0 + 65*j**4/8 + 9*j**3 + 11*j**2/2 - j - 19. Let p(f) be the second derivative of g(f). Factor p(i).
3*(i + 9)*(7*i + 2)
Let j(i) be the third derivative of -13 - 1/360*i**5 + i**2 - 19/36*i**3 - 5/36*i**4 + 0*i. Find a such that j(a) = 0.
-19, -1
Let n(c) be the third derivative of -c**6/40 - c**5/5 - 3*c**4/8 - c**2 - 3457. Suppose n(q) = 0. Calculate q.
-3, -1, 0
Let a(y) = y - 6. Let i be a(11). Suppose -i = 2*m - 3*m. Factor -5*c + 293 + m*c**2 - 293.
5*c*(c - 1)
Let j be (-945)/(-525)*((-140)/(-98))/(12/21). Factor 1 - 2*x**3 + j*x + 3/2*x**2.
-(x - 2)*(x + 1)*(4*x + 1)/2
Factor -63/2*j - 65/4*j**2 + 2.
-(j + 2)*(65*j - 4)/4
Suppose 0*i - i - 3*q + 11 = 0, 0 = -2*q + 4. Suppose -i*h + 23 = z, 2*z + h - 13 = -z. Find a such that 2*a**2 - 3 + a - 4*a + 3*a**z + a**2 = 0.
-1, 1
Let h = -435 - -439. Let u be (-4)/6 - (-16)/6. Factor b**2 + 7*b**2 + h + 4*b**4 + 0*b**2 - 16*b**u.
4*(b - 1)**2*(b + 1)**2
Let v = -477806/779 - -25152/41. Find o such that 28/19*o + 16/19 + v*o**3 + 14/19*o**2 = 0.
-4, -2, -1
Suppose -t - t + 282 = -3*s, 2*t = -s + 290. What is k in -21*k**5 + 166*k**4 - 104*k**2 + t*k + 94*k**4 - 15*k**3 - 833*k**3 + 344*k**2 = 0?
-2/7, 0, 2/3, 6
Suppose 0 = 11*v + 31*v - 10*v - 64. Factor -336/5*a + 288/5 + 10*a**v - 2/5*a**3.
-2*(a - 12)**2*(a - 1)/5
Let p(s) be the first derivative of 1/90*s**6 + 0*s - 1/6*s**4 + 0*s**2 - 11/3*s**3 + 13 + 0*s**5. Let l(f) be the third derivative of p(f). Factor l(x).
4*(x - 1)*(x + 1)
Let w(l) be the second derivative of 1 - 57*l - 3/70*l**5 - 4/7*l**3 + 0*l**2 + 8/21*l**4 - 1/105*l**6. Factor w(r).
-2*r*(r - 2)*(r - 1)*(r + 6)/7
Let x be ((-3)/(-2))/((-27)/(-126)). Suppose -12 = -x*k + k. Factor -k*c**3 + 2*c**2 - 4*c**3 + 7*c**2 + 5*c**3 + 27 - 27*c.
-(c - 3)**3
Let d(t) be the first derivative of -t**6/6 - 3*t**5/4 + 27*t**4 + 349*t**3/12 - 489*t**2/4 + 54*t + 1201. Determine f so that d(f) = 0.
-12, -2, 1/4, 1, 9
Let y be 3425/411 - 11 - (-1)/((-1)/(-10)). Find k, given that -y*k**4 - 50/3*k**3 + 46/3*k + 50/3*k**2 + 4/3*k**5 - 28/3 = 0.
-2, -1, 1/2, 1, 7
Let y(o) be the first derivative of -25/2*o - 15/4*o**2 + 3/2*o**3 - 1/8*o**4 - 171. Let y(k) = 0. Calculate k.
-1, 5
Let d(b) be the first derivative of b**6/16 - 27*b**5/40 + 39*b**4/32 + 9*b**3/8 - 21*b**2/8 - 1146. What is k in d(k) = 0?
-1, 0, 1, 2, 7
Factor 419*k**2 - 817*k**2 + 395*k**2 + 990*k + 993.
-3*(k - 331)*(k + 1)
Solve -1/3*l**2 + 1/12*l**3 - 1/2 - 11/12*l = 0.
-1, 6
Find x such that 6400/3*x + 1/3*x**4 + 1499/2*x**2 - 65/2*x**3 - 1250 = 0.
-3, 1/2, 50
Let u(w) be the second derivative of 2*w**6/75 + 3*w**5/25 - 13*w**4/15 - 2*w**3 + 24*w + 4. Suppose u(n) = 0. What is n?
-5, -1, 0, 3
Let q be ((-15)/(-10))/(657/15330). Solve 5/3*s**2 + 5/3*s**4 - q*s + 25/3*s**3 - 30 = 0.
-3, -1, 2
Let s be ((-36)/44)/((-10170)/24860). Suppose -52/7 - 51/7*n + 1/7*n**s = 0. Calculate n.
-1, 52
Let j(l) be the first derivative of -2/15*l**3 + 24/5*l + 11/5*l**2 + 64. Factor j(i).
-2*(i - 12)*(i + 1)/5
Let i = -278648 - -278664. Factor 0 + 92/3*s**3 - i*s**2 + 0*s + 8/3*s**4.
4*s**2*(s + 12)*(2*s - 1)/3
Factor 222 - 504 + 2476*n - 2619*n - n**2.
-(n + 2)*(n + 141)
Let o(j) be the third derivative of j**7/630 - 617*j**6/360 + 1643*j**2. What is u in o(u) = 0?
0, 617
Let r(v) be the third derivative of -1/70*v**7 - 7/4*v**5 + 49/8*v**4 - 13/40*v**6 + 0 + 0*v**3 + 23*v - v**2. Solve r(b) = 0 for b.
-7, 0, 1
Let a(g) be the second derivative of g**4/20 - 181*g**3/6 + 301*g**2/5 + 877*g. Factor a(i).
(i - 301)*(3*i - 2)/5
Let u be -2*(-5)/(15/3). Solve 201*h**2 - 387*h**2 + 2*h**3 + 198*h**u - 2*h**4 = 0 for h.
-2, 0, 3
Let b(p) = -p**3 + 23*p**2 - 95*p - 373. Let x be b(15). Suppose 2/3*l**x + 4 + 14/3*l = 0. What is l?
-6, -1
Let h be 22776/42 + -4 + -11. Let u = h + -527. Factor -2/7*n**5 - u*n**4 + 18/7*n**3 - 22/7*n**2 + 8/7*n + 0.
-2*n*(n - 1)**3*(n + 4)/7
Let y = 386373 - 2704609/7. Factor -y*a**2 - 22/7*a - 20/7.
-2*(a + 1)*(a + 10)/7
Let v(q) be the third derivative of 1/105*q**7 - 1/9*q**6 + 0*q - 4/3*q**4 + 16/9*q**3 - 34 + 8/15*q**5 - 2*q**2. Factor v(l).
2*(l - 2)**3*(3*l - 2)/3
Let h be (-580)/(-3248) + 7/((-98)/(-8)). What is i in h - 9/2*i**2 - 15/4*i = 0?
-1, 1/6
Let d = 224575 - 224571. Factor 2*s**3 - 2/5*s**d - 96/5*s + 16/5*s**2 + 0.
-2*s*(s - 4)**2*(s + 3)/5
Let a = 1139/3500 - 38/125. Let d(y) be the second derivative of -1/70*y**6 + 0 + 1/28*y**4 + a*y**5 - 1/14*y**3 + 0*y**2 - 8*y. What is u in d(u) = 0?
-1, 0, 1
Solve 404/5*p + 196/5*p**2 + 204/5 - 4/5*p**3 = 0.
-1, 51
Let s = 203600 - 203598. What is l in 0 + 8/9*l - 2/9*l**3 - 8/9*l**s + 2/9*l**4 = 0?
-2, 0, 1, 2
Let t(v) = -2767*v - 41502. Let u be t(-15). Find r such that -13/2 - 1/2*r + 1/2*r**u + 13/2*r**2 = 0.
-13, -1, 1
Let a(z) = -z**2 - 12*z - 15. Let j be a(-10). Let q(w) = w**2 - w - 1. Let f(b) = -7*b**2 - b + 8. Let p(d) = j*f(d) + 40*q(d). Factor p(h).
5*h*(h - 9)
Let q(t) = 3*t**2 + 21*t + 18. Let b(z) = 4*z**2 + 4*z. Let w(a) = 5*a**2 + 5*a. Let s(c) = -6*b(c) + 5*w(c). Let i(l) = -q(l) + 4*s(l). Factor i(m).
(m - 18)*(m + 1)
Determine c, given that -3*c**2 + 31 + 993*c - 21 - 40 + 30 = 0.
0, 331
Suppose 736/7*g + 512/7*g**3 - 1824/7*g**2 + 18/7*g**5 + 0 + 120*g**4 = 0. What is g?
-46, -2, 0, 2/3
Factor 16/5*p**3 - 624/5*p + 0 - 2492/5*p**2.
4*p*(p - 156)*(4*p + 1)/5
Let y = 333081 + -333078. Let p be 42/(-15) - -3 - -2. Solve 16/5*m - 4/5 - p*m**y - 4/5*m**4 + 3/5*m**2 = 0 for m.
-2, 1/4, 1
Let y(f) be the first derivative of f**5/130 - 2*f**4/39 + 4*f**3/39 - 19*f - 38. Let c(s) be the first derivative of y(s). Let c(g) = 0. Calculate g.
0, 2
Let i(b) = 17*b**3 - 19*b**2 - b + 114. Let h(r) = -46*r**3 + 56*r**2 + 2*r - 332. Let p(y) = 3*h(y) + 8*i(y). Factor p(s).
-2*(s - 7)*(s - 3)*(s + 2)
Suppose 27*i - 28 = 13*i. Let y(z) be the first derivative of -5/3*z**5 + 5/9*z**3 - 5*z**4 + 25 + 10*z**i + 20/3*z. Let y(w) = 0. What is w?
-2, -1, -2/5, 1
Let x(j) be the first derivative of 0*j + 5*j**4 - 18*j**2 - 4*j**3 - 4/5*j**5 - 20. Factor x(s).
-4*s*(s - 3)**2*(s + 1)
Let 29/4*x**2 + 0 - 1/4*x**3 + 0*x = 0. Calculate x.
0, 29
Let g(v) be the first derivative of v**4/12 - v**3/6 + 53*v - 106. Let l(b) be the first derivative of g(b). Factor l(f).
f*(f - 1)
Let m(j) be the first derivative of -1/20*j**4 + 0*j**3 - 7/40*j**6 + 17/100*j**5 - 9/2*j**2 + 0*j + 19. Let f(g) be the second derivative of m(g). Factor f(w).
-3*w*(5*w - 1)*(7*w - 2)/5
Let t(w) be the third derivative of 13*w**6/240 - 19*w**5/60 - w**4/12 + 14*w**3/3 + 423*w**2 - 2*w. Find c, given that t(c) = 0.
-14/13, 2
Let 0 - 24*z - 6*z**2 + 2/3*z**3 = 0. Calculate z.
-3, 0, 12
Let l(x) be the third derivative of x**5/180 + 13*x**4/9 - 1265*x**3/18 + 101*x**2 - 2*x - 2. Suppose l(y) = 0. What is y?
-115, 11
Factor 2673/2*y + 2187/2 - 3/2*y**5 - 9/2*y**4 + 567*y**2 + 81*y**3.
-3*(y - 9)*(y + 3)**4/2
Factor -336*m - 4 - 75481*m**3 - 72*m**2 + 4 + 75484*m**3.
3*m*(m - 28)*(m + 4)
Factor -655*l - 6675/2 + 5/2*l**2.
5*(l - 267)*(l + 5)/2
Let c(i) be the third derivative of -i**6/120 - 623*i**5/60 - 4030*i**4 + 16224*i**3 - 3*i**2 + 295*i - 2. Factor c(s).
-(s - 1)*(s + 312)**2
Let b(o) be the first derivative of -219 + 0*o + 2/7*o**3 + 0*o**2 - 3/28*o**4. Factor b(h).
-3*h**2*(h - 2)/7
Let q(w) be the second derivative of -3/4*w**2 + 1/80*w**5 - 1/24*w**3 + 1/8*w**4 - 269*w + 0. Factor q(t).
(t - 1)*(t + 1)*(t + 6)/4
Suppose -n - 2 = -2*d, 0 = 3*n + 481 - 493. Let i(z) be the first derivative of -12/7*z**2 + 36/7*z + 4/21*z**d + 17. Solve i(h) = 0 for h.
3
Let a(c) be the second derivative of 0 + 0*c**2 + 18/7*c**3 - 1/70*c**6 + 39/140*c**5 - 12/7*c**4 - 87*c. Determine g so that a(g) = 0.
0, 1, 6
Let v(x) = x**3 - x**2 - x. Let j(w) = -w**2 - 2*w - 1. Let m(h) = -5*h - 10. Let b(n) = 10*j(n) - m(n). Let k(u) = -b(u) - 5*v(u). Factor k(y).
-5*y*(y - 4)*(y + 1)
Let v(b) be the third derivative of 17/120*b**6 + 43*b**2 + 17/60*b**5 + b + 1/30*b**7 + 1/4*b**4 + 0 + 0*b**3 + 1/336*b**8. Factor v(z).
z*(z + 1)**2*(z + 2)*(z + 3)
Let h be 1/(924/88 + -10). Factor -4802*v - 2/3*v**3 - 98*v**h - 235298/3.
-2*(v + 49)**3/3
Let -1/3*r**3 + 0*r + 19/3*r**2 + 0 = 0. What is r?
0, 19
Let p(n) = -n**4 - n**3 - n + 1. Let y(c) = 18*c**2 + 24*c**4 - 18 - 57*c - 44*c**4 - 5*c + 30*c**3. Let b(i) = 6*p(i) - y(i)