*l**4/36 - 16*l**3/3 - l + 116. Let g(a) be the third derivative of v(a). Factor g(k).
-(k + 1)*(k + 20)/6
Let k(w) = -w**3 - 3*w**2 + 6*w + 33. Let n be k(-4). Factor n*q + 12*q**2 + 3*q**2 - 4 + q**3 - 2 - q**2 + 18.
(q + 1)**2*(q + 12)
Let o(q) = -q**2 - 8*q - 14. Let l be o(-4). Factor -s**l + 49 - 49.
-s**2
Let w(m) = -10*m + 140 - 13*m - 135 + 159 + 208. Let s be w(16). Let -92/5*g**3 - 52/5*g**2 + 0 - 8/5*g - 12/5*g**s + 36/5*g**5 = 0. What is g?
-1, -1/3, 0, 2
Let 0 + 3/4*c**3 + 0*c - 1/8*c**4 - 5/8*c**2 = 0. Calculate c.
0, 1, 5
Factor 752*x**2 + 7*x**3 + 9121*x - 3*x**3 - 3531*x + 135424 + 31210*x.
4*(x + 4)*(x + 92)**2
Let m(s) = 369*s - 736. Let z be m(2). Let n(k) be the first derivative of 23 - 2/3*k**z + 2/3*k + 2/9*k**3. Solve n(l) = 0 for l.
1
Let g(l) = -9*l - 665. Let i be g(-76). Let t(x) be the third derivative of 0 - i*x**2 - 1/18*x**5 + 0*x**4 + 0*x**3 + 0*x + 1/180*x**6. Solve t(m) = 0.
0, 5
Let t(p) be the second derivative of -p**6/45 + 7*p**5/30 - p**4/3 - 32*p**3/9 + 32*p**2/3 + 10*p + 265. Suppose t(s) = 0. What is s?
-2, 1, 4
Let n(h) be the first derivative of -121 - 4*h + 1/3*h**3 + 3/2*h**2. Factor n(y).
(y - 1)*(y + 4)
Let v(b) = -15*b**4 - 85*b**3 - 110*b**2 + 210*b + 5. Let h(g) = -7*g**4 - 43*g**3 - 55*g**2 + 105*g + 2. Let a(o) = -5*h(o) + 2*v(o). Factor a(q).
5*q*(q - 1)*(q + 3)*(q + 7)
Let t(f) be the first derivative of 1/21*f**6 + 4/21*f**3 + 12/7*f**2 - 36 - 1/2*f**4 + 0*f**5 - 16/7*f. Suppose t(m) = 0. Calculate m.
-2, 1, 2
Let k(s) be the second derivative of s**5/20 - 15*s**4 - 12*s + 5. Factor k(h).
h**2*(h - 180)
Let i(z) be the first derivative of -z**5/25 + 3*z**4/5 + 91*z**3/15 - 51*z**2/5 + 244. Factor i(h).
-h*(h - 17)*(h - 1)*(h + 6)/5
Let m(w) be the third derivative of -w**7/525 - 14*w**6/75 + 118*w**5/75 - 4*w**4 - 27*w**2 - w. Factor m(f).
-2*f*(f - 2)**2*(f + 60)/5
Let t = -3462 + 3462. Let r(o) be the second derivative of 0*o**2 + 10*o + 0*o**4 + t - 1/35*o**5 + 2/21*o**3. Factor r(w).
-4*w*(w - 1)*(w + 1)/7
Suppose 132 - 38 = -1807*w + 1886*w - 64. Factor 1/4*h**3 - 3/2*h**2 + 0 + w*h.
h*(h - 4)*(h - 2)/4
Let a(n) be the third derivative of -24389/12*n**4 + 0 - 1/420*n**7 - 707281/12*n**3 - 841/20*n**5 + 52*n**2 + 0*n - 29/60*n**6. Let a(i) = 0. What is i?
-29
Let b be 1035/105 - -4 - 11. Let x(k) be the first derivative of -8/7*k - 46/21*k**3 + b*k**2 + 1/2*k**4 + 32. Factor x(i).
2*(i - 2)*(i - 1)*(7*i - 2)/7
Let a(l) = 40*l**2 - 38*l - 2. Let f be a(1). Factor -2/5*n**4 + f*n + 4/5*n**3 + 0 - 2/5*n**2.
-2*n**2*(n - 1)**2/5
Let l = 624 + -541. Suppose -34*r + 19 = -l. Determine n so that 10/3*n**5 + 4/3*n**2 - 4/3*n**4 + 0*n - 10/3*n**r + 0 = 0.
-1, 0, 2/5, 1
Let t(a) be the third derivative of a**6/40 - 199*a**5/20 - 205*a**4 - 1656*a**3 - 164*a**2 + 13*a. Factor t(p).
3*(p - 207)*(p + 4)**2
Let o be (-12)/27*(-18)/4. Solve -343*b - 135*b**o - 15 + 145*b**3 + 53*b + 155 + 145*b - 5*b**4 = 0 for b.
-1, 1, 28
Determine t so that -222*t**3 + 306 - 13*t**3 + 100*t**3 - 885*t + 6*t**4 + 612*t**2 = 0.
1/2, 2, 3, 17
Let y(s) = -2*s**2 + 5513*s - 1501520. Let b(l) = 7*l**2 - 16528*l + 4504560. Let h(m) = -3*b(m) - 8*y(m). Determine c so that h(c) = 0.
548
Suppose -143*l - 185*l - 7 = -7. Let l + 26/3*i**2 + 4*i**3 + 4/3*i = 0. Calculate i.
-2, -1/6, 0
Let u(i) be the first derivative of i**4 - 144*i**3 + 1798*i**2 - 3168*i - 6481. Factor u(p).
4*(p - 99)*(p - 8)*(p - 1)
Let k(z) be the third derivative of -1 + 0*z - 1/40*z**6 + 3/4*z**4 + 1/20*z**5 + 0*z**3 - 39*z**2. What is s in k(s) = 0?
-2, 0, 3
Let v(b) be the third derivative of b**6/30 - 151*b**5/15 + 299*b**4/6 - 298*b**3/3 + 267*b**2 + 11. Factor v(u).
4*(u - 149)*(u - 1)**2
Let s be ((-23)/18)/((-195)/585). Let w(d) be the first derivative of -5*d**2 - 7/8*d**4 - 13 + s*d**3 + 2*d. Suppose w(z) = 0. What is z?
2/7, 1, 2
Let o be (-62 + 1251)*(-2)/(-6). Let u = o + -393. Factor -5/2*d + u - 5/6*d**2.
-5*(d - 1)*(d + 4)/6
Suppose 0 = l + l + b - 169, -l + 82 = -2*b. Let t be (9/l)/(258/48 - 5). What is j in -20/7*j + 50/7 + t*j**2 = 0?
5
Determine g so that g**5 - 15*g**4 + 15676*g**3 - 15609*g**3 + 300 - 59*g - 261*g - 33*g**2 = 0.
-2, 1, 5, 6
Let f = 6385 - 6383. Let g be -3 - (-2 - 6/36*6). What is c in -1/5*c**5 + 0*c**f - 1/5*c + 2/5*c**3 + 0 + g*c**4 = 0?
-1, 0, 1
Solve 231*t - 588 + 3/4*t**3 - 24*t**2 = 0.
4, 14
Factor 0*b**2 + 0*b - 4/3*b**5 + 76/3*b**3 + 0 - 24*b**4.
-4*b**3*(b - 1)*(b + 19)/3
Let v be 2 + (-60)/(20/(-4)). Suppose 2*l = -3*l - 2*s + 64, 5*l + s = 62. Find i, given that -6*i**2 - v*i + 13*i + l + 22*i = 0.
-1/2, 4
Let g(r) be the second derivative of r**7/28 + 11*r**6/60 + 11*r**5/40 + r**4/24 - r**3/6 + 6*r + 58. Find d such that g(d) = 0.
-2, -1, 0, 1/3
Find m, given that 142/5*m - 8/5*m**2 - 102/5 = 0.
3/4, 17
Let u be ((1 - (-10)/12)*(-16356)/(-957))/(5 - 4). Determine r so that -24*r**4 + u*r + 4 - 32/3*r**5 + 136/3*r**3 + 74*r**2 = 0.
-3, -1/2, -1/4, 2
Let t be (17 + -15)*32/2. Factor -16*y - 3*y**2 + 14*y**2 - 4*y**2 + t - 5*y**2.
2*(y - 4)**2
Let c be -12 + 8/(2 - 3). Let l be (-42)/(-18) + c*(-2)/24. Suppose 0 + 1/4*m**5 + 0*m - 1/4*m**3 + 3/4*m**l - 3/4*m**2 = 0. Calculate m.
-3, -1, 0, 1
Let v(a) = -10*a**3 - 192*a**2 + 5778*a - 59576. Let s = -150 - -152. Let c(l) = 2*l**3 + l**2 - 2*l - 1. Let h(o) = s*v(o) + 12*c(o). Factor h(j).
4*(j - 31)**3
Factor 39/7*i - 1/7*i**2 - 38/7.
-(i - 38)*(i - 1)/7
Let u be (-32)/3*((-120)/(-16))/(-5). What is g in -23*g**2 + 20 - 37 + 71*g**2 - 308*g + 409 - 4*g**3 + u*g**2 = 0?
2, 7
Suppose -793*d + 18*i - 7*i - 78 = -798*d, -2*i = -6. Solve -18 + 3/2*x**2 + 1/12*x**4 + d*x - 11/12*x**3 = 0 for x.
-3, 2, 6
Let p(f) = -f**3 - 11*f**2 - 59*f + 49. Let d(c) = -c**2 - 24 + 7*c**2 + 29*c + 46*c**3 - 45*c**3. Let n(v) = 11*d(v) + 6*p(v). Factor n(l).
5*(l - 2)*(l - 1)*(l + 3)
Let r = 42 - 38. Suppose x + 3*k = -0*k + 18, -r*x - 13 = -5*k. Factor -4*m + x*m**2 - m + 3*m + 5*m.
3*m*(m + 1)
Let m be (-136)/(-884)*(16 - 3). Let f(u) be the first derivative of -1/24*u**6 + 0*u**5 + 0*u**3 + 0*u + 1/8*u**4 + 2 - 1/8*u**m. Factor f(i).
-i*(i - 1)**2*(i + 1)**2/4
Let 27*b**2 + 46*b**2 + 9*b**2 - 41 + 49 + 164*b - 2*b**2 = 0. What is b?
-2, -1/20
Suppose o - q + 53 = 0, -4*o + q - 1 = 205. Let c = o + 103/2. Factor 0*t**4 + c*t**2 - 1/2 - 3/4*t + t**3 - 1/4*t**5.
-(t - 2)*(t - 1)*(t + 1)**3/4
Let a(q) be the first derivative of q**5/20 + q**4/8 - q**3/12 - q**2/4 - 4419. Find d such that a(d) = 0.
-2, -1, 0, 1
Let f(d) be the first derivative of 125*d**4/4 - 950*d**3/3 - 395*d**2/2 - 40*d + 3. Determine w so that f(w) = 0.
-1/5, 8
Let u(q) be the second derivative of -27*q**2 + 92*q - 1/6*q**4 + 0 - 28/3*q**3. Factor u(s).
-2*(s + 1)*(s + 27)
Let s = 4090 - 4049. Let i(h) be the second derivative of -s*h + 0*h**2 + 0 + 5/3*h**4 - 25/6*h**3. Let i(c) = 0. Calculate c.
0, 5/4
Let d(i) be the third derivative of i**9/3780 + i**8/1680 - i**7/315 + 31*i**4/12 + 3*i**2 + 5. Let g(o) be the second derivative of d(o). Factor g(a).
4*a**2*(a - 1)*(a + 2)
Factor -2/5*a**4 + 16/5*a**2 + 0*a - 4/5*a**3 + 0.
-2*a**2*(a - 2)*(a + 4)/5
Let w(y) = 37*y - 367. Let g be w(10). Suppose 340 + 5*z**3 + 20241*z + 105*z**2 - 19881*z + 0*z**g + 0*z**3 = 0. What is z?
-17, -2
Let g be (-1945)/(-45) - (87/27 - 3). Factor 47 + g + 45*a + 10 + 30*a**2 - 25*a**2.
5*(a + 4)*(a + 5)
Let h be ((-12)/28)/((-963)/749). Factor -h*u + 4 - 13/3*u**2.
-(u + 1)*(13*u - 12)/3
Let q(l) be the second derivative of -l**5/15 - l**4 + 14*l**3/3 - 22*l**2/3 - 418*l - 2. Factor q(n).
-4*(n - 1)**2*(n + 11)/3
Factor 0 + 42/13*j - 20/13*j**2 + 2/13*j**3.
2*j*(j - 7)*(j - 3)/13
Let i(w) be the first derivative of -2*w**3/9 - 764*w**2/9 + 1534*w/9 + 4401. Determine c so that i(c) = 0.
-767/3, 1
Let o = 32556/27055 + -18/5411. Suppose 0 - o*m**2 + 1/5*m**3 + m = 0. Calculate m.
0, 1, 5
Suppose 2*x + 4 = 4*r, 5*r = -10*x + 5*x + 5. Determine c, given that x + 6*c**3 + 4/3*c - 10/3*c**4 + 2/3*c**5 - 14/3*c**2 = 0.
0, 1, 2
Let x(h) be the third derivative of h**6/160 + 37*h**5/480 - h**4/192 - 7*h**3/8 + 1504*h**2. Factor x(q).
(q - 1)*(q + 6)*(6*q + 7)/8
Let g = 26 + -29. Let m be g - 5*(-3)/(5 - 2). What is k in 3*k**2 - 16*k**m + 18*k**2 + 5*k**3 = 0?
-1, 0
Let h(g) = -2*g - 6. Let z be h(-4). Let q be (10057/(-2034) - (