y) be the third derivative of t(y). Find g such that r(g) = 0.
-1, 0, 1
Let i = -5898 + 5902. Factor 1/4*g**i - g + 1/4 - g**3 + 3/2*g**2.
(g - 1)**4/4
Suppose 26*s - 119*s + 328 = 71*s. Factor -9 + s*f**2 + 1/2*f**3 - 3/2*f.
(f - 2)*(f + 3)**2/2
Suppose 11 = 4*k + 4*h - 1, 0 = 4*k - h - 12. Suppose 5*t + j = -3, k*j = 2*t + j - 6. What is a in 2*a**4 - a**3 + 2*a**3 + t*a**4 - 3*a**3 = 0?
0, 1
Factor 0 + 59/5*z**2 + 1/5*z**4 - 9*z - 3*z**3.
z*(z - 9)*(z - 5)*(z - 1)/5
Let y(h) = 3*h**4 - h**3 - 7*h**2 - 5*h. Let o(x) = -7*x**2 + 4*x**2 - 3*x**2 + 2*x**4 - 2*x - 2*x. Let j(f) = -5*o(f) + 4*y(f). Determine r so that j(r) = 0.
0, 1
Let k(o) = -19*o**2 + 8*o + 2. Let w(a) be the first derivative of -82*a**3 + 105*a**2/2 + 27*a - 16. Let r(p) = -27*k(p) + 2*w(p). Factor r(b).
3*b*(7*b - 2)
Let f(j) be the first derivative of j**3/15 + 9*j**2/10 + 18*j/5 - 50. Determine o so that f(o) = 0.
-6, -3
Let g(b) be the third derivative of -4/9*b**3 + 0*b + 40*b**2 + 0 + 1/360*b**6 + 1/6*b**4 - 1/30*b**5. Solve g(s) = 0.
2
Let q(b) = b**2 + 14*b + 24. Let s be q(-12). Let y(c) be the first derivative of 2/3*c - 3 + s*c**2 - 2/9*c**3. Factor y(g).
-2*(g - 1)*(g + 1)/3
Suppose 59 + 297*p + 147*p**2 + 15*p**5 - 885*p**2 + 520*p**3 - 74*p**4 - 5 - 74*p**4 = 0. What is p?
-2/15, 1, 3
Let l(s) = s**3 - 12*s**2 + 12*s - 11. Let t(d) = d**2 + 4*d - 1. Let p be t(-6). Let c be l(p). Find b, given that 3*b**5 + 9 - 9 + c*b**5 = 0.
0
Factor q**4 + 8*q + 262*q**3 - 6*q**4 + 11*q**4 + 7*q**2 - 279*q**3 - 4*q**4.
q*(q - 8)*(q - 1)*(2*q + 1)
Suppose -5*u = -22*x + 21*x + 3, -2*x + 6 = 3*u. Let t(k) be the first derivative of 0*k + 2 - 2/39*k**x + 0*k**2 - 1/26*k**4. Suppose t(i) = 0. What is i?
-1, 0
Let i(t) be the second derivative of t**6/30 - 9*t**5/40 + t**4/4 + 2*t**3 - 22*t. Let q(j) be the second derivative of i(j). Factor q(h).
3*(h - 2)*(4*h - 1)
Suppose -k = -5*s + 83, -4*s + 3*k + 89 = s. Factor s + 6*d**2 + 14*d**2 + 199*d - 167*d + 4*d**3.
4*(d + 1)*(d + 2)**2
Let l(o) be the second derivative of 1/6*o**4 + 1/30*o**5 + 10*o - 2*o**2 + 0*o**3 + 0. Let y(m) be the first derivative of l(m). Factor y(h).
2*h*(h + 2)
Let v(m) be the first derivative of 1/4*m**4 - 2*m**2 + 10 - 2/3*m**3 + 8*m. Factor v(t).
(t - 2)**2*(t + 2)
Let s(a) = -2*a**2 + 33*a - 119. Let q be s(11). Determine p, given that -2/5 + 12/5*p**2 + q*p = 0.
-1, 1/6
Suppose -5*w - k = -3*k - 10, 4*k - 16 = w. Factor -w*r**4 + 4*r**2 - r**2 + r**2.
-4*r**2*(r - 1)*(r + 1)
Let t(j) be the first derivative of -j**3 - 60*j**2 - 39. Find m such that t(m) = 0.
-40, 0
Let c(i) be the first derivative of 1/60*i**5 + 5/2*i**2 + 0*i**3 + 2 + 1/24*i**4 + 0*i. Let u(w) be the second derivative of c(w). What is x in u(x) = 0?
-1, 0
Suppose 65*o**4 - 407*o**3 + 302*o**3 + 200*o**3 + 10*o + 55*o**2 + 15*o**5 = 0. What is o?
-2, -1, -1/3, 0
Let f(x) be the second derivative of 0*x**2 - 5/56*x**7 + 0 + 0*x**3 + 23/40*x**6 + 0*x**4 + 36*x + 3/8*x**5. Solve f(t) = 0 for t.
-2/5, 0, 5
Let b = -4495 + 4497. Let -2/5*x**2 + 12/5*x - b = 0. Calculate x.
1, 5
Let p(y) = y**3 + 5*y - 49 - 8*y**2 + 51 + 7*y. Let f be p(6). Factor -2/9*u + 2/9*u**3 + 0 + 0*u**f.
2*u*(u - 1)*(u + 1)/9
Let o(b) be the first derivative of b**3/5 + 6*b**2 + 192*b/5 + 96. Let o(r) = 0. What is r?
-16, -4
Let r(w) be the third derivative of 5/24*w**4 + 0*w - 1/12*w**5 - 1/24*w**6 + 1/42*w**7 + 0*w**3 + 32*w**2 + 0. Solve r(f) = 0.
-1, 0, 1
Let y = 145 - 142. Suppose -21 + 27 = y*g. Factor -3 - 6*z**g - 3/2*z**3 - 15/2*z.
-3*(z + 1)**2*(z + 2)/2
Let i(y) be the second derivative of -y**6/180 + y**5/60 + y**4/6 - y**3/2 - 9*y**2/4 + 9*y - 9. Factor i(q).
-(q - 3)**2*(q + 1)*(q + 3)/6
Suppose 4*r = 5*v + 1254, -5*v + 6*v - 2 = 0. Let q = r + -2206/7. Factor -8/7 + 8/7*y - 8/7*y**3 + q*y**2 + 2/7*y**4.
2*(y - 2)**2*(y - 1)*(y + 1)/7
Let x(l) be the third derivative of -l**7/105 + l**6/60 + l**5/15 + 58*l**2. Factor x(u).
-2*u**2*(u - 2)*(u + 1)
Let i(r) be the first derivative of r**5/15 + 19*r**4/12 + 14*r**3 + 54*r**2 + 72*r + 112. Factor i(n).
(n + 1)*(n + 6)**3/3
Let d(b) = -2*b**3 + b**2 - 2*b. Let r(i) = -5*i**3 + 26*i**2 + 165*i + 405. Let a(x) = -12*d(x) + 4*r(x). Factor a(z).
4*(z + 5)*(z + 9)**2
Let t(a) be the third derivative of 4/39*a**4 + 7/6*a**3 + 0*a + 0 + 1/2340*a**6 - 2/195*a**5 + a**2. Let u(p) be the first derivative of t(p). Solve u(q) = 0.
4
Let v(x) be the first derivative of x**6/14 + 3*x**5/35 - 27*x**4/28 - 5*x**3/7 + 24*x**2/7 + 36*x/7 - 39. Let v(j) = 0. What is j?
-3, -1, 2
Let z(g) = -g**2 - g - 1. Let k(p) = 3*p**2 + 5*p + 3. Let x(t) = k(t) + 4*z(t). Let f(o) = 9*o**2 + 11*o - 15. Let v(q) = -f(q) - 5*x(q). Factor v(h).
-4*(h - 1)*(h + 5)
Determine v so that -240*v + 63 + 4 + 8 + 192*v**2 = 0.
5/8
Let m = -17309 + 17312. Factor 4/11*a**m + 0 + 2/11*a**4 + 2/11*a**2 + 0*a.
2*a**2*(a + 1)**2/11
Let m(z) = z**3 - 61*z**2 + 271*z - 379. Let l(o) = 5*o**3 - 245*o**2 + 1085*o - 1515. Let a(c) = 4*l(c) - 15*m(c). Find i such that a(i) = 0.
3, 5
Suppose 2*y = -x - 2, 5*y - 26 = 7*y + 5*x. Factor 2/3*u**y + 8/3*u + 8/3.
2*(u + 2)**2/3
Let a(q) be the third derivative of -1/165*q**5 + 0*q**4 - 7/660*q**6 + 0 + 0*q - 1/231*q**7 + 0*q**3 - 7*q**2. Find f, given that a(f) = 0.
-1, -2/5, 0
Let d be 2 + 6 - (1 + 1 + 0). Factor -2*b**3 + 3*b**2 + d*b - 3 - 7*b + 3*b**3.
(b - 1)*(b + 1)*(b + 3)
Let i(m) = m**3 + 7*m**2 + 2*m + 7. Let y be i(-6). Suppose -35*h + 16 = -y*h. Factor -4*j**2 - 5 + 5 + 6*j**3 + 29*j**h - 19*j**4.
2*j**2*(j + 1)*(5*j - 2)
Let w(j) = 8*j**5 + 8*j**4 - 13*j**3 + 7*j**2 + 7*j. Let h(l) = l**5 + l**4 - l**3 + l**2 + l. Let m(c) = 21*h(c) - 3*w(c). Suppose m(a) = 0. Calculate a.
-3, 0, 2
Let w(a) be the second derivative of -a**4/12 + 17*a**3/6 + 19*a**2 - 722*a. Find g such that w(g) = 0.
-2, 19
Suppose 2*g = -4*f - 224, -4*f + 4*g - 97 - 127 = 0. Let m be (-122)/f - (95/20 + -4). Solve -8/7*t**4 + 6/7*t**2 + 2/7 - m*t + 10/7*t**3 = 0 for t.
-1, 1/4, 1
Let t(c) be the third derivative of -c**6/96 + 5*c**4/8 - 10*c**3/3 + 13*c**2. Find p, given that t(p) = 0.
-4, 2
Let x(g) be the third derivative of g**6/200 + 57*g**5/100 + 783*g**4/40 - 841*g**3/10 + 653*g**2. Factor x(w).
3*(w - 1)*(w + 29)**2/5
Factor -c**4 - 28*c**2 - 6 + 7*c**3 + 353*c + 11*c**2 - 336*c.
-(c - 3)*(c - 2)*(c - 1)**2
Let o(t) be the second derivative of -t**10/60480 + t**8/13440 + 23*t**4/12 - 12*t. Let d(x) be the third derivative of o(x). What is g in d(g) = 0?
-1, 0, 1
Let r be (-2)/10 - (-4)/(-60)*-33. Let i(a) be the first derivative of -3 - a**4 + 2*a - 9/2*a**r + 4*a**3. Factor i(g).
-(g - 2)*(2*g - 1)**2
Let z(w) be the second derivative of -w**6/30 - w**5/2 + 23*w**4/12 - 2*w**3 - 2*w + 10. Factor z(v).
-v*(v - 1)**2*(v + 12)
Let k(c) be the second derivative of -22*c**6/15 - 97*c**5/5 - 82*c**4 - 344*c**3/3 + 80*c**2 + 3*c - 19. Let k(j) = 0. Calculate j.
-5, -2, 2/11
Let h(o) be the third derivative of o**7/168 - o**6/40 + o**5/40 + o**4/24 - o**3/8 + 48*o**2 + 2. Suppose h(x) = 0. What is x?
-3/5, 1
Suppose f = 4*m - 1, -52 = -3*m - 3*f - 25. Let -m - 1/2*r**2 + 2*r = 0. What is r?
2
Let a(f) be the third derivative of -11/144*f**4 + 0*f + 0 + 4/315*f**7 - 7/180*f**5 + 1/288*f**8 - 2*f**2 + 1/180*f**6 - 1/18*f**3. Let a(x) = 0. What is x?
-1, -2/7, 1
What is p in 723/2*p**3 + 126*p**4 + 6*p + 0 - 735/2*p**5 - 126*p**2 = 0?
-1, 0, 2/35, 2/7, 1
Let p(i) = -i**3 - i**2 + i. Suppose 12 = 4*s + 4. Let k(x) = -3*x**3 - 8*x**2 + 3*x + 10. Let l(o) = s*p(o) + k(o). Solve l(m) = 0 for m.
-2, -1, 1
Suppose 4*r - 23 = 5*t, -8 = 5*r + 4*t - 6. Let -2/3*m**r + 0*m**3 + 1/3*m**4 + 1/3 + 0*m = 0. What is m?
-1, 1
Let j be 1 + 4 + 1/(-3)*15. Let s(u) be the second derivative of -2/5*u**2 - 1/30*u**4 - 1/5*u**3 - 2*u + j. Factor s(i).
-2*(i + 1)*(i + 2)/5
Let g(h) = -h**3 - 9*h**2 - 2*h + 53. Let p be g(-8). Let i(r) be the first derivative of 0*r - 1/4*r**4 + 1/2*r**2 - 1/10*r**p - 3 + 1/6*r**3. Factor i(w).
-w*(w - 1)*(w + 1)*(w + 2)/2
Let b(t) be the third derivative of 7*t**7/1440 + 7*t**6/360 + t**5/30 - t**4/3 + t**2. Let l(c) be the second derivative of b(c). Factor l(n).
(7*n + 4)**2/4
Suppose 5*c = 2*n + 30, 0 = -n - 2*n - 5*c - 20. Let g be -4 - (n + (-5 - -7)). Suppose 0*p - 3/2*p**g + 3/4*p**5 + 0 + 0*p**2 + 3/4*p**3 = 0. What is 