etermine d so that v(d) = 0.
0, 2
Let i(l) = -21*l**2 + 1300*l - 1257. Let s(x) = -4*x**2 + 260*x - 252. Let t(q) = -2*i(q) + 11*s(q). Factor t(m).
-2*(m - 129)*(m - 1)
Let n(w) be the first derivative of -5*w**2/2 - 12*w + 19. Let x be n(-3). Let -4*z - 40 + 9*z**3 - 30*z**2 - 56*z + z**x - 15*z**3 = 0. Calculate z.
-2
Let w(k) be the second derivative of -k**4/24 - 20*k**3 - 236*k**2 - 25*k + 14. Factor w(d).
-(d + 4)*(d + 236)/2
Suppose -5*r + 2*l = 28, 4*r = -217*l + 214*l + 65. Determine c, given that 8/11*c - 2/11*c**r - 6/11 = 0.
1, 3
Factor -18*c**2 - 1361 + 40*c - 15*c**2 - 14*c**2 + 51*c**2 + 305.
4*(c - 12)*(c + 22)
Let t be (17 + -18)/(1/(-3)). Determine b, given that -6*b**2 - 60*b + 65 - 5*b**2 + 9*b**2 - t*b**2 = 0.
-13, 1
Suppose 288*k - 332262 = -591*k. Factor -128/9*z**4 + k*z - 162 - 312*z**2 + 992/9*z**3.
-2*(z - 1)*(4*z - 9)**3/9
Factor -44 - 2/5*s**2 + 222/5*s.
-2*(s - 110)*(s - 1)/5
Suppose -2*x = s + 24, 5*s - 2*x - 30 = 6. Factor 0 + 2/11*p**5 - 4/11*p**s - 2/11*p + 0*p**3 + 4/11*p**4.
2*p*(p - 1)*(p + 1)**3/11
Factor 84*t + 3/2*t**2 - 174.
3*(t - 2)*(t + 58)/2
Let o = -421901 - -421903. Find g, given that 32/7 - 30/7*g**o + 20/7*g - 2/7*g**4 - 20/7*g**3 = 0.
-8, -2, -1, 1
Let h(p) be the second derivative of -9*p**6/5 - 3267*p**5/10 - 1077*p**4 - 4292*p**3/3 - 952*p**2 + 4905*p - 1. Factor h(q).
-2*(q + 119)*(3*q + 2)**3
Suppose 21 = 23*p - 23 - 25. Let h(u) be the second derivative of -1/120*u**4 + 1/2*u**2 - 1/20*u**p + 12*u + 0. Factor h(a).
-(a - 2)*(a + 5)/10
Let b = 1594 + -1582. Suppose 3*r + 3*m = -b, 55*r - 4*m = 51*r + 16. Let -4/17*t + r + 2/17*t**2 = 0. What is t?
0, 2
Suppose -7*s - 248 = -11*s. Suppose -s*o + 61*o = -2. What is x in 12*x**5 + 4 + 20*x - 29*x**3 + 3*x**o - x**4 + 0 - 3*x**5 - 6*x**4 = 0?
-1, -2/9, 1, 2
Determine z, given that 21*z**2 + 74*z**2 - 3*z**3 - 180*z + 248 - 53*z**2 - 32 = 0.
2, 6
Let p(m) = -84*m**2 + 20776*m - 6920. Let y(o) = 102*o**2 - 20776*o + 6919. Let d(z) = 5*p(z) + 4*y(z). What is n in d(n) = 0?
1/3, 1731
Let s(w) be the first derivative of 1/210*w**5 + 18 + 1/42*w**4 + 1/21*w**3 - 14*w + 1/21*w**2. Let l(y) be the first derivative of s(y). Factor l(t).
2*(t + 1)**3/21
Factor -29*w + 72*w**2 + 3*w - 1140 + 149*w + 0*w**3 - 2*w**3 + 59*w.
-2*(w - 38)*(w - 3)*(w + 5)
Let f(o) be the first derivative of -o**4/10 + 266*o**3/15 - 132*o**2/5 - 11262. Factor f(g).
-2*g*(g - 132)*(g - 1)/5
Factor 3/4*t**2 - 129/4*t + 63/2.
3*(t - 42)*(t - 1)/4
Let -1131/2*m**2 - 53582633/2 + 1/2*m**3 + 426387/2*m = 0. What is m?
377
Let p(o) be the third derivative of -5*o**8/336 - 23*o**7/42 - 127*o**6/24 - 83*o**5/4 - 30*o**4 - 1411*o**2. Solve p(i) = 0.
-16, -3, -1, 0
Let n be (-3)/(-2) - ((-41)/2 + 22). Let k(u) be the second derivative of 3/14*u**4 + n + 11/21*u**3 - 6*u + 2/7*u**2. Let k(z) = 0. What is z?
-1, -2/9
Let d(f) be the third derivative of f**5/60 - 5*f**4/24 - 6*f**3 + 2*f**2 + 2*f - 4144. Solve d(a) = 0.
-4, 9
Factor 243/2*v - 27*v**2 - 15/2*v**3 + 81.
-3*(v - 3)*(v + 6)*(5*v + 3)/2
Let k be (28 + -5 - 9676/413)/(-6*(-1)/(-7)). Suppose -1352 - k*q**2 + 52*q = 0. Calculate q.
52
Let y(w) be the first derivative of 361/2*w + 116 + 19/2*w**2 + 1/6*w**3. Let y(n) = 0. Calculate n.
-19
Suppose -970 + 589 = -3*u. Suppose -16 = -2*q + 2*v, 0 = -4*q - 5*v - u + 114. Find w such that 1/5*w**q + 3/5 + 1/5*w**2 - w = 0.
-3, 1
Let h(t) = -7*t**2 + 107*t - 12. Let c(q) = 8*q**2 + 11*q - 24*q + 5*q + 13 - 82*q - 19*q. Let x(y) = -6*c(y) - 5*h(y). Determine r so that x(r) = 0.
2/13, 9
Suppose 152*h = 149*h + 18. Let d be (-54)/(-36) - h/4. Solve 2/3*g - 2/3*g**3 + 0 + d*g**2 = 0.
-1, 0, 1
Let n(r) be the second derivative of r**6/180 + r**5/120 - r**4/4 - 4*r**3/9 + 8*r**2/3 - 3*r - 32. Determine c, given that n(c) = 0.
-4, -2, 1, 4
Determine a, given that 2/5*a**3 - 36/5*a - 64/5 + 6*a**2 = 0.
-16, -1, 2
Let k(y) be the second derivative of 2*y**6/15 + 12*y**5/5 + 15*y**4 + 36*y**3 + 26*y + 3. Find d, given that k(d) = 0.
-6, -3, 0
Let r(n) be the second derivative of n**4/24 - 7*n**3/6 - 15*n**2/4 + 1032*n. Find p, given that r(p) = 0.
-1, 15
Suppose -4*s + 16 = 0, 5*c - 6 = 6*c - 2*s. Determine u, given that -9 - 4*u**c + 1436*u - 4*u**5 - 1460*u + 28*u**3 + 4*u**4 + 9 = 0.
-2, -1, 0, 1, 3
Determine u so that -1/6*u**3 - 552 - 116*u - 47/6*u**2 = 0.
-23, -12
Let y(s) be the third derivative of -3*s**8/112 - 3*s**7/2 - 11*s**6/5 + 1046*s**5/45 - 422*s**4/9 + 136*s**3/3 - 4*s**2 - 35*s - 2. Find t such that y(t) = 0.
-34, -3, 2/3
Let b(r) be the second derivative of 1/45*r**6 + 2/3*r**2 - 1/6*r**4 - 134*r - 2 + 1/9*r**3 - 1/30*r**5. Determine k so that b(k) = 0.
-1, 1, 2
Let l(d) be the first derivative of 3*d**4/4 - 241*d**3 + 360*d**2 - 6116. Solve l(o) = 0.
0, 1, 240
Let d = 170 - 167. Factor 36 + 4*p**3 - d*p**2 - p**2 - 467*p + 431*p.
4*(p - 3)*(p - 1)*(p + 3)
Factor -264992/11 - 2/11*q**2 - 1456/11*q.
-2*(q + 364)**2/11
Suppose -70 = -9*r - 7. Solve 93*l + 72 + 52*l + r*l - 6*l**2 - 11*l = 0 for l.
-1/2, 24
Let c = -360469/3 + 120157. What is a in -56*a - c*a**2 - 1176 = 0?
-42
Let d(i) be the second derivative of i**6/180 - 13*i**5/120 - 7*i**4/8 - 83*i**3/36 - 17*i**2/6 + 678*i. Factor d(j).
(j - 17)*(j + 1)**2*(j + 2)/6
Suppose -160/7 + 6*g**3 + 32/7*g**2 - 24*g + 2/7*g**4 = 0. Calculate g.
-20, -2, -1, 2
What is j in -353 + 12*j**5 - 176 - 1135*j**2 + 91*j**2 + 561*j**3 + 385 + 804*j - 135*j**4 = 0?
1/4, 2, 3, 4
Let k(v) = v**4 + 4*v**3 - 25*v**2 + 12*v - 2. Let a(r) = 12*r**4 + 51*r**3 - 327*r**2 + 156*r - 27. Let p(l) = -2*a(l) + 27*k(l). Factor p(y).
3*y*(y - 1)**2*(y + 4)
Solve -247*s**3 - 143*s**3 + 4*s**4 + 386*s**3 - 48*s**2 = 0 for s.
-3, 0, 4
Let i(k) be the third derivative of k**5/3 - 73*k**4/18 - 20*k**3/9 + 116*k**2 + 2*k. Factor i(l).
4*(l - 5)*(15*l + 2)/3
Let l(x) be the third derivative of -x**5/240 - x**4/48 + 21*x**3/8 + 2*x**2 + 405. Factor l(b).
-(b - 7)*(b + 9)/4
Suppose -4*q = 4*u + 9784, -5*u + 4878 = q - 3*q. Let j = q + 46446/19. Factor 2/19*r**2 + j*r + 8/19.
2*(r + 1)*(r + 4)/19
Let r be -5*(-5)/(-25) - -2*1. Let z be r/4*-4 + 4. Factor -c**2 + 0 + 1/2*c**4 + 1/2*c**z + 0*c.
c**2*(c - 1)*(c + 2)/2
Determine m, given that -21*m**2 + 1/2*m**3 + 294*m - 1372 = 0.
14
Let b(t) = 5*t**2 + 10*t. Suppose 0 = -0*s - s - 4. Suppose g + 4*k - 3 = 0, 2*g = 5*k + 2 - 9. Let i(l) = l**2 - l. Let p(v) = g*b(v) + s*i(v). Factor p(f).
-3*f*(3*f + 2)
Let j(d) be the second derivative of -1/285*d**6 - 4/57*d**3 + 4 - 11*d - 3/38*d**4 + 12/19*d**2 + 3/95*d**5. What is c in j(c) = 0?
-1, 2, 3
Let z = 21940/2973 - 46/991. Find m such that -m**3 - z*m - 8/3 - 17/3*m**2 = 0.
-4, -1, -2/3
Let w(u) be the first derivative of 1709168367*u**4/4 - 6185169*u**3 + 67149*u**2/2 - 81*u + 353. Determine a, given that w(a) = 0.
3/829
Suppose -5*l = 5*x - 21655, -9*l = -10*l - 1. What is j in -x*j + 7*j**2 - 2*j**2 + j**2 - 4*j**3 + 222*j**2 + 27436 = 0?
19
Suppose 4*x = 5*y - 19, 22 - 33 = -3*y + 2*x. Let f(l) be the third derivative of 0 + 7*l**2 + 3/2*l**y + 1/60*l**5 + 0*l + 1/4*l**4. Factor f(d).
(d + 3)**2
Let d(f) be the third derivative of 5*f**8/336 - 5*f**7/42 - 25*f**6/24 + 125*f**5/12 + 2*f**2 - 695. Let d(j) = 0. What is j?
-5, 0, 5
Let t(y) = 17*y + 96. Let q be t(-4). Suppose 30*w = q*w + 4. Factor 0*z + 0 - 3/8*z**w + 51/8*z**3.
3*z**2*(17*z - 1)/8
Let r(f) be the third derivative of f**7/350 - f**6/100 - 9*f**5/100 + f**4/20 + 4*f**3/5 + 17*f**2 + 93*f. Solve r(u) = 0.
-2, -1, 1, 4
Let w(h) = -62*h**2 + 1182*h - 49. Let n be w(19). Let d be -7 + 7 + (-19)/(-3). Find z such that d*z**2 - 33*z - 1/3*z**3 + n = 0.
1, 9
Let t(z) be the third derivative of 0*z + 0*z**4 - 1/1080*z**6 + 2*z**2 + 7/270*z**5 - 18 + 0*z**3. Find l, given that t(l) = 0.
0, 14
Let m(b) = -b**5 - 4*b**4 - 8*b**3 - 10*b**2 - 5*b - 7. Let w(f) = f**4 + f**3 + f**2 + f + 1. Suppose 210 = 2*n + 252. Let g(d) = n*w(d) - 3*m(d). Factor g(v).
3*v*(v - 2)*(v - 1)**2*(v + 1)
Let p(f) = -2*f**2 + 391*f - 12666. Let k be p(41). What is z in -17/2*z - 1/2*z**4 - 17/2*z**2 - k - 7/2*z**3 = 0?
-3, -2, -1
Let g = 725/1869 + -34/623. Let s(h) be the first derivative of g*h**4 - 20 + 0*h - 4/9*h**3 + 0*h**2. Find q, given that s(q) = 0.
0, 1
Let z(q) = 3*q + 2. Let p be z(-6). Let h = p + 19. Factor 35*g**h - 1