l**2 + 0*l + 0 + 0*l**3 - 1/60*l**6 + 4/315*l**7 - 25/72*l**4. What is v in z(v) = 0?
-1, 0, 5
Factor 160 - 8*u**2 + 13*u**2 + 165*u - 255*u.
5*(u - 16)*(u - 2)
Let j(i) be the second derivative of i**4/6 + 19*i**3/3 + 18*i**2 + i - 4. Solve j(k) = 0 for k.
-18, -1
Let i(o) be the first derivative of -o**7/5040 + o**6/1080 - 31*o**3/3 - 5. Let x(s) be the third derivative of i(s). Find b, given that x(b) = 0.
0, 2
Factor -1156/13 + 4182/13*q - 480/13*q**2 + 14/13*q**3.
2*(q - 17)**2*(7*q - 2)/13
Let n(p) = -p**2 - 26*p - 84. Let x be n(-4). Let r(h) be the first derivative of -4/3*h - 8/9*h**3 - 4 + 5/3*h**2 + 1/6*h**x. Let r(i) = 0. Calculate i.
1, 2
Let u(g) be the second derivative of -1/10*g**5 + 3 + 1/90*g**6 - 2/9*g**3 - 10*g + 0*g**2 + 1/4*g**4. What is p in u(p) = 0?
0, 1, 4
Suppose 5*d = 5*h - 50, 3*h + 3*d - 18 = -2*h. Let v(q) = -q**2 + q + 1. Let k(i) = 18*i**2 + 10*i - 22. Let a(b) = h*v(b) + k(b). Factor a(y).
4*(y + 2)*(3*y - 2)
Let n(j) be the third derivative of -j**6/30 + 31*j**5/15 - 5*j**4 - 24*j**2. Suppose n(c) = 0. What is c?
0, 1, 30
Let b(v) = 2*v**2 + 2*v. Let p = 10 + -10. Suppose 12 = 5*i + 2*o, p = 3*i + o - 5 - 2. Let l(r) = 4*r**2 + 4*r. Let t(q) = i*l(q) - 5*b(q). Factor t(z).
-2*z*(z + 1)
Let l(p) be the third derivative of -p**7/630 + p**6/120 - p**4/18 - 11*p**2. Solve l(k) = 0.
-1, 0, 2
Let a(i) be the second derivative of i**5/170 - i**4/17 + 11*i**3/51 - 6*i**2/17 + 2*i - 14. Factor a(j).
2*(j - 3)*(j - 2)*(j - 1)/17
Let g be ((18/24)/(3/6))/(5/10). Let 8*l - 12*l**4 + 42*l**g - 10/3*l**5 - 104/3*l**2 + 0 = 0. What is l?
-6, 0, 2/5, 1
Let q(s) be the second derivative of s**5/90 - 4*s**3/9 - 16*s**2/9 - s + 6. Factor q(x).
2*(x - 4)*(x + 2)**2/9
Let k(m) be the second derivative of 1/42*m**4 + 3*m + 3/7*m**2 + 4/21*m**3 + 0. Factor k(z).
2*(z + 1)*(z + 3)/7
Let c(r) be the first derivative of r**6/8 - 9*r**5/4 + 93*r**4/8 - 17*r**3/2 - 189*r**2/8 + 147*r/4 - 767. Determine h, given that c(h) = 0.
-1, 1, 7
Suppose 3*g - 47 = -4*t - 29, 3*g = 2*t. What is n in -25/2*n + 5/2 + 45/2*n**3 + 15/2*n**g = 0?
-1, 1/3
Let 12/5*u**2 + 32/15 + 2/15*u**3 + 22/5*u = 0. Calculate u.
-16, -1
Factor -294*k - 2058 - 2/9*k**3 - 14*k**2.
-2*(k + 21)**3/9
Find q, given that -135*q + 63*q - 121*q**4 + 96*q**4 - 5*q**5 + 60 - 68*q + 45*q**3 + 65*q**2 = 0.
-6, -2, 1
Factor 3114752 + 50784*i + 276*i**2 + 1/2*i**3.
(i + 184)**3/2
Suppose 5*f - 34 = -4*v, -v - 170 = 4*f - 184. Factor 1 - 1/6*r**f + 1/6*r.
-(r - 3)*(r + 2)/6
Let h = -46 - -73. Factor -2*j**4 + 64*j - 48*j**2 - 27 + 7*j**3 - h + 22 + 9*j**3.
-2*(j - 2)**4
Let u = 31724 - 31720. Let 3/2*c**u - 9/2*c**2 + 3 + 3/2*c**3 - 3/2*c = 0. What is c?
-2, -1, 1
Let p(r) be the second derivative of r**4/16 + 135*r**3/4 + 54675*r**2/8 + 573*r. Let p(v) = 0. Calculate v.
-135
Determine j, given that -39*j**4 + 24*j**3 + 26*j**3 - 8*j**3 - 24*j**5 - 9*j - 9*j - 5*j**2 + 44*j**2 = 0.
-2, -1, 0, 3/8, 1
Let p(b) be the first derivative of -b**9/13608 + b**8/7560 + 16*b**3 + 46. Let k(s) be the third derivative of p(s). Determine n so that k(n) = 0.
0, 1
Let b(f) = f**2 - 12*f - 28. Let g be b(14). Let k(w) be the third derivative of 3*w**2 + 0*w**4 + g*w + 1/3*w**3 - 1/30*w**5 + 0. Factor k(p).
-2*(p - 1)*(p + 1)
Let q(y) = y. Let t be q(2). Suppose 0 = t*r - 4*r + 2. Factor -r + 0*x**3 + x**2 - x**3 + x + 0*x**3.
-(x - 1)**2*(x + 1)
Let t(g) be the second derivative of 2/15*g**3 + 1/25*g**5 + 2/15*g**4 + 0*g**2 + 0 + 19*g. Factor t(x).
4*x*(x + 1)**2/5
Let i(t) be the first derivative of t**5/270 + t**4/54 + t**3/27 - 3*t**2/2 + 29. Let b(h) be the second derivative of i(h). Factor b(m).
2*(m + 1)**2/9
Let g(x) be the third derivative of -1/78*x**5 - 11*x**2 - 1/780*x**6 + 1/1365*x**7 + 0*x + 0 + 0*x**3 - 1/52*x**4. Determine c so that g(c) = 0.
-1, 0, 3
Let f(d) be the third derivative of d**6/40 + d**5/10 - 13*d**4/8 + 5*d**3 + 52*d**2. Let f(p) = 0. What is p?
-5, 1, 2
Let y(f) = 210*f. Let g be y(1). Find r, given that 18 - 57*r + 1617*r**4 - 1029*r**5 + 23 - 44 - g*r**3 - 318*r**2 = 0.
-1/7, 1
Let p be 3 + (110/(-10) - -14). Let w(u) be the second derivative of -3/160*u**5 - 1/32*u**4 + 7*u + 0*u**2 + 1/112*u**7 + 1/80*u**p + 0 + 0*u**3. Factor w(z).
3*z**2*(z - 1)*(z + 1)**2/8
Let k = -17 - -18. Suppose -k = w - 4. Let -5*s**3 + 4*s**w + 4*s**3 - s**3 - 2*s = 0. What is s?
-1, 0, 1
Let k(a) be the first derivative of -a**4 - 8*a**3/3 + 16*a**2 + 300. Factor k(p).
-4*p*(p - 2)*(p + 4)
Let y be (-3)/((-63)/203) - 9. Let c(q) be the second derivative of 0 + 5/9*q**3 + y*q**2 + 1/30*q**5 + 6*q + 2/9*q**4. Factor c(b).
2*(b + 1)**2*(b + 2)/3
Let w(m) be the third derivative of -m**5/150 - m**4/6 + 13*m**3/5 + 4*m**2 + 58. Let w(p) = 0. Calculate p.
-13, 3
Suppose 60*a - 59*a = 2*j + 7, 0 = 5*j + 4*a - 28. Factor 2/15*o**2 + 2/15*o - 4/15*o**3 + j.
-2*o*(o - 1)*(2*o + 1)/15
Suppose -4*m = -196 + 176. Let j(k) be the third derivative of 0*k + 4*k**2 - 1/24*k**3 + 1/48*k**4 + 0 - 1/240*k**m. What is o in j(o) = 0?
1
Let q(c) be the second derivative of c**7/168 - c**6/30 + c**5/80 + c**4/8 + 19*c. Factor q(s).
s**2*(s - 3)*(s - 2)*(s + 1)/4
Determine i so that 0 + 12*i**3 + 16/3*i + 2/3*i**5 + 14/3*i**4 + 40/3*i**2 = 0.
-2, -1, 0
Let n be 20/15 - 82/(-6). Suppose 5 = 5*m - n. Solve 10*d**2 - 20*d - 6*d**2 - 72*d**m + 4 + 132*d**3 - 48*d**3 = 0 for d.
-1/2, 1/3, 1
Let c(q) be the third derivative of 2*q**7/105 + 17*q**6/30 - 37*q**5/15 + 19*q**4/6 - q**2 - 32. Factor c(j).
4*j*(j - 1)**2*(j + 19)
Let r = 5803 - 5800. Factor 0 + 0*s**2 + 3/7*s**5 - 9/7*s**4 + 0*s + 6/7*s**r.
3*s**3*(s - 2)*(s - 1)/7
Suppose 16/7*y**3 - 2/7*y**4 + 0 + 0*y - 2*y**2 = 0. Calculate y.
0, 1, 7
Let f = -89821/2 - -44915. Suppose f*t**2 + 15/2*t**4 - 3/4*t - 9/4*t**5 + 0 - 9*t**3 = 0. What is t?
0, 1/3, 1
Let w = 40882 + -40880. Factor 2/11*z**w - 16/11*z + 0.
2*z*(z - 8)/11
Suppose 92 = -4*c - 5*j + 95, -2*c - j = -3. Let k(t) be the first derivative of 0*t + 20/3*t**3 - 5/2*t**c - 2. Determine o, given that k(o) = 0.
0, 1/4
Suppose 0 = -5*n - l + 38, 0 = -2*l - l - 6. Suppose 0 = w - 4*z + n, -w = w + 5*z - 23. Solve -w*y + 5*y + 6*y**3 - 3*y - 4*y**4 = 0.
-1/2, 0, 1
Factor 17298/5 + 372/5*y + 2/5*y**2.
2*(y + 93)**2/5
Let v(b) be the second derivative of -4/5*b**6 + 1/21*b**7 + 0 + 0*b**2 - 12*b**3 - 28*b + 2*b**4 + 7/2*b**5. Solve v(g) = 0 for g.
-1, 0, 1, 6
Let g(r) = -5*r - 5. Let t(h) = 14*h + 15. Let m(u) = -17*g(u) - 6*t(u). Let w be m(6). Factor 3*p**2 - w - 1 + 7 - 6*p - 2.
3*(p - 1)**2
Suppose n - 6*n = 60. Let s be (-123)/(-90) - n/90. Factor 0 + 0*l**2 - 3/2*l**3 + s*l.
-3*l*(l - 1)*(l + 1)/2
Find r such that -16/5 + 36/5*r - 28/5*r**2 + 9/5*r**3 - 1/5*r**4 = 0.
1, 2, 4
Find k, given that 2/15*k**5 + 232/3*k**3 - 88/15*k**4 - 26624/15*k - 2432/15*k**2 - 32768/15 = 0.
-2, 16
Let f(d) be the first derivative of -2/5*d**5 + 4*d**2 - 4*d**3 + 9 + 2*d**4 - 2*d. Determine k so that f(k) = 0.
1
Suppose -t - 5*x + 222 = 170, 4*x - 40 = 0. Factor -108/7 - 36/7*a - 3/7*a**t.
-3*(a + 6)**2/7
Let j(i) = -247*i - 494. Let l be j(-2). Factor 1/9*v**2 + 1/9*v**5 - 1/9*v**4 + 0 + l*v - 1/9*v**3.
v**2*(v - 1)**2*(v + 1)/9
Let j(a) be the third derivative of a**8/280 + a**7/60 - a**5/15 + a**3/6 + 17*a**2. Let c(z) be the first derivative of j(z). Let c(r) = 0. Calculate r.
-2, -1, 0, 2/3
Let p(w) be the second derivative of -w**6/450 - 11*w**5/600 + w**4/40 + w**3/3 + 14*w. Let t(o) be the second derivative of p(o). Factor t(x).
-(x + 3)*(4*x - 1)/5
Let c(h) be the second derivative of 10/49*h**7 + 0*h**2 + 0 - 1/35*h**5 + 0*h**4 + 0*h**3 - h - 4/105*h**6. Factor c(o).
4*o**3*(3*o - 1)*(5*o + 1)/7
Let h be -1 + 16 + 82 + -94. Factor 11/5*d**2 + 1/5 + 7/5*d + d**h.
(d + 1)**2*(5*d + 1)/5
Let z(l) be the first derivative of -l**5/42 + l**4/28 + 2*l**3/21 - 9*l**2/2 - 13. Let u(v) be the second derivative of z(v). Suppose u(a) = 0. Calculate a.
-2/5, 1
Suppose -5 = -4*n + 3. Solve -3*s**n - 4*s**3 + 5*s**2 - s**2 + 7*s**2 = 0.
0, 2
Let q = -268 + 272. Let d(r) be the first derivative of -q - 1/9*r**3 + r - 1/3*r**2. Factor d(c).
-(c - 1)*(c + 3)/3
Let i(k) = 101*k**2 - 24*k - 17. Let b be 9/(-3 + 12/8). Let v(m) = -34*m**2 + 8*m + 6. Let u(s) = b*i(s) - 17*v(s). Suppose u(c) = 0. Calculate c.
0, 2/7
Suppose 57*n**