 460. Let j(f) = -16*d(f) - 5*q(f). Suppose j(w) = 0. What is w?
-37, -1
Let v(p) = 4*p**2 + 96*p - 8. Let f(k) = 4*k**2 + 97*k - 6. Let r(m) = 4*f(m) - 3*v(m). Factor r(o).
4*o*(o + 25)
Suppose -10 = -3*x - 5*d + 20, -3*x - d + 18 = 0. Solve 8*i**4 - 12*i**3 - i**2 + 5*i**x - 7*i**3 + 7*i**2 = 0 for i.
-3, 0, 2/5, 1
Let m(n) = n**2 + 15*n + 25. Let c be m(-17). Suppose 0 = 60*k - c*k. Let -1/3*r**4 + k*r + 0*r**3 + 1/3*r**2 + 0 = 0. What is r?
-1, 0, 1
Let h(l) = l**3 - 4*l**2 - 22. Let j be h(5). Determine a, given that -10 + 50*a**j - 12*a + 18*a**2 - 3*a + 0*a + 27*a**2 = 0.
-1, -2/5, 1/2
Suppose -4*j = 6*f + 137 - 131, 6 = -2*j - 4*f. Suppose -2*l + 2*l**2 + 2/5*l**4 - 12/5 + 2*l**j = 0. Calculate l.
-3, -2, -1, 1
Let j(v) be the first derivative of -5 - 1/4*v**4 + 1/3*v**3 - v + 1/2*v**2. Factor j(n).
-(n - 1)**2*(n + 1)
Suppose 10*f + 15*f = 75. Let v(x) be the second derivative of 2/3*x**f + 2*x**2 - x + 0 - 2/3*x**4. What is w in v(w) = 0?
-1/2, 1
Let d = 98 + -90. Suppose -4*b = d*b. Factor 2/9*t + b - 2/9*t**3 + 0*t**2.
-2*t*(t - 1)*(t + 1)/9
Let r(i) = 2*i**4 - 9*i**3 - 88*i**2 + 11*i. Let g(q) = 3*q**4 - 8*q**3 - 87*q**2 + 12*q. Let h(n) = -7*g(n) + 6*r(n). Suppose h(t) = 0. What is t?
-3, 0, 2/9, 3
Let d(k) be the third derivative of 15*k**2 - 1/48*k**4 + 0 + 1/240*k**6 + 0*k + 0*k**5 - 1/24*k**3 + 1/840*k**7. Factor d(c).
(c - 1)*(c + 1)**3/4
Let 36*w**2 - w**3 - 13*w**3 + 3*w**4 + 12*w**2 - 9*w**3 - w**3 = 0. What is w?
0, 4
Let y(j) be the first derivative of -j**5 + 10*j**4 - 110*j**3/3 + 60*j**2 - 45*j + 591. Find f such that y(f) = 0.
1, 3
Let a be (1 + 6/(-8))/(370/592). Suppose -1/5*w**2 + 0*w + 0 + a*w**3 = 0. What is w?
0, 1/2
Let d(u) be the third derivative of -u**8/1344 - u**7/140 - 11*u**6/480 - u**5/40 - 146*u**2. Let d(b) = 0. What is b?
-3, -2, -1, 0
Suppose 2*b - 5*w - 27 = 0, 5*b + 0*w = -3*w + 21. Factor j**5 - 9*j**4 - 4*j**5 - 6*j**3 - 3*j**2 + 3*j**3 - b*j**3.
-3*j**2*(j + 1)**3
Let v be (-3 + 2 - 0) + 24. Suppose 2*j = v - 15. What is y in -3/5*y**j + 3/5*y**3 - 3/5*y + 3/5*y**2 + 0 = 0?
-1, 0, 1
Let r(c) be the second derivative of -11*c + 1/20*c**5 + 1/2*c**3 + 0*c**2 + 1/3*c**4 + 0. Solve r(m) = 0 for m.
-3, -1, 0
Solve -1/3*y**4 + 0*y**2 + 0 - 7*y**3 + 0*y = 0.
-21, 0
Solve 0 + 4/5*i + 2/5*i**2 = 0.
-2, 0
Factor 4/3*b**2 + 2/9*b**3 + 0 + 10/9*b.
2*b*(b + 1)*(b + 5)/9
Let u(o) be the first derivative of 2*o**3/15 - 7*o**2/5 - 12*o - 303. Factor u(s).
2*(s - 10)*(s + 3)/5
Factor 8/11*w**2 - 2/11*w**3 - 60/11 + 2*w.
-2*(w - 5)*(w - 2)*(w + 3)/11
Let x(n) be the second derivative of -n**4/3 - 2*n**3 + 8*n**2 - 38*n - 2. Suppose x(p) = 0. Calculate p.
-4, 1
Let i = 122 - 120. Let j be 12/(-8)*i*(-4)/8. Factor 3/2*h + j*h**2 + 0.
3*h*(h + 1)/2
Let u(k) be the second derivative of -4*k**7/315 - k**6/45 - k**5/60 + 7*k**4/4 + 3*k - 14. Let j(t) be the third derivative of u(t). Find d such that j(d) = 0.
-1/4
Let v(a) be the first derivative of -a**7/42 + 2*a**6/15 - 3*a**5/20 - a**4/3 + 2*a**3/3 + 7*a + 8. Let k(r) be the first derivative of v(r). Factor k(x).
-x*(x - 2)**2*(x - 1)*(x + 1)
Let t(b) be the first derivative of 2*b**6/3 + 4*b**5/5 - b**4 - 4*b**3/3 - 434. Let t(v) = 0. Calculate v.
-1, 0, 1
Let z(y) = y**2 - 4*y + 7. Let u be z(0). Suppose 15*n - 7*n = u*n. Find x, given that 2/3*x**2 - 1/3*x + 0*x**3 + n - 2/3*x**4 + 1/3*x**5 = 0.
-1, 0, 1
Let z be (-14)/(-49) + 4/(-14). Let l be z - -1 - (-24)/8. Factor -2 - 3 + 0*f**2 - f**2 - 2*f + l.
-(f + 1)**2
Let x be ((-8)/(-10))/(6/(-30)). Let u be (-1 + -3)/(x + 2). Suppose 8*r + 3*r**u - 16*r + 9*r = 0. Calculate r.
-1/3, 0
Let h(r) be the first derivative of -r**7/5040 - r**6/2160 - 22*r**3/3 - 7. Let p(f) be the third derivative of h(f). Factor p(w).
-w**2*(w + 1)/6
Factor 0 + 3/7*r**4 + 18/7*r**3 + 18/7*r + 33/7*r**2.
3*r*(r + 1)*(r + 2)*(r + 3)/7
Let s(t) be the first derivative of 1/4*t**4 + 0*t**5 + 0*t**2 - 1/30*t**6 + 2 + 1/3*t**3 + 6*t. Let z(r) be the first derivative of s(r). Factor z(u).
-u*(u - 2)*(u + 1)**2
Suppose -3*k + 4*i = 3, -2*k + 684*i + 3 = 683*i. Factor -4/3*h**4 + 8/3*h**2 - 8/3*h**k + 4/3*h - 4/3 + 4/3*h**5.
4*(h - 1)**3*(h + 1)**2/3
Solve 45/4*n + 3/4*n**2 + 39/2 = 0 for n.
-13, -2
Let r be ((-40)/(-160))/((-2)/(1 + -3)). Suppose -r*z**3 + 1/4*z + 0 - 1/4*z**4 + 1/4*z**2 = 0. What is z?
-1, 0, 1
Suppose -8068 - 18128 - 2*m**2 - 2909 + 336*m - 85137 + 620*m = 0. Calculate m.
239
Let -45*a + 2*a**5 - 6 - 2*a**4 - 4*a**5 - 70*a**2 + a**5 - 13*a**4 - 5 - 50*a**3 = 0. What is a?
-11, -1
Let m = -7310 - -29039/4. Let x = 51 + m. Factor 0*j**4 - 3/4*j + 3/2*j**3 + 0 + 0*j**2 - x*j**5.
-3*j*(j - 1)**2*(j + 1)**2/4
Suppose 0 = -85*j + 3546 - 146. Let 68/3*b + 32/3*b**4 - j*b**2 - 4 + 16*b**3 = 0. What is b?
-3, 1/2
Let w(n) be the first derivative of n**5/2 + 125*n**4/8 - 5*n**3/6 - 125*n**2/4 - 651. Determine b so that w(b) = 0.
-25, -1, 0, 1
Let i(g) be the first derivative of 2*g**6/5 - 9*g**5/5 + 3*g**4 - 2*g**3 + 3*g/5 - 88. Factor i(v).
3*(v - 1)**4*(4*v + 1)/5
Let h be ((-7)/(-10))/((-954)/(-2385)). Let h*d - 1/4*d**2 + 0 = 0. Calculate d.
0, 7
Let d = 5847 - 5844. Suppose -25/2*j + 5/2*j**4 - 3/2*j**d - 3 - 27/2*j**2 = 0. What is j?
-1, -2/5, 3
Let n be ((-408)/60 + 5)*(-1080)/228. Factor 0*g**2 - n + 108/19*g - 12/19*g**3 + 2/19*g**4.
2*(g - 3)**3*(g + 3)/19
Suppose 5*x - 80 = -35. Suppose 14*q - 20 = x*q. Factor -4/3*f**5 - 8/3*f - 12*f**3 - 28/3*f**2 + 0 - 20/3*f**q.
-4*f*(f + 1)**3*(f + 2)/3
Let n(i) be the second derivative of i**7/840 + i**6/96 + i**5/30 + i**4/24 - 25*i**2/2 - 41*i. Let a(j) be the first derivative of n(j). Factor a(t).
t*(t + 1)*(t + 2)**2/4
Suppose -13692 = 3*x - 13701. Find q, given that 2*q**4 + 1/3*q - 3*q**5 + 0 - 2*q**2 + 8/3*q**x = 0.
-1, 0, 1/3, 1
Let n(u) be the third derivative of 1/1440*u**6 + 1/480*u**5 - 5/6*u**3 + 10*u**2 + 0*u - 1/48*u**4 + 0. Let s(b) be the first derivative of n(b). Factor s(l).
(l - 1)*(l + 2)/4
Let g(f) be the second derivative of f**6/45 - 5*f**4/18 + 4*f**2/3 - 15*f. Suppose g(s) = 0. Calculate s.
-2, -1, 1, 2
Let p be -1*(-6)/(-10) - (-2315)/225. Let r = p - -44/45. Find s, given that -2/3*s**2 - r + 16/3*s = 0.
4
Let j(d) be the first derivative of 3/2*d**2 + 4*d**3 - 6*d - 9/4*d**4 + 14. Suppose j(m) = 0. Calculate m.
-2/3, 1
Let c(p) be the third derivative of p**5/420 - 109*p**4/84 + 11881*p**3/42 + 213*p**2. What is l in c(l) = 0?
109
Let c(k) = -k**2 - 40*k - 274. Let q be c(-31). Suppose 0 + 1/9*v**q + 16/9*v**2 - 4/3*v**3 + 0*v**4 + 0*v = 0. What is v?
-4, 0, 2
Let w be (15/(-24))/((-570)/80 + 7). Let n(z) be the first derivative of 0*z**3 + 0*z**2 + 0*z + 2/85*z**w - 1/34*z**4 - 8. Factor n(i).
2*i**3*(i - 1)/17
Let s(n) be the third derivative of -n**5/510 + n**4/102 + n**3/17 + 93*n**2. Determine p, given that s(p) = 0.
-1, 3
Let y = 562 + -559. Factor -1/2*h + 1/2*h**4 - 1/2*h**5 - h**2 + 1/2 + h**y.
-(h - 1)**3*(h + 1)**2/2
Let g = -1361 - -1364. Let j(w) be the first derivative of 16*w - 56*w**2 + 2 + 196/3*w**g. Factor j(t).
4*(7*t - 2)**2
Let f be 210/2*(-3)/(-5) + -5. Let p be f/18 - (-3 - (-24)/4). Factor 2/9*o + p*o**2 + 0.
2*o*(o + 1)/9
Let c = 436 - 436. Let j(n) be the second derivative of c*n**2 + 1/6*n**3 + 3*n + 1/12*n**4 + 0. Factor j(r).
r*(r + 1)
Let g(t) be the first derivative of 3*t**5/5 - 3*t**4/4 - 2*t**3 - 31. Determine n so that g(n) = 0.
-1, 0, 2
Determine g, given that 0*g**2 - 3/7*g**3 + 0*g**4 + 3/7*g**5 + 0*g + 0 = 0.
-1, 0, 1
Let x = 2814 - 2814. Let -2/5*o**3 + 0 + 4/5*o**4 + x*o + 0*o**2 = 0. What is o?
0, 1/2
Let h(v) be the third derivative of -v**6/100 + 113*v**5/75 - 5*v**4/4 - 763*v**2. Determine i so that h(i) = 0.
0, 1/3, 75
Solve 0*d - 2/5*d**4 - 2/5*d**3 + 0*d**2 + 0 = 0 for d.
-1, 0
Factor 111/5 + 113/5*b**2 - 223/5*b - 1/5*b**3.
-(b - 111)*(b - 1)**2/5
Let a(l) be the third derivative of l**8/10080 + 2*l**7/2835 - l**6/810 - 3*l**5/4 + 7*l**2. Let v(x) be the third derivative of a(x). Factor v(z).
2*(z + 2)*(9*z - 2)/9
Let v = -20795 - -20798. Suppose 20/7*y**v + 1476/7*y - 648/7 + 352/7*y**2 = 0. What is y?
-9, 2/5
Let j = 5 - 3. Suppose 2*y = g + 11, 0*y - 3*g - 18 = -y. Factor -2 + 0*r + y*r**2 + j - 3*r.
3*r*(r - 1)
Let b(w) be the second derivative of -25/3*w**3 - 3/2*w**5 - 25*w - 5*w**4 - 15/2*w**2