et z be 246/(-656)*56/(-3). Let j(d) be the second derivative of 2*d**2 + 2/21*d**z + 13*d + 0 - 2*d**3 + 2/3*d**4 + 2/5*d**5 - 2/5*d**6. Factor j(m).
4*(m - 1)**4*(m + 1)
Suppose 3*p + 12 = 0, 0 = -2*u - u - 2*p + 10. Suppose 0 = u*t + 9*t - 765. Find d, given that 0*d - d**4 - 68*d**3 + 56*d**3 - 48*d**2 - 13*d - t*d = 0.
-4, 0
Suppose 4*r + 5*g = -0 + 56, -5*g = 0. Let b = 8 + -6. Factor -4 + 14*a - 6*a**b - a**3 - 9*a - r*a.
-(a + 1)**2*(a + 4)
Let w(x) be the third derivative of x**6/120 + 7*x**5/30 + 7*x**4/3 + 32*x**3/3 + 970*x**2. Factor w(t).
(t + 2)*(t + 4)*(t + 8)
Let l be ((-2)/32)/(1909/(-15272)). Let t = 4 + -2. Let -1/2*x - l*x**t + 0 = 0. What is x?
-1, 0
Let g = 1225 - 1129. Let h be (-5 - 8/(g/(-51)))*-4. Suppose 0*d**2 + 3/4*d + 0 - 3/4*d**h = 0. What is d?
-1, 0, 1
Let 78*k**2 + 744 - 70*k - 76*k**2 - 676 = 0. What is k?
1, 34
Let s be 10/(-145) + (-27256)/(-1624) + -15. Factor -s*l**3 - 8/7*l + 0 + 4*l**2.
-4*l*(l - 2)*(3*l - 1)/7
Let l(h) = h**3 + h**2 + 2. Let v(j) = -1269*j**2 - 6936 + 2836*j**3 + 1530 - 2860*j**3 - 19260*j. Let u(c) = -3*l(c) - v(c). Factor u(a).
3*(a + 30)**2*(7*a + 2)
Let o = -10339/2 + 5172. Let h(w) be the first derivative of 1/5*w**5 - w**3 - 10 + 1/4*w**4 - o*w**2 - 2*w. Factor h(d).
(d - 2)*(d + 1)**3
Let r(a) be the third derivative of -a**7/105 - 5*a**6/12 + 9*a**5/10 + 25*a**4/12 - 26*a**3/3 - 4795*a**2. Find x such that r(x) = 0.
-26, -1, 1
Suppose -61*s + 270 = -52*s. Suppose 70*m = 85*m - s. Find z, given that 2/7*z - 4/7 + 4/7*z**m - 2/7*z**3 = 0.
-1, 1, 2
Let i = 180747/11 + -361439/22. Factor -7 - i*p + 1/2*p**2.
(p - 7)*(p + 2)/2
Suppose 640*t = 646*t + 66. Let x be t/(22/(-12))*9/18. Factor 441/2*s + 81 + 46*s**2 + 5/2*s**x.
(s + 9)**2*(5*s + 2)/2
Let h(g) = 145*g**2 - 1749*g + 110. Let x be h(12). Determine q so that 0 + 2/5*q**4 - 2*q + x*q**3 - 2/5*q**2 = 0.
-5, -1, 0, 1
Suppose 0 = 144*q - 142*q - 48. Let k = q + -17. Determine t so that -4*t**3 - 32*t**4 + 30*t**3 + 8*t**5 - 2 + 15*t**2 + k*t**2 - 6 - 16*t = 0.
-1/2, 1, 2
Let c(y) be the first derivative of -15*y**5 - 185*y**4 + 2875*y**3/3 - 1160*y**2 + 260*y + 6356. Suppose c(m) = 0. What is m?
-13, 2/15, 1, 2
Let w(j) be the first derivative of 2*j**5/25 - 34*j**4/5 + 2566*j**3/15 - 4288*j**2/5 + 6144*j/5 - 5151. Determine r, given that w(r) = 0.
1, 3, 32
Suppose -454*k - 172*k + 2334 = 152*k. Let 6/11*b + 18/11 - 10/11*b**2 + 2/11*b**k = 0. What is b?
-1, 3
Let t be ((-157500)/(-9261) + -17)*42. What is k in -68/7 - 38/7*k - t*k**2 = 0?
-17, -2
Let m(x) be the third derivative of x**7/105 + 9*x**6/10 + 973*x**5/30 + 510*x**4 + 5200*x**3/3 - 4*x**2 - 53. Solve m(a) = 0.
-20, -13, -1
Suppose 134 - 159 = -5*f, 0 = 4*n + 4*f - 20. Factor 3/4*m**2 - 57/4*m + n.
3*m*(m - 19)/4
Let y(t) be the second derivative of -t**6/75 + 8*t**5/25 + 29*t**4/15 - 16*t**3/15 - 57*t**2/5 + 1766*t. Determine v so that y(v) = 0.
-3, -1, 1, 19
Let v be (-8)/((-21*4)/6). Let n = -18650 + 18652. Determine f so that -10/7*f**n - v*f + 0 = 0.
-2/5, 0
Let y(i) be the third derivative of i**6/24 + i**5 + 175*i**4/24 - 1960*i**2. Find j, given that y(j) = 0.
-7, -5, 0
Let b(y) be the first derivative of -7 + 7*y**2 - 12*y - 2/3*y**3. Solve b(d) = 0.
1, 6
Let z(c) be the third derivative of c**6/40 + 19*c**5/4 - 147*c**4/4 + 5519*c**2. Factor z(h).
3*h*(h - 3)*(h + 98)
Let q(i) be the third derivative of 8/5*i**3 - 3/350*i**7 - 1/200*i**6 + 8/25*i**5 + 0 - 67*i**2 + 0*i - 11/10*i**4. Find h, given that q(h) = 0.
-4, 2/3, 1, 2
Let k = 2/4617 - 8943139/23085. Let s = 388 + k. Let 0*y + 0*y**4 + 0*y**2 - s*y**5 + 0 + 0*y**3 = 0. Calculate y.
0
Let u(b) be the third derivative of 7/45*b**5 + 0 + 61*b - 2*b**2 - 2/45*b**7 + 1/6*b**4 + 5/1008*b**8 + 0*b**3 - 17/360*b**6. Let u(y) = 0. What is y?
-1, -2/5, 0, 1, 6
Factor -10 + 10 - 23 + 70*c + 88 + 5*c**2.
5*(c + 1)*(c + 13)
Solve -3/7*a**4 + 3/7*a + 3*a**2 - 18/7 - 3/7*a**3 = 0.
-3, -1, 1, 2
Let k = -686251/7 + 98036. Find o, given that -3/7*o - k + 1/7*o**2 + 3/7*o**3 = 0.
-1, -1/3, 1
Let 25/2 + 149/2*h - 3*h**2 = 0. Calculate h.
-1/6, 25
Find w such that 392*w - 28*w**4 + 192 + 11306*w**5 - 60*w**3 + 11319*w**5 + 172*w**2 - 22621*w**5 = 0.
-2, -1, 3, 8
Suppose 4*r + 29 = 9. Let d be (-3)/(4 + 21/r). Factor 23*z - 4*z**2 + 5*z**2 - 46*z + 7 + d*z.
(z - 7)*(z - 1)
Let i = 6389 + -6374. Let m(f) be the second derivative of 0 - 2/105*f**6 + 0*f**2 + i*f + 0*f**5 + 1/7*f**4 - 4/21*f**3. Factor m(p).
-4*p*(p - 1)**2*(p + 2)/7
Let n = 52101 - 260503/5. Let -12/5*o - n*o**2 - 2 = 0. Calculate o.
-5, -1
Let r be (194/(-36) + (-52)/468)*8/(-22). Factor -16/9*k**4 + 0 + 2/9*k**5 + 4*k**3 + 10/9*k - 32/9*k**r.
2*k*(k - 5)*(k - 1)**3/9
Suppose 125 - 559 = -7*q. Factor -6*z + 2*z**4 - 65*z**3 - q*z**2 + 63*z**3 + 52*z**2.
2*z*(z - 3)*(z + 1)**2
Let o = 224 - -4948. Let u = 36285/7 - o. Factor -3/7*n**3 - u + 9/7*n**2 + 27/7*n.
-3*(n - 3)**2*(n + 3)/7
Let c(m) be the second derivative of -m**5/240 - m**4/96 + m**3/4 - 41*m**2 - m - 9. Let v(l) be the first derivative of c(l). Solve v(p) = 0 for p.
-3, 2
Let z(p) be the first derivative of p**4/12 - 37*p**3/9 - 125*p**2/3 - 344*p/3 - 1732. Factor z(n).
(n - 43)*(n + 2)*(n + 4)/3
Let v = -14207 + 14207. Let b(w) be the third derivative of -1/9*w**3 - 1/90*w**5 + 0 - 1/18*w**4 + v*w - 28*w**2. Factor b(q).
-2*(q + 1)**2/3
Let j be 16 + (-1265)/33*6/20. Factor j*u**2 + 6 - 1/2*u**3 - 10*u.
-(u - 6)*(u - 2)*(u - 1)/2
Let w = 3831 + -3829. Factor 0*p + 0 - 2/7*p**5 - 2*p**3 + 6/7*p**w + 10/7*p**4.
-2*p**2*(p - 3)*(p - 1)**2/7
Let q(n) be the third derivative of -n**5/80 - 31*n**4/4 - 247*n**3/8 - 2099*n**2. Find a such that q(a) = 0.
-247, -1
Factor -4595*a + 95*a**4 + 85*a**2 + 4595*a + 5*a**5 + 175*a**3.
5*a**2*(a + 1)**2*(a + 17)
Let u = 17310 - 17308. What is i in 21/2*i**u + 27*i - 3/2*i**3 + 0 = 0?
-2, 0, 9
Let d(o) be the third derivative of 1/20*o**5 + 1/200*o**6 + 0*o + 0 + 18/5*o**3 + 74*o**2 - 4/5*o**4. Factor d(r).
3*(r - 2)**2*(r + 9)/5
Let g(f) = -58*f**2 + 192*f + 1530. Let k(d) = -18*d**2 + 64*d + 510. Let y(x) = -5*g(x) + 16*k(x). Let y(u) = 0. What is u?
-17, -15
Suppose -4*j + 16 = 0, a + 4*j = -0*a + 20. Let s be 2 + ((-221)/204 - 1/a). Determine x so that 4/9*x**3 + 4/9*x**2 + 2/9*x**5 - s*x**4 + 2/9 - 2/3*x = 0.
-1, 1
Let h(z) = -15*z + 108. Let d be h(6). Let x be ((-16)/(-36))/(4/d). Factor 4/5*m**x + 4/5 - 8/5*m.
4*(m - 1)**2/5
Let i = 147581/66618 - -51/7402. Determine m so that -1/3*m**3 + i*m**2 + 2 - 13/3*m = 0.
2/3, 3
Let t(g) = -g**3 + 7*g + 9. Let y be t(-4). Let m = -45 + y. Factor 3 + 134*h**2 + 15*h - 122*h**2 + m.
3*(h + 1)*(4*h + 1)
Let i be (49830/(-3775))/(4/6) - -23. Determine b so that -2/5*b**2 + i*b + 18/5 = 0.
-1, 9
Suppose 4*s - 2 = -l, 4*s + 16 = 5*l - 42. Suppose -39 + 19 = -l*o. Let -4/3 - 1/3*u**o - 4/3*u = 0. What is u?
-2
Factor 75*j - 621/7 + 3/7*j**3 + 93/7*j**2.
3*(j - 1)*(j + 9)*(j + 23)/7
Let w(x) be the second derivative of -x**7/1680 + x**6/72 + 11*x**5/240 - x**3/3 + 13*x. Let h(m) be the second derivative of w(m). Factor h(y).
-y*(y - 11)*(y + 1)/2
Let l(z) = -23*z**3 + 6160*z**2 + 4914*z + 986. Let i(r) = 114*r**3 - 30815*r**2 - 24569*r - 4931. Let u(f) = 6*i(f) + 33*l(f). Factor u(a).
-3*(a - 246)*(5*a + 2)**2
Factor -96 - 232*i + 43*i**2 - 795*i**3 - 27*i**2 + 60*i**2 + 827*i**3.
4*(i - 2)*(i + 4)*(8*i + 3)
Let t be (-82)/(9840/(-3780)) - 30. Suppose -t - 3/4*u + 3/4*u**2 = 0. Calculate u.
-1, 2
Let d(s) be the second derivative of s**7/273 + 41*s**6/65 + 1857*s**5/65 - 2294*s**4/39 - 7688*s**3/13 - 14129*s. Find m such that d(m) = 0.
-62, -2, 0, 3
Let b(o) be the first derivative of 235 - 1/2*o**4 - 841*o**2 + 116/3*o**3 + 0*o. Factor b(w).
-2*w*(w - 29)**2
Let k(q) = -q**2 - 2*q - 6. Let v(x) = 2*x**2 - 79*x + 24. Let r(u) = 12*k(u) + 3*v(u). Let r(o) = 0. What is o?
-87/2, 0
Suppose 4*q + 22 = 5*w, 2*w + 3*q = 38 - 43. Suppose -2/17*g**w + 8/17*g - 8/17 = 0. Calculate g.
2
Factor -2*t**2 + 599*t - 850*t - 3236806 + 1363*t + 4064*t - 112066.
-2*(t - 1294)**2
Suppose 2*w - 7*w + 1 = -4*j, -4*w + 4 = 0. Let c be (j + (-51)/81)*(-93)/(-155). Factor -8/9*n**3 + 0*n - c*n**4 - 8/9*n**2 + 0.
-2*n**2*(n + 2)**2/9
Let n(y) be the first derivative of 5*y**3/3 + 185*y**2/2 - 190*y - 35. Factor n(b).
5*(b - 1)*(b + 38)
Let n(