+ 6*t(b). What is i in j(i) = 0?
207
Let d(j) be the second derivative of -j**4/6 - 5*j**3/3 + 14*j**2 - 2*j + 15. Factor d(i).
-2*(i - 2)*(i + 7)
Let n(l) be the first derivative of -l**3/6 + 211*l**2/2 - 44521*l/2 + 133. What is r in n(r) = 0?
211
Suppose -4*k - 21 = -m, 0*k + 5*k = m - 25. Let u(i) be the first derivative of 3*i**2 - 3/2*i**4 + 2/5*i**m - 4*i + 2/3*i**3 - 15. Factor u(q).
2*(q - 2)*(q - 1)**2*(q + 1)
Let y(w) be the second derivative of -1/4*w**4 + 17*w**3 - 867/2*w**2 + 7*w + 0. Suppose y(p) = 0. What is p?
17
Let i(j) be the first derivative of j**4/30 - 112*j**3/45 + 884*j**2/15 - 5408*j/15 + 1736. Factor i(m).
2*(m - 26)**2*(m - 4)/15
Let m be (-74 + 85)*(-4)/(-22). Suppose 0 = 2*b - 4*c + 2, -5 = 4*b + 4*c - 25. Factor 2/3 + 1/3*a**b + 5/3*a + 4/3*a**m.
(a + 1)**2*(a + 2)/3
Solve 0*g + 81/8*g**2 + 0 - 1/8*g**3 = 0 for g.
0, 81
Let s(u) be the third derivative of -2 + 455/3*u**4 + 0*u + 1/24*u**6 + 3*u**2 + 53/12*u**5 + 1690/3*u**3. Let s(l) = 0. Calculate l.
-26, -1
Suppose 2*u - 4 = 3*d - 4*d, -u + 5 = d. Let y(k) be the first derivative of -1/5*k**5 + 0*k + 3/4*k**4 - k**2 - 1/6*k**d + 20 + 1/3*k**3. Solve y(g) = 0.
-2, -1, 0, 1
Suppose 0 = -16*n - 1 + 17. Let f be ((-3)/(-12))/(n/12). Factor 5*v**f - v**3 - 28*v**2 + 40*v**2.
4*v**2*(v + 3)
Let h(z) = -2*z + 6. Let y(m) = -m**2 + 20*m - 35. Let t be y(18). Let g be h(t). Factor 13*r**3 + 15*r**2 - 8*r**3 - 10 - 5*r**g - 10*r**3 + 5*r.
-5*(r - 1)**2*(r + 1)*(r + 2)
Suppose i = -3*c + 5*i + 18, 6 = -3*c - 4*i. Suppose -5*j + c = t, 4 = 2*t + j - 0. Factor -10*z**2 + 0*z**4 + 3*z**t - z**4 + 3*z**3 + z + 4*z**2.
-z*(z - 1)**3
Let o(d) be the second derivative of -d**7/504 - d**6/6 - 6*d**5 - 13*d**4/12 + d**2 - 41*d. Let u(f) be the third derivative of o(f). Factor u(w).
-5*(w + 12)**2
Solve -225 + 496*x - 388*x**3 + 161 + 2*x**5 + 65*x**4 - 32*x**5 - 72*x**2 + 149*x**4 = 0 for x.
-1, 2/15, 2, 4
Let b = -488 - -496. Suppose 5 = 5*f + 4*o + 6, o - b = -4*f. Suppose 4*s**4 - 8/3*s + 4/3*s**5 + 4/3*s**f - 4*s**2 + 0 = 0. What is s?
-2, -1, 0, 1
Let g(x) be the third derivative of -x**7/42 - 737*x**6/24 - 733*x**5/2 - 10975*x**4/6 - 14620*x**3/3 - 4*x**2 + x - 307. Solve g(m) = 0 for m.
-731, -2
Solve 0*q + 10*q**2 + 0 + 118/9*q**4 + 14/9*q**5 + 86/3*q**3 = 0 for q.
-5, -3, -3/7, 0
Let d be ((-2)/(-16))/(1317/21072). Factor -d*i**2 - 14/5 - 26/5*i + 2/5*i**3.
2*(i - 7)*(i + 1)**2/5
Suppose j - 14 = -2*j + 4*u, -4 = j + 3*u. Suppose -j*h + 1 = -7. Factor k**4 + 4*k**3 - 4*k**4 + 16*k**5 + 4*k**h - 21*k**4.
4*k**3*(k - 1)*(4*k - 1)
Determine u, given that 2*u**3 + 3876*u**2 - 6*u**3 - 1291851 - 937020*u + 350951 = 0.
-1, 485
Let r(m) be the first derivative of m**4/6 + 224*m**3/9 + 839*m**2/3 + 1456*m/3 - 8722. Let r(q) = 0. Calculate q.
-104, -7, -1
Let x(n) be the first derivative of -2*n**3/15 - 67*n**2/5 + 136*n/5 + 898. Suppose x(a) = 0. Calculate a.
-68, 1
Determine h so that 204/5*h + 16 - 198/5*h**3 - 26*h**4 + 10*h**2 - 6/5*h**5 = 0.
-20, -1, -2/3, 1
Let v(u) be the second derivative of -11*u**6/75 + 6*u**5/25 - u**4/30 - 5560*u. Let v(c) = 0. Calculate c.
0, 1/11, 1
Factor -15*b**3 + 5*b**5 + 1267*b**2 + 20*b - 10*b**4 + 1332*b**2 - 2579*b**2.
5*b*(b - 2)**2*(b + 1)**2
Suppose -4*u + 82 = -t, 4*t + 86 = 4*u + t. Suppose -24*h**4 + 4*h**5 + 1588*h**2 - 1588*h**2 + u*h**3 = 0. What is h?
0, 1, 5
Let j(t) be the first derivative of -4*t**3/3 + 272*t**2 - 540*t - 3547. Suppose j(q) = 0. What is q?
1, 135
Let p(x) = -x**4 - x**3 + 2*x**2 - 1. Let r(g) = -10*g**4 + 15 - 30 - 23*g**3 - 22*g**3 - 105*g**2 + 0. Let d(a) = 15*p(a) - r(a). Factor d(s).
-5*s**2*(s - 9)*(s + 3)
Suppose -4 = -2*h + 4. Suppose -h*w - 10 = -50. Factor -9*r**2 - 25 - 3*r**2 + 11*r**2 - w*r.
-(r + 5)**2
Let r(u) be the third derivative of -u**6/180 - u**5/15 + 15*u**4/4 + 108*u**3 - 3*u**2 + 8*u - 26. Determine f so that r(f) = 0.
-9, 12
Let k be (-6)/2 + (-3399)/(-1030). Let m(c) be the second derivative of 0*c**2 + 10*c - 3/50*c**6 + k*c**5 + 0 + 9/20*c**4 - 2/5*c**3. Let m(u) = 0. What is u?
-1, 0, 1/3, 4
Let u(f) be the first derivative of -27*f**6/2 - 162*f**5/5 + 405*f**4/4 + 166*f**3 + 6*f**2 - 72*f + 997. Solve u(y) = 0 for y.
-3, -2/3, 1/3, 2
Let d(t) be the third derivative of t**7/245 - 3*t**6/70 + t**5/14 - 162*t**2 - t. Suppose d(x) = 0. What is x?
0, 1, 5
Let h(a) be the third derivative of a**8/21 + 37*a**7/105 + 3*a**6/20 - 49*a**5/30 - 17*a**4/12 + 4*a**3 - 9776*a**2. Let h(x) = 0. What is x?
-4, -1, 3/8, 1
Let p = 257986/3 - 85995. Factor -o**2 - p*o**3 + 8/3 + 2*o.
-(o - 2)*(o + 1)*(o + 4)/3
Let x = 1538349/7 + -219764. Factor -4 - x*a**3 - 32/7*a - 11/7*a**2.
-(a + 2)**2*(a + 7)/7
Let l(v) be the third derivative of -v**7/1848 + 19*v**6/1980 - 7*v**5/330 + 259*v**4/24 - 16*v**2 - 1. Let r(h) be the second derivative of l(h). Factor r(t).
-(3*t - 14)*(5*t - 2)/11
Suppose -7*p - 23*p = -60. Suppose 0*s**p - 3*s**2 - 8*s**2 + 330*s + 6*s**2 + 0*s**2 - 5445 = 0. Calculate s.
33
Let d(k) be the third derivative of k**7/210 - 13*k**6/60 - 151*k**5/60 - 31*k**4/6 - 1618*k**2. Factor d(a).
a*(a - 31)*(a + 1)*(a + 4)
Let x = 42212/7 - 6030. Let v(u) be the first derivative of 1/28*u**4 + 0*u + 6 - x*u**3 + 9/14*u**2. What is b in v(b) = 0?
0, 3
Let v(u) be the second derivative of u**6/105 - u**5/14 + 4*u**4/21 - 4*u**3/21 - 117*u. Factor v(t).
2*t*(t - 2)**2*(t - 1)/7
Let u be (195/(-13))/5 + 6. Let f(m) be the first derivative of -140*m**2 + 80*m - 1 + 245/3*m**u. What is a in f(a) = 0?
4/7
Let m be (2/4)/((-6)/(-72)). Suppose 4*v + 2*r = 3*r + 9, 0 = -2*r + m. Let -v*t**2 + 2*t - 2*t**2 + 4 + 87*t**3 + t**2 - 89*t**3 = 0. What is t?
-2, -1, 1
Let p(u) be the second derivative of u**6/30 + 8*u**5/15 - 22*u**4/3 + 32*u**3 - 11*u**2 - 206*u. Let i(f) be the first derivative of p(f). Factor i(k).
4*(k - 2)**2*(k + 12)
Let z(d) = -10*d**2 - 2608*d - 4980. Let g(k) = -55*k**2 - 14780*k - 28220. Let t(q) = 7*g(q) - 40*z(q). Factor t(c).
5*(c + 2)*(3*c + 166)
Let i(q) = 36*q**2 - 8*q + 27. Let w be i(3). Suppose 5*p**5 - 8*p**3 - 10*p**4 + 337 - 2*p**3 + 40*p**2 - 35*p - w = 0. What is p?
-2, 1
Factor 855*v**4 + 847*v**4 - 36*v + 36*v**3 - 1700*v**4 - 2*v**2.
2*v*(v - 1)*(v + 1)*(v + 18)
Factor -4*r + 633*r + 1104 + 2*r**2 - 475*r.
2*(r + 8)*(r + 69)
Let m(n) be the second derivative of n**4/60 - 15*n**3/2 - 693*n**2/5 + 3049*n. Let m(r) = 0. What is r?
-6, 231
Let a(c) = 3*c**4 - 2*c**3 + 7*c**2 + 7*c + 21. Let g = -286 + 284. Let s(z) = -z**4 - z**2 - z - 3. Let q(y) = g*a(y) - 14*s(y). Factor q(p).
4*p**3*(2*p + 1)
Let q(o) be the first derivative of 15*o**4/4 + 625*o**3/3 + 305*o**2 - 4495. Find f such that q(f) = 0.
-122/3, -1, 0
Let b = -6255 - -56297/9. Factor b*g**4 - 22/9*g**2 + 200/9 - 40/3*g + 4/3*g**3.
2*(g - 2)**2*(g + 5)**2/9
Let l(j) be the first derivative of 1/240*j**6 + 0*j**2 - 7/3*j**3 - 1/80*j**5 + 0*j - 16 - 1/8*j**4. Let i(a) be the third derivative of l(a). Factor i(g).
3*(g - 2)*(g + 1)/2
Let d(c) = c. Let w(t) = -19. Let o(r) = -3*d(r) + w(r). Let j be o(-8). Suppose -3*l**3 + 3 + 9*l**4 - 15*l**2 + j*l + 3 - 2*l + 0*l = 0. What is l?
-1, -2/3, 1
Let f(a) = 16*a**5 + a**4 - 5*a**3 + 2*a - 2. Let r(t) = -2*t**5 + 2*t**3 - t + 1. Let b(w) = -3*f(w) - 6*r(w). Determine j so that b(j) = 0.
-1/3, 0, 1/4
Let x(z) = z**2 - 4*z. Let h be x(4). Let c be 0/(84/(-21) + -1 + 1). Find o such that 1/4*o**3 - 1/2*o**2 + c*o + 1/4*o**4 + h = 0.
-2, 0, 1
Let i be (-416)/14 - (-20)/(-70). Let d be 5/(-10)*i*(-2)/(-3). Find s such that s + 4*s + d*s + 3*s**2 = 0.
-5, 0
Let o(c) be the second derivative of c**6/90 + 3*c**5/20 - 11*c**4/36 - c**3/2 + 5*c**2/3 - 1809*c. Factor o(r).
(r - 1)**2*(r + 1)*(r + 10)/3
Let a(c) be the first derivative of 99/10*c**2 - 121/5*c + 7/5*c**3 - 84 + 1/20*c**4. Factor a(t).
(t - 1)*(t + 11)**2/5
Let q(v) be the second derivative of -8/9*v**3 + 7/36*v**4 - 1/120*v**5 + 0 - 32/3*v**2 + 47*v. Find b, given that q(b) = 0.
-2, 8
Let g be -9*1*(-4 - 11). Let s = g + -130. Factor 6*q**4 + 20 - 20 - 2*q**s.
-2*q**4*(q - 3)
Let m(f) be the third derivative of f**8/5880 + f**7/735 + f**6/420 - 61*f**3/3 + 19*f**2 - f. Let z(j) be the first derivative of m(j). Factor z(u).
2*u**2*(u + 1)*(u + 3)/7
Let f(c) = -13*c**2 + c + 29. Let y(m) = 72*m**2 - 4*m - 160. L