3. Let j be w(-8). Let -z**3 + 2*z**3 - 3*z**5 + 4*z**j - 4*z**3 - 2*z**2 = 0. Calculate z.
-1, 0, 2
Factor 260/9 - 2/9*b**2 - 14*b.
-2*(b - 2)*(b + 65)/9
Let g(n) = -3*n**3 + 18*n**2 + 72*n + 6. Let k(b) = -6*b**3 + 34*b**2 + 144*b + 11. Let r(d) = 11*g(d) - 6*k(d). Factor r(v).
3*v*(v - 6)*(v + 4)
Let u = -1/35 - -2/21. Let m(c) be the first derivative of -1/20*c**4 - u*c**3 + 0*c + 1/25*c**5 + 5 + 1/10*c**2. Factor m(v).
v*(v - 1)**2*(v + 1)/5
Let f(n) be the second derivative of -n**8/36960 + n**4/12 + 6*n. Let s(t) be the third derivative of f(t). Factor s(o).
-2*o**3/11
Let r(a) be the first derivative of 3*a**4/8 + a**3/2 - 3*a**2/4 - 3*a/2 + 55. Suppose r(p) = 0. Calculate p.
-1, 1
Let s = -273/5 - -42347/770. Let k = s + -3/14. Factor -4/11*l**4 + 4/11*l**2 + k*l - 2/11*l**5 + 0 + 0*l**3.
-2*l*(l - 1)*(l + 1)**3/11
Let y(p) be the second derivative of 0 + 0*p**4 + 1/7*p**2 + 1/140*p**5 + 17*p - 1/14*p**3. Factor y(s).
(s - 1)**2*(s + 2)/7
Let u(h) be the third derivative of -h**6 - 19*h**2 + 0*h**3 + 0 - 3/10*h**5 + 368/315*h**7 + 0*h - 8/21*h**8 + 3/4*h**4. Find t, given that u(t) = 0.
-1/3, 0, 3/4
Let a(c) be the third derivative of -34*c**2 + 0 + 1/120*c**6 + 0*c**3 + 0*c - 1/75*c**5 - 1/525*c**7 + 1/120*c**4. Factor a(b).
-b*(b - 1)**2*(2*b - 1)/5
Let j(b) be the second derivative of 7*b**4 - 122*b**3/9 - 4*b**2/3 - 499*b. Find a, given that j(a) = 0.
-2/63, 1
Let -496*v**3 + 69192*v**2 + 99740268 + 4/3*v**4 - 4289904*v = 0. Calculate v.
93
Let v(r) = r**3 - r**2 - r + 1. Let f(m) = 47*m**3 - 138*m**2 - 206*m - 66. Let c(q) = 5*f(q) + 10*v(q). Let c(x) = 0. Calculate x.
-4/7, 4
Let p(l) be the third derivative of -l**5/40 + 3*l**4/8 - 9*l**3/4 + 222*l**2. Find q such that p(q) = 0.
3
Let c(n) = -6*n - 17. Let g be c(-4). Let o be 2/g + -2 + 2. Let 8/7*z**4 - 8/7*z**2 + 0 + 2/7*z - o*z**3 = 0. What is z?
-1, 0, 1/4, 1
Let x = -6253/4 + 1564. What is j in -x*j**2 + 1/4 + 1/2*j = 0?
-1/3, 1
Let u(q) be the third derivative of -q**6/15 - 161*q**5/30 - 49*q**4/3 - 13*q**3 + 749*q**2. Factor u(x).
-2*(x + 1)*(x + 39)*(4*x + 1)
Suppose 5*d = -2*v + 5, 2*v = -118*d + 114*d + 2. Factor 1/2*m**d - 18 + 24*m - 13/2*m**2.
(m - 6)**2*(m - 1)/2
Factor 4*v - 982*v**2 + 1964*v**2 - 986*v**2.
-4*v*(v - 1)
Solve -5/4*w - 15/2 + 5/4*w**2 = 0.
-2, 3
Let r(m) be the second derivative of -m**7/63 - m**6/45 - 29*m + 2. Suppose r(q) = 0. Calculate q.
-1, 0
Suppose 10*m + 17 = 57. Let n be (1 - (-10)/m) + (-150)/100. Factor 3/2 - 15/4*s**3 + 3/4*s**4 + 27/4*s**n - 21/4*s.
3*(s - 2)*(s - 1)**3/4
Let n(h) be the third derivative of h**5/60 + h**4/4 + 2*h**3/3 + 3*h**2. Let x(p) = p**2 + 1. Suppose -2*i = -0*i + 2. Let k(w) = i*n(w) + 4*x(w). Factor k(s).
3*s*(s - 2)
Let u = -133 - -137. Factor -i**2 + 9*i**3 - 12*i**2 - u*i**3 + 3*i**2.
5*i**2*(i - 2)
Let q(m) be the first derivative of m**6/720 + m**5/120 + m**4/48 + 17*m**3/3 + 8. Let n(l) be the third derivative of q(l). Factor n(p).
(p + 1)**2/2
Let m(l) be the third derivative of 21*l**2 + 0*l - 1/90*l**5 + 0 + 2/9*l**4 + 0*l**3. Determine x so that m(x) = 0.
0, 8
Let j(t) be the second derivative of t**7/84 + t**6/90 - 8*t**3/3 + 24*t. Let w(y) be the second derivative of j(y). Suppose w(x) = 0. Calculate x.
-2/5, 0
Suppose 29*f + 40 = 31*f. Suppose 2*t - 30 = -f. Let 16/5*x**4 + 0 - 2/5*x**3 + 0*x**2 - 32/5*x**t + 0*x = 0. Calculate x.
0, 1/4
Let w be 22/(16 - (9 + 0)). Let -8/7*u + 4/7*u**5 - w*u**4 + 8/7 - 22/7*u**2 + 40/7*u**3 = 0. Calculate u.
-1/2, 1, 2
Find f, given that 0*f + 0 - 28/3*f**3 + 1/3*f**4 + 196/3*f**2 = 0.
0, 14
Suppose -27*c + 33*c = 150. Find g such that 67*g**3 + g**5 + c - 17 + 2*g**4 - 10*g**2 + 4*g - 72*g**3 = 0.
-2, -1, 1, 2
Let g(y) be the third derivative of y**5/105 + 54*y**4/7 + 17496*y**3/7 + 373*y**2. Factor g(w).
4*(w + 162)**2/7
Let k(d) be the first derivative of -5 + 3/11*d**4 - 18/55*d**5 - 8/11*d + 2/3*d**3 - 4/11*d**2. Determine h so that k(h) = 0.
-2/3, 1
Let r(j) be the third derivative of 0 - 1/12*j**4 + j**2 + 1/9*j**3 + 0*j - 1/90*j**5 + 1/60*j**6. Solve r(p) = 0.
-1, 1/3, 1
Let w(i) be the third derivative of -i**9/272160 - i**8/45360 + i**7/7560 + 3*i**5/10 - 26*i**2. Let h(l) be the third derivative of w(l). Factor h(p).
-2*p*(p - 1)*(p + 3)/9
Let a(w) be the first derivative of 0*w**2 - 10 + 1/14*w**4 + 0*w - 2/21*w**3. Suppose a(q) = 0. What is q?
0, 1
Factor n**4 - 1162 - n**2 - 6*n + 1157 + 6*n**3 + 5*n**2.
(n - 1)*(n + 1)**2*(n + 5)
Let u(r) be the second derivative of -1/72*r**4 + 0*r**2 - 1/18*r**3 + r + 0 + 1/120*r**5. Factor u(s).
s*(s - 2)*(s + 1)/6
Let m(n) be the third derivative of -n**8/224 - n**7/168 + 19*n**6/480 + n**5/80 - 13*n**4/96 + n**3/12 - 2*n**2 - 65*n. Find t, given that m(t) = 0.
-2, -1, 1/6, 1
Let n(y) = y + 57. Let x(s) = 28. Let g(f) = 3*n(f) - 7*x(f). Let h be g(9). Factor 2/5*m**h + 12/5*m + 18/5.
2*(m + 3)**2/5
Let r = -2/6247 + 3167237/24988. Let -r - 39/2*y - 3/4*y**2 = 0. What is y?
-13
Factor 72*j**5 - j**4 - j**2 + 2*j**2 + 3*j**3 - 2*j - 73*j**5.
-j*(j - 1)**2*(j + 1)*(j + 2)
Let x(t) = -22*t**3 - 20*t**2 + 6*t + 180. Let c(a) = 14*a**3 + 14*a**2 - 4*a - 120. Let d(s) = -8*c(s) - 5*x(s). Solve d(g) = 0.
-5, -3, 2
Let b(i) be the third derivative of -i**8/1680 - i**7/630 + i**6/45 + 2*i**5/15 + 5*i**4/12 - 6*i**2. Let s(p) be the second derivative of b(p). Solve s(c) = 0.
-2, -1, 2
Factor -155*r + 60*r**2 + 81*r + 38 - 14*r + 10 + 2*r**4 - 18*r**3.
2*(r - 3)*(r - 2)**3
Factor -4*x**5 + 2*x**4 + x**3 - 1559*x + 5*x**5 + 1559*x.
x**3*(x + 1)**2
Let m = 2/1493 - -82111/2986. Find l, given that 51/2*l**4 - 9/2*l**5 - m*l**3 - 71/2*l**2 + 24*l + 18 = 0.
-2/3, 1, 3
Let a(r) be the third derivative of -10*r**2 - 1/30*r**5 - 25/3*r**3 - 5/6*r**4 + 0*r + 0. Factor a(v).
-2*(v + 5)**2
Determine l so that -1800/7 - 2/7*l**2 - 120/7*l = 0.
-30
Suppose -1054 = q - 250. Let i = -5616/7 - q. Factor -12/7 + 3/7*n**3 - i*n + 3/7*n**2.
3*(n - 2)*(n + 1)*(n + 2)/7
Suppose -3*r - 39 = 2*q + 21, 5*r + 2*q = -96. Let d be (-13)/r + -1 + (-7)/(-9). Solve 1/2*a**4 - d*a**2 + 1/4*a**5 + 0 - 1/4*a + 0*a**3 = 0.
-1, 0, 1
Let w(l) be the first derivative of -22 - 2*l + 2*l**2 - 2/3*l**3. Factor w(x).
-2*(x - 1)**2
Factor -92/3*w + 44/3*w**2 + 0 + 1/3*w**3.
w*(w - 2)*(w + 46)/3
Let k(s) be the third derivative of s**6/30 - 7*s**5/15 - 20*s**4/3 - 88*s**3/3 - 5*s**2 - 5*s. Factor k(u).
4*(u - 11)*(u + 2)**2
Let x(o) = o**4 + 22*o**3 - 230*o**2 + 774*o - 565. Let m(t) = 2*t**4 + 20*t**3 - 229*t**2 + 774*t - 564. Let q(n) = 2*m(n) - 3*x(n). Let q(z) = 0. Calculate z.
1, 7, 9
Factor 132*y**3 + 3*y**2 - 11*y**2 - 20*y + 8 - 49*y**3 - 63*y**3.
4*(y - 1)*(y + 1)*(5*y - 2)
Let f be (-11 - -17) + (140/(-24))/1. Let x(b) be the third derivative of 5*b**2 + 0 + 0*b**3 + 0*b - f*b**4 - 1/15*b**5. Factor x(p).
-4*p*(p + 1)
Find x, given that 0 + 3/2*x**2 - 6*x = 0.
0, 4
Let l(p) = 2*p + 3. Let u be l(0). Suppose -2*j - 2 = -u*j. Solve 0*i**2 + i + 1 + 4*i**j - 9 + 3*i = 0.
-2, 1
Let y be (-30)/(-3 - (-30)/(-20)). Let z(i) be the first derivative of -8 + i**2 - y*i**3 + 4*i. Factor z(g).
-2*(2*g - 1)*(5*g + 2)
Let z(k) = k**2 - 11*k + 15. Let s be z(8). Let q be (s/12)/(12/(-8)). Find u, given that 0 + q*u**3 - 1/2*u + 1/4*u**2 - 1/4*u**4 = 0.
-1, 0, 1, 2
Let x(m) be the second derivative of m**4/8 + 9*m**3/2 - 57*m**2/4 + 164*m. Factor x(l).
3*(l - 1)*(l + 19)/2
Let m(v) be the third derivative of 0 - 1/1080*v**6 - 13/216*v**4 + 0*v + 1/9*v**3 - 39*v**2 + 2/135*v**5. Factor m(q).
-(q - 6)*(q - 1)**2/9
Factor 1/4*s**2 - 3/2 + 5/4*s.
(s - 1)*(s + 6)/4
Solve 1/3*n**3 + 64/3 + 4*n**2 + 16*n = 0.
-4
Suppose -4 = 3*i - 2*g, -4 + 8 = -i + 2*g. Let d(f) be the second derivative of -1/2*f**4 + i*f**2 + 4*f + 0 + 2/3*f**3 + 1/10*f**5. Factor d(x).
2*x*(x - 2)*(x - 1)
Let q(r) be the first derivative of 1 + 0*r + 0*r**2 + r**3 - 3/4*r**4. Factor q(l).
-3*l**2*(l - 1)
Let h(g) be the third derivative of -g**5/60 + 31*g**4/3 - 7688*g**3/3 + 576*g**2 - 2. Factor h(d).
-(d - 124)**2
Suppose 5*x = -m + 6, -4*x + 6*m + 28 = m. Factor 42*r**2 + 64*r**3 - 99*r**x + 25*r**2 + 4*r.
4*r*(4*r - 1)**2
Let o(n) be the first derivative of -n**4/2 - 8*n**3/3 - 5*n**2 - 4*n + 3. Factor o(k).
-2*(k + 1)**2*(k + 2)
Let x(u) be the second derivative of 0 + 3*u**2 + 2*u + 1/36*u**5 + 