. Calculate n.
-7, -3, -2, 1, 3
Let y(s) be the first derivative of s**4/48 + s**3/8 - 9*s**2/4 - 71*s - 24. Let z(q) be the first derivative of y(q). Factor z(r).
(r - 3)*(r + 6)/4
Suppose 502*r - 58*r - 8 = -22 + 14. Let -2/9 - 4/9*j + 4/9*j**3 + r*j**2 + 2/9*j**4 = 0. Calculate j.
-1, 1
Factor -264 + 1563/7*x + 282/7*x**2 + 3/7*x**3.
3*(x - 1)*(x + 7)*(x + 88)/7
Let u = 494 + -251448/509. Let r = u + 517/2036. Factor r*t**2 - 5/2*t + 25/4.
(t - 5)**2/4
Let z(m) = m**3 + m**2 + 1. Let b(h) = -18*h - 26*h**2 + 8*h**3 + 23 + 25*h**2 - 13*h**3 + 46*h. Let a(j) = b(j) + z(j). What is q in a(q) = 0?
-2, -1, 3
Suppose -199 + 319 = 60*p. Let k(v) be the first derivative of -11 - 1/2*v**3 + 6*v + 9/4*v**p. Factor k(g).
-3*(g - 4)*(g + 1)/2
Let f = -445 + 495. Solve 9*i**2 - 14*i**2 - 55 - f*i + 10*i**2 = 0.
-1, 11
Determine r, given that 65*r**4 - 16*r**3 - 41*r**3 + 6*r**5 + 5*r - r**5 + 65*r - 18*r**3 - 65*r**2 = 0.
-14, -1, 0, 1
Suppose 5*p - 41 = -31. Suppose -p*l = l + 4*a - 46, -24 = -2*l - a. Determine m, given that -18*m**2 + l*m**2 - 3*m + 13*m**2 - 4 - 5*m = 0.
-2/5, 2
Let v(i) be the third derivative of -3/14*i**3 + 1 + 0*i + 17/168*i**4 + 1/210*i**5 - i**2. Solve v(d) = 0 for d.
-9, 1/2
Let b = -368 + 368. Factor b*j**2 + 16 - 20*j - 25*j + 19 - 3*j**2 + 67.
-3*(j - 2)*(j + 17)
Let z(d) = d + 1. Suppose 114*j - 122*j = -8. Let m(b) = -12*b - b**2 + 3*b**2 + 9 + 1. Let c(a) = j*m(a) + 2*z(a). Suppose c(g) = 0. What is g?
2, 3
Let p be -7*(4 + -2 - 5). Suppose 3*f + 6 = 0, p*f = -u + 19*f - 2. Let -2/9*h**3 - 2 - 2/3*h + 10/9*h**u = 0. Calculate h.
-1, 3
Let -1/7*z**2 + 4/7*z - 4/7 = 0. What is z?
2
Let g(k) be the first derivative of 0*k**3 + 6 - k**5 + 0*k**4 + 0*k + 0*k**2 - 5/6*k**6. Factor g(u).
-5*u**4*(u + 1)
Suppose -5*b - g = -0*b - 178, 0 = -3*b + 5*g + 90. Suppose 20 = -4*y, b = -7*u + 12*u - 4*y. Factor -5*w**2 - 1/2*w**u - 16 - 16*w.
-(w + 2)*(w + 4)**2/2
Let c(b) = -b**4 + 14*b**3 + 57*b**2 + 30*b + 4. Let y(f) = 2*f**2 - f + 1. Let q(p) = -c(p) + 4*y(p). Factor q(h).
h*(h - 17)*(h + 1)*(h + 2)
Let z(v) be the first derivative of -2/5*v**3 - 1/10*v**6 + 34 + 3/20*v**4 + 6/25*v**5 + 0*v**2 + 0*v. Determine n so that z(n) = 0.
-1, 0, 1, 2
Let n be (12/20 - 2 - 4/(-10))/((-4)/80). Suppose 2/5*t**2 - 102/5 + n*t = 0. Calculate t.
-51, 1
Let x be 18 + -5*(-114)/(-19) + -1 + 15. Solve -2/5*f**5 + 0 - 448/5*f**3 - 512/5*f**x + 62/5*f**4 + 0*f = 0 for f.
-1, 0, 16
Let p(c) be the second derivative of c**7/5040 - c**6/480 + 39*c**4/4 - 51*c + 3. Let f(v) be the third derivative of p(v). Find g, given that f(g) = 0.
0, 3
Let z(a) = -104*a**2 + a - 3. Let b be z(-2). Let m = 423 + b. Factor m*d**3 - 4/3*d**2 + 0 - 2/3*d**5 + 0*d**4 + 0*d.
-2*d**2*(d - 1)**2*(d + 2)/3
Suppose 285*w - 6384 = 14501 - 6635. Let p(d) be the third derivative of -5/4*d**4 + 0 + 1/60*d**5 - w*d**2 + 0*d + 75/2*d**3. What is y in p(y) = 0?
15
Let x = 1461 + -1458. Let b(p) be the third derivative of 15*p**2 + 0*p**x + 0*p**4 + 1/455*p**7 + 0*p - 1/2184*p**8 - 1/260*p**6 + 0 + 1/390*p**5. Factor b(g).
-2*g**2*(g - 1)**3/13
Let o be (20/2)/((17 - (-1976)/(-133))/((-6)/(-21))). Factor 2/3*v**4 + o*v - 4/3*v**3 + 2 - 8/3*v**2.
2*(v - 3)*(v - 1)*(v + 1)**2/3
Let t(b) be the first derivative of b**5/20 - 5*b**4/12 - b**3/6 + 5*b**2/2 - 38*b + 21. Let n(l) be the first derivative of t(l). Factor n(f).
(f - 5)*(f - 1)*(f + 1)
Let t(o) = o**2 - 94*o - 592. Let p(u) = -2*u**2 + 187*u + 1282. Let g(q) = -4*p(q) - 9*t(q). Factor g(b).
-(b - 100)*(b + 2)
Let k(q) be the first derivative of -274/3*q**3 - 173 - 128*q - 3/5*q**5 + 53/4*q**4 + 176*q**2. Determine g, given that k(g) = 0.
2/3, 1, 8
Let l(p) be the second derivative of p**6/90 - 2*p**5/15 + p**4/2 - 33*p**3/2 - 117*p. Let b(m) be the second derivative of l(m). Factor b(q).
4*(q - 3)*(q - 1)
Let j be 36/(-30) + (-28)/3430*-182. Factor -18/7*k + 12/7*k**2 + 0 - j*k**3.
-2*k*(k - 3)**2/7
Let k(i) be the second derivative of 1/20*i**5 - 1/6*i**4 + 5*i - 1/6*i**3 + 7 + i**2. Factor k(n).
(n - 2)*(n - 1)*(n + 1)
Let k(w) be the third derivative of -w**5/60 + 383*w**4/24 + 64*w**3 - 1525*w**2. Factor k(s).
-(s - 384)*(s + 1)
Let k(h) be the second derivative of -48*h + 0*h**2 + 1/3*h**3 + 1/36*h**4 + 0. Factor k(r).
r*(r + 6)/3
Factor -160392*v**2 - 3/2*v**4 - 1965/2*v**3 + 0 + 161376*v.
-3*v*(v - 1)*(v + 328)**2/2
Let c(h) = -4*h**3 + 2*h + 1. Let p be c(-1). Find g, given that 475 + 301 + 811 + p*g**2 - 138*g = 0.
23
Let s(z) = -14*z**2 - 13*z + 7. Suppose 134 = 12*a + 38. Let f(k) = -22*k**2 - 20*k + 10. Let w(d) = a*s(d) - 5*f(d). Factor w(v).
-2*(v - 1)*(v + 3)
Let j = 72756946/5305195 + 2/757885. Factor 4/7*i**3 + 0 - 100/7*i**2 + j*i.
4*i*(i - 24)*(i - 1)/7
Let s(u) = -45*u**2 - 21*u - 6. Suppose -27 - 99 = -7*o. Let z(y) = -4*y. Let n(m) = o*z(m) - s(m). Let n(l) = 0. Calculate l.
2/15, 1
Let p(u) be the first derivative of -8*u**6/15 - 13*u**5/5 - u**4 + 32*u**3/3 + 8*u**2 + 19*u - 50. Let n(k) be the first derivative of p(k). Solve n(r) = 0.
-2, -1/4, 1
Let o be ((-48)/10)/(891/2310). Let z = o + 124/9. Factor -10/3*f - 2/3*f**3 + z + 8/3*f**2.
-2*(f - 2)*(f - 1)**2/3
Let q(n) be the first derivative of 3*n**5/35 + 9*n**4/14 - 19*n**3/7 - 36*n**2/7 - 401. Solve q(z) = 0 for z.
-8, -1, 0, 3
Let i(f) be the second derivative of -f**6/6 + 73*f**5/4 + 125*f**4/4 - 365*f**3/6 - 185*f**2 + 5671*f. Find l, given that i(l) = 0.
-1, 1, 74
Let -7/3*o**2 - 2*o**3 + 0 + 1/3*o**4 + 0*o = 0. What is o?
-1, 0, 7
Let z(c) be the second derivative of -c**4/3 + 174*c**3 - 520*c**2 - 1472*c. Find w such that z(w) = 0.
1, 260
Suppose -637*s - 31254 - 767*s + 26394 - 4*s**3 - 132*s**2 = 0. What is s?
-15, -9
Let m be (1/3)/(2/12). Let x be m - ((-4 - -1) + -1). Factor -4*a**3 - 10*a**2 + x*a**2 - a + 9*a.
-4*a*(a - 1)*(a + 2)
Let r(o) = -o**4 - o**3 - 2*o**2 - 2*o + 5. Let n(h) = -2*h**4 - 86*h**3 - 336*h**2 + 4*h - 10. Let j(k) = -n(k) - 2*r(k). Let j(y) = 0. What is y?
-17, -5, 0
Let k(q) = q**2 + 18*q + 10. Let x be k(-18). Suppose x*f = -7*f + 7*f. Find p, given that f*p + 5/2*p**2 + 0 = 0.
0
Let y be 786/(-10)*(585/(-84))/39 - (-1)/4. Factor -16/7*z**2 - 24/7 + y*z.
-4*(z - 6)*(4*z - 1)/7
Let i = 56/153 + -631/2142. Let n(t) be the first derivative of 1/4*t**4 - 5/21*t**3 - 3/35*t**5 + 0*t + i*t**2 - 9. Factor n(v).
-v*(v - 1)**2*(3*v - 1)/7
Let s = 29 - -4. Let p = 12 - 8. Factor -7*y**2 + 6 + 12*y**3 + 31*y**2 - 13*y + 2*y**4 + 0*y**p + s*y.
2*(y + 1)**3*(y + 3)
Let d(c) be the first derivative of -116*c**3/3 - 6558*c**2 - 904*c - 2512. Solve d(h) = 0 for h.
-113, -2/29
Factor 111/2*i - 3/4*i**2 + 0.
-3*i*(i - 74)/4
Let l(a) = 13*a**2 + 31*a - 48. Let p(w) = -22*w**2 - 61*w + 80. Let t(d) = 5*l(d) + 3*p(d). Solve t(h) = 0 for h.
-28, 0
Let y(t) = -15*t**3 - 4830*t**2 - 20925*t - 20270. Let f(l) = -l**3 - 345*l**2 - 1494*l - 1448. Let z(p) = -85*f(p) + 6*y(p). Solve z(x) = 0.
-2, 73
Let k(j) = 13*j**2 + 7*j - 10. Let r be k(2). Suppose 50 - r = -3*m. Factor 12*p**m + 8*p**3 + 0 + 0*p + 4/3*p**4.
4*p**2*(p + 3)**2/3
Let s(d) be the first derivative of d**6/21 + 52*d**5/7 - 66*d**4/7 - 260*d**3/21 + 131*d**2/7 - 314. Let s(k) = 0. What is k?
-131, -1, 0, 1
Determine v so that -672*v + 13236*v**3 - 26468*v**3 + 13241*v**3 - 141*v**2 - 708 = 0.
-2, 59/3
Let -9293*t**2 - 9450*t**2 - 180 + 62*t**3 - 80*t + 18*t**3 + 18928*t**2 - 5*t**4 = 0. What is t?
-2, -1, 1, 18
Let g(p) be the third derivative of p**6/480 - p**5/10 + 39*p**4/32 + 169*p**3/12 + 296*p**2 + 2*p - 4. Factor g(n).
(n - 13)**2*(n + 2)/4
Suppose 0 = -10*q + 161 + 359. Suppose -4 = -28*b + q. Determine w so that 2/5 + 4/5*w**4 - 7/5*w - 6/5*w**b + 7/5*w**3 = 0.
-2, -1, 1/4, 1
Let m be (-1)/(-13) + -40*(-20)/(-260) + 2*4. Let a = 7 - 3. What is w in 0 - w**3 + 1/2*w + 0*w**a + 1/2*w**m + 0*w**2 = 0?
-1, 0, 1
Suppose -1/7*k**4 + 43/7*k + 24/7 - k**3 + 13/7*k**2 = 0. What is k?
-8, -1, 3
Let a(n) = 17. Let d(i) = 5. Let t(l) = 2*a(l) - 7*d(l). Let g(m) = -3*m**2 - 39*m + 40. Let r(o) = -g(o) + 2*t(o). Let r(p) = 0. What is p?
-14, 1
Let t(a) = -3*a**2 - a + 2. Let x(g) be the second derivative of 3*g**4/4 + 2*g**3/3 - 5*g**2/2 - 37*g. Let i(r) = 11*t(r) + 4*x(r). Find f such that i(f) = 0.
-1, -2/3
Let o = 9581 - 124499/13. Let -10/13*k**4 + 58/13*k + o*k**3 - 90/13*k