 0*n = 0. What is n?
-1, 1
Let c(t) = -11*t**3 + 4*t**2 + 6*t - 12. Let k(l) = 23*l**3 - 7*l**2 - 13*l + 26. Let r(n) = -13*c(n) - 6*k(n). Factor r(q).
5*q**2*(q - 2)
Let k = 437 - 437. Factor 6/13*m**3 + k*m - 2/13*m**4 - 4/13*m**2 + 0.
-2*m**2*(m - 2)*(m - 1)/13
Let r(b) be the third derivative of -b**10/37800 - b**9/7560 + b**8/1680 - 13*b**5/60 + b**2. Let v(z) be the third derivative of r(z). Factor v(t).
-4*t**2*(t - 1)*(t + 3)
Let v(l) = -3*l**2 + 32*l + 227. Let d(p) = -5*p**2 + 33*p + 228. Let q(t) = -4*d(t) + 6*v(t). Find s such that q(s) = 0.
-15
Let z(l) be the third derivative of -l**7/350 + 223*l**6/50 - 149187*l**5/50 + 11089567*l**4/10 - 2472973441*l**3/10 + 7*l**2 - 2. Factor z(x).
-3*(x - 223)**4/5
Let u(o) be the first derivative of -o**5/240 - o**4/24 + 9*o**2/2 + 3*o + 1. Let h(b) be the second derivative of u(b). Factor h(m).
-m*(m + 4)/4
Let h(a) be the second derivative of a**7/84 + a**6/10 + 9*a**5/40 + a**4/6 + 132*a. Factor h(t).
t**2*(t + 1)**2*(t + 4)/2
Let b(z) be the second derivative of 3*z**4/4 - 11*z**3/4 - 3*z**2/2 + 3*z + 14. What is a in b(a) = 0?
-1/6, 2
Let s(j) be the second derivative of j**4/3 - 22*j**3/3 + 251*j. Factor s(a).
4*a*(a - 11)
Let f(m) = -m**4 - m**3 - m**2 - 1. Let a(t) = t**4 + 8*t**3 - 7*t**2 + 4*t + 2. Let v(r) = -a(r) - 2*f(r). Factor v(k).
k*(k - 4)*(k - 1)**2
Let h(g) be the second derivative of -g**7/42 + 7*g**6/30 - 3*g**5/5 - g**4/3 + 8*g**3/3 - 9*g - 1. Factor h(v).
-v*(v - 4)*(v - 2)**2*(v + 1)
Let n(h) be the third derivative of h**10/37800 - h**9/7560 + h**5/5 + 9*h**2. Let z(f) be the third derivative of n(f). Find q, given that z(q) = 0.
0, 2
Let b = -2/16535 - -16539/33070. Let v = 55/2 - 26. Factor 1/2*s**5 - s + 0 + b*s**3 - v*s**2 + 3/2*s**4.
s*(s - 1)*(s + 1)**2*(s + 2)/2
Let s(z) = -2*z - 7. Let i be s(-6). Factor -16*g**4 - 11*g**2 + 2*g + 21*g**3 + 7*g**i - 16*g**5 + 13*g**5.
g*(g - 2)*(g - 1)*(2*g - 1)**2
Let t(v) = v + 24. Let j be t(-20). Let q(g) = -g + 7. Let h be q(j). Solve 1/4*m**5 + 0*m - 1/4*m**2 + 0 - 3/4*m**4 + 3/4*m**h = 0 for m.
0, 1
Let c(d) be the third derivative of d**5/90 + d**4/12 - 2*d**3 - 77*d**2. Let c(u) = 0. What is u?
-6, 3
Let y be ((-1)/(-4))/(1/8). Suppose 4*m - 18 = -3*q, y*q = -0*q - m + 7. Determine c so that -c + 1 - q*c**2 + 1 + c**2 + 0*c**2 = 0.
-2, 1
Let w(p) be the third derivative of -p**6/240 + p**4/16 - p**3/6 + 180*p**2. Factor w(r).
-(r - 1)**2*(r + 2)/2
Let p(g) = -6*g**2 - 49*g - 23. Let y(b) = 3*b**2 + 27*b + 12. Let r(t) = 3*p(t) + 5*y(t). Factor r(c).
-3*(c + 1)*(c + 3)
Let c(p) be the third derivative of 7/180*p**5 - 11/144*p**4 - 1/1260*p**7 + p**2 + 0 + 0*p - 1/120*p**6 + 1/12*p**3 + 1/2016*p**8. Suppose c(k) = 0. What is k?
-3, 1
Let i(l) be the third derivative of 0 + 0*l**4 + 1/560*l**8 - 2/25*l**5 + 2*l**2 + 3/50*l**6 - 3/175*l**7 + 0*l + 0*l**3. Factor i(h).
3*h**2*(h - 2)**3/5
Let k(c) be the third derivative of -c**5/5 - c**4/4 + 4*c**3 + 28*c**2. Let x(l) = l**2. Let a(i) = -k(i) - 9*x(i). Let a(t) = 0. C