. Suppose j(w) = 0. What is w?
0, 3
Let q(u) be the first derivative of -u**4/16 - 11*u**3/6 + 95. Factor q(c).
-c**2*(c + 22)/4
Let y(u) be the third derivative of -u**6/120 + 3*u**5/20 - u**4/3 + u**3/2 - 3*u**2. Let i be y(8). Factor -3*l**4 - l**5 + i*l**4.
-l**5
Let y be 0 + -6 - (-11 + 10). Let a be (-564)/(-420) + 1/y. Factor a - 50/7*q**2 - 18/7*q**3 - 24/7*q.
-2*(q + 1)*(q + 2)*(9*q - 2)/7
Suppose -4*n - o = -60, -13*o = -2*n - 12*o + 24. Let y(t) be the second derivative of 4*t - 6*t**2 - n*t**3 - 49/4*t**4 + 0. Find p such that y(p) = 0.
-2/7
Let h(p) be the third derivative of p**10/30240 + p**9/12096 - p**8/4032 - p**7/1008 + p**5/4 - 22*p**2. Let l(j) be the third derivative of h(j). Factor l(w).
5*w*(w - 1)*(w + 1)**2
Let v(u) be the second derivative of -3*u**6/5 + 39*u**5/10 - 20*u**4/3 + 4*u**3 - 527*u. Factor v(s).
-2*s*(s - 3)*(3*s - 2)**2
Let a(n) = -21*n**4 - 267*n**3 + 2367*n**2 - 3267*n - 1170. Let c(v) = 3*v**3 - 2. Let d(r) = -a(r) + 18*c(r). Determine l, given that d(l) = 0.
-21, -2/7, 3
Suppose 3*l - 2*l - 2 = 0. Suppose 0 = -3*i - 262 + 268. Factor 2 - 39*v**i + l + 4*v - 1 + 40*v**2.
(v + 1)*(v + 3)
Let z(p) be the second derivative of 21*p**5/20 - 11*p**4/4 - 5*p**3 + 12*p**2 - 28*p - 11. Suppose z(v) = 0. Calculate v.
-1, 4/7, 2
Let c(l) be the third derivative of l**6/480 + 5*l**5/48 + 47*l**4/96 + 23*l**3/24 - 226*l**2. Determine j, given that c(j) = 0.
-23, -1
Let g be (-915)/2160 - 8/(-18). Let p(x) be the third derivative of 1/12*x**3 + 6*x**2 + 1/240*x**6 - 1/120*x**5 - g*x**4 + 0 + 0*x. Factor p(m).
(m - 1)**2*(m + 1)/2
Suppose 2*s - 7 = -3. Determine h so that h**2 - 1 - s*h + 3 + 0 - 1 = 0.
1
Let i(w) be the first derivative of 3*w**2 - 3*w**4 + 5/3*w**3 - 18 + w. Factor i(r).
-(r - 1)*(3*r + 1)*(4*r + 1)
Let x be (16/(-6))/((-4)/6). Let z be 1 - -4 - (0 + (-2 - -5)). Factor 40*w**x + 32*w**2 + 4*w - 8*w**z + 77*w**3 + 8*w**2 + 9*w**4.
w*(w + 1)*(7*w + 2)**2
Let p = -69 + 72. Suppose -4*d + 0*i = -p*i - 3, 2*d = 3*i + 3. Factor -2/3 + 2/3*a**2 + d*a.
2*(a - 1)*(a + 1)/3
Let h be 104/21 + (12 - 1032/84) - -6. Factor 2/3*p**5 - 16/3*p**3 + h*p - 32/3*p**2 + 64/3 + 4/3*p**4.
2*(p - 2)**2*(p + 2)**3/3
Let j be -8*286/(-88) - 24. Factor -9/4*l + 3*l**j - 3/4*l**3 + 0.
-3*l*(l - 3)*(l - 1)/4
Let y(t) be the second derivative of -1/6*t**3 - 1/20*t**5 + 0*t**2 - 1/6*t**4 + 12*t + 0. What is i in y(i) = 0?
-1, 0
Let k = -36 - -386. Let c be (-4*(-7)/k)/(4/45). Factor 3/5*x - 1/10*x**2 - c.
-(x - 3)**2/10
Let t(x) be the third derivative of x**7/630 - x**6/180 - x**5/15 + x**4/2 + 6*x**2. Let y(o) be the second derivative of t(o). Factor y(u).
4*(u - 2)*(u + 1)
Let f(s) = 22*s**4 + 22*s**3 - 78*s**2 - 106*s + 44. Let r(g) = -21*g**4 - 23*g**3 + 77*g**2 + 107*g - 42. Let w(v) = -5*f(v) - 6*r(v). Factor w(p).
4*(p - 2)*(p + 2)**2*(4*p - 1)
Let o(p) = p**2 + 12*p - 253. Let t be o(11). Suppose -2/3*u**3 + 0 - u**4 + 0*u + t*u**2 = 0. What is u?
-2/3, 0
Let x(b) be the first derivative of b**6/60 + 3*b + 6. Let c(q) be the first derivative of x(q). Determine t, given that c(t) = 0.
0
Let j = 1112 + -1108. Factor 242*q**3 - 1188/5*q**2 + 248/5*q - 16/5 + 2662/5*q**j.
2*(q + 1)*(11*q - 2)**3/5
Let t(s) be the third derivative of 0*s + 14*s**2 + 0*s**3 + 1/270*s**5 + 0 + 1/108*s**4. What is b in t(b) = 0?
-1, 0
Suppose -48 = -3*c - 36. Let x be (-104)/(-30) + -2 + c/3. Suppose 4/5*g + x*g**3 - 8*g**4 + 22/5*g**2 + 0 = 0. Calculate g.
-2/5, -1/4, 0, 1
Let s be 12*(-5 - 632/(-120)). Let -16/5 + 64/5*q**4 - 52/5*q**2 - s*q**5 - 52/5*q**3 + 64/5*q = 0. Calculate q.
-1, 1/2, 2
Let q(v) be the second derivative of -v**4/3 - 58*v**3/3 - 841*v**2/2 - 43*v + 4. Factor q(k).
-(2*k + 29)**2
Factor -929 + 297*t**2 - 60*t - 20*t**3 + 629 + 80*t**3 + 3*t**4.
3*(t - 1)*(t + 1)*(t + 10)**2
Let i(t) be the third derivative of -t**5/60 + t**4/3 - 7*t**3/6 - 71*t**2. Factor i(k).
-(k - 7)*(k - 1)
Factor 5*h**4 - 2*h**2 - 18*h**2 - 2*h**3 + 2*h + 15*h**2.
h*(h - 1)*(h + 1)*(5*h - 2)
Let g(w) = 4*w**5 - 2*w**4 - 6*w**3 + 2*w**2. Let r(b) = 11*b + 2*b - 6*b - 6*b. Let l(p) = 2*g(p) + 4*r(p). Suppose l(m) = 0. Calculate m.
-1, -1/2, 0, 1
Let w(t) be the second derivative of -t**6/57 + 9*t**5/95 + t**4/38 - 32*t**3/57 - 12*t**2/19 + 89*t - 2. Let w(b) = 0. What is b?
-1, -2/5, 2, 3
Suppose -173*m - 40 = -177*m. Let o(w) = 2*w - 18. Let t be o(m). Factor 0*x - 7/2*x**5 - 6*x**4 - 3/2*x**3 + x**t + 0.
-x**2*(x + 1)**2*(7*x - 2)/2
Let k(l) be the second derivative of l**7/504 - l**6/72 + 5*l**4/6 - 34*l. Let n(c) be the third derivative of k(c). Factor n(d).
5*d*(d - 2)
Suppose 5*y = -3*z - 6, -3*z - 48*y + 46*y = -3. Solve -1/2*m**5 + 5/2*m**4 - 4*m**z + 0*m + 2*m**2 + 0 = 0.
0, 1, 2
Suppose 0 = -39*l + 44*l - 10. Let y(m) be the first derivative of -1/4*m**4 - m**3 + 1/5*m**5 + 1/2*m**2 + l*m + 7. Factor y(d).
(d - 2)*(d - 1)*(d + 1)**2
Find a such that 20/9*a + 2/9*a**4 + 16/9*a**2 - 20/9*a**3 - 2 = 0.
-1, 1, 9
Suppose 3*m = -k - k - 3, -3*k + 4*m + 38 = 0. Let t be (5/(75/k))/((-14)/(-10)). Factor 2/7*s**2 + t*s**3 + 0 - 4/7*s.
2*s*(s - 1)*(s + 2)/7
Let v(c) = c**3 + 8*c**2 + 9*c + 16. Let g be v(-7). Factor -3*r**g + 6*r**3 - 8*r - 16*r - 4 + 16.
3*(r - 2)*(r + 2)*(2*r - 1)
Let s(k) = k**3 + k**2. Let g(t) = 12*t - 5*t**3 + 5*t - 8*t**2 - 21*t. Let i(a) = -g(a) - 4*s(a). Factor i(b).
b*(b + 2)**2
Factor 2*k**2 + 547*k - 95 - k**2 + 340 - 793*k.
(k - 245)*(k - 1)
Let p(v) be the third derivative of 0 - 1/735*v**7 + 1/210*v**5 + 0*v**4 - 1/420*v**6 + 1/1176*v**8 + 0*v + 28*v**2 + 0*v**3. Let p(d) = 0. What is d?
-1, 0, 1
Let j = 433441737/1797565 + 19/163415. Let m = 1212/5 - j. Factor -m*k - 16/11*k**2 - 4/11 - 4/11*k**3 + 2/11*k**5 + 4/11*k**4.
2*(k - 2)*(k + 1)**4/11
Let b(n) be the first derivative of -n**4 + 32*n**3/3 - 40*n**2 + 64*n + 102. Find i, given that b(i) = 0.
2, 4
Let s(g) = g**3 + 9*g**2 + 2. Let m be s(-9). Factor 6 + 13*k + 2 - 4*k**m - 17*k.
-4*(k - 1)*(k + 2)
Suppose 427*o - 396*o - 58 - 4 = 0. What is f in -3/7*f**5 + 6/7*f**4 + 9/7*f**3 - 12/7*f**o + 0 - 12/7*f = 0?
-1, 0, 2
Let k(p) be the third derivative of 0*p + 0*p**4 + 0*p**5 + 0 + p**2 + 0*p**3 + 1/630*p**7 - 1/180*p**6 + 1/1008*p**8. Determine n, given that k(n) = 0.
-2, 0, 1
Let u(y) be the second derivative of -y**7/840 + y**6/360 + y**5/60 + 13*y**3/6 - 20*y. Let w(c) be the second derivative of u(c). Factor w(t).
-t*(t - 2)*(t + 1)
Let v(d) = d + 3. Let g = -3 + 8. Let u be v(g). Factor -3*b - 4*b - 8*b + 90*b**2 - b - u.
2*(5*b - 2)*(9*b + 2)
Let t = 360 - 360. Factor 0 - 1/2*u**5 - 1/2*u**4 + 0*u + t*u**3 + 0*u**2.
-u**4*(u + 1)/2
Let f(l) be the second derivative of -5*l**7/21 + 31*l**6/6 - 44*l**5 + 520*l**4/3 - 640*l**3/3 - 640*l**2 - 21*l + 1. Factor f(j).
-5*(j - 4)**4*(2*j + 1)
Let a(k) be the second derivative of k**4/24 + 2*k**3 - 81*k**2/4 - 6*k + 7. Find d, given that a(d) = 0.
-27, 3
Let p be (-1 - -698) + -18 + 16. Solve 695*v - p*v + 4*v**4 - 12*v**3 + 8*v**2 = 0 for v.
0, 1, 2
Let r(d) be the first derivative of -2*d**5/25 - 3*d**4/2 - 136*d**3/15 - 12*d**2 + 288*d/5 - 387. Determine t, given that r(t) = 0.
-6, -4, 1
Suppose 5*c = -4*r, -c + 5*c - 36 = 4*r. Let s(l) be the first derivative of -4/9*l**2 - 3 - 2/9*l**c - 2/45*l**5 - 4/9*l**3 - 2/9*l. Factor s(p).
-2*(p + 1)**4/9
Let m(g) = -5*g**4 - 20*g + 15. Let o(h) = h**3 + h - 1. Let u be 13*-1 + 3/(-6)*-6. Let n(b) = u*o(b) - m(b). Factor n(l).
5*(l - 1)**3*(l + 1)
Find u such that -298*u**3 - 72 - 831*u**2 + 243*u**2 - 351*u**3 - 17*u**5 + 144*u**2 - 732*u - 650*u**2 - 172*u**4 = 0.
-3, -2, -2/17
Let b(k) = -20*k - 44. Let s be b(8). Let d be (36/(-30))/(s/40). Factor -2/17*z**2 + d*z + 0.
-2*z*(z - 2)/17
Suppose 6*t = -3*t + 18. Let b(p) = 16*p**2 - 1. Let z be b(1). Factor z*a**2 + t*a**3 - 15*a**2.
2*a**3
Let h = 10 + 6. Solve 8 - h - 4*l + 4*l**2 + 8*l = 0.
-2, 1
Let i = 892 + -890. Factor -4/5*g**i - 36/5 + 24/5*g.
-4*(g - 3)**2/5
Factor 0 + 2/5*f**2 + 0*f + 2/5*f**3.
2*f**2*(f + 1)/5
Let a(m) be the third derivative of m**7/10080 - m**5/120 - 5*m**4/12 - 14*m**2. Let h(o) be the second derivative of a(o). Factor h(i).
(i - 2)*(i + 2)/4
Let s = 19145 + -19143. Suppose -s*i**3 + 4/3*i + 2/3*i**2 + 0 = 0. Calculate i.
-2/3, 0, 1
Let u(b) = b**3 - 67*b**2 + 880*b + 100. Let a be u(