q**3 + 0 + w*q + 3/2*q**2.
-q**2*(q - 3)/2
Let x(i) = i**3 - 3*i**2 + 3*i - 6. Let j be x(3). Suppose j*c = 4*c - 14. Let 2 - 5*m**2 - m**4 - 7*m - 4 + c*m + 5*m**3 - 4*m**2 = 0. Calculate m.
1, 2
Let g be ((-36)/(-32)*2)/(4/16). Suppose 4*c = -x - g, x + 3*c + 12 = 2*x. Factor -d**2 + 0*d**2 - 2*d**3 + x*d**2 + 4*d**3 - 2*d - 2*d**4.
-2*d*(d - 1)**2*(d + 1)
Let j(f) be the third derivative of -1/60*f**7 - 34*f**2 + 0 + 0*f**3 + f + 1/10*f**5 - 3/80*f**6 + 1/12*f**4. Factor j(r).
-r*(r - 1)*(r + 2)*(7*r + 2)/2
Let y(j) be the third derivative of j**8/84 + 34*j**7/105 + 37*j**6/15 + 82*j**5/15 - 25*j**4/2 - 66*j**3 + 2*j**2 - 126. Solve y(t) = 0 for t.
-11, -3, -1, 1
Let j(o) be the third derivative of -o**8/50400 - o**7/6300 + 9*o**5/20 - 65*o**2. Let w(q) be the third derivative of j(q). Determine u, given that w(u) = 0.
-2, 0
Let w(i) be the second derivative of i**7/112 - i**6/5 - 33*i**5/160 + 363*i**4/16 + 951*i. Factor w(v).
3*v**2*(v - 11)**2*(v + 6)/8
Let s be (74/148)/(1/124*2). Suppose -s*q = -30*q + 3*b - 15, 4*b = 20. Let -2/3*j**2 + q + 4/3*j - 2/3*j**3 = 0. Calculate j.
-2, 0, 1
Suppose -31229*s + 960 = -31149*s. Factor 1/2*y**3 - 13 - 51/2*y - s*y**2.
(y - 26)*(y + 1)**2/2
Let q(i) be the third derivative of -i**7/840 - i**6/60 - 7*i**5/80 - 3*i**4/16 + 1054*i**2. Factor q(k).
-k*(k + 2)*(k + 3)**2/4
Factor -47*j - 4*j**3 - 512 - 148*j - 173*j + 140*j**2.
-4*(j - 32)*(j - 4)*(j + 1)
Let r(i) be the second derivative of i**4/6 - 31*i**3/3 + 234*i**2 + 2284*i + 1. Let r(b) = 0. What is b?
13, 18
Let h(s) be the second derivative of -4*s + 0*s**2 - 13/5*s**5 + 0 + 2/15*s**6 - 22/3*s**3 + 23/3*s**4. What is v in h(v) = 0?
0, 1, 11
Suppose 0 = 77*d - 55*d - 550. Let g(x) be the first derivative of d + 2/27*x**3 + 8/9*x + 4/9*x**2. Factor g(n).
2*(n + 2)**2/9
Suppose q + 1 = -p, 4*q + 5*p + 8 + 1 = 0. Factor 39 + 29*z**4 - 36*z**2 - 32*z**q + 7*z**3 - 49*z**3 + 42*z.
-3*(z - 1)*(z + 1)**2*(z + 13)
Let i(a) = -2*a**2 + a + 780. Let m be i(20). Let j(r) be the first derivative of 1/6*r**3 + m*r**4 - 1/30*r**5 + 0*r - 1/6*r**2 - 19. Factor j(n).
-n*(n - 1)**2*(n + 2)/6
Let h(j) = -79*j + 727. Let x be h(9). Let t(b) be the first derivative of -x + 0*b - 5*b**3 + 15/4*b**4 - b**5 + 5/2*b**2. What is v in t(v) = 0?
0, 1
Let o(x) be the second derivative of 1/45*x**4 - 1/150*x**5 + 0*x**2 + 33*x + 1/15*x**3 + 0. Factor o(k).
-2*k*(k - 3)*(k + 1)/15
Find m such that 37/4*m + 11/2*m**2 - 15 + 1/4*m**3 = 0.
-20, -3, 1
Suppose -10*l - 7*l + 84 = 11*l. Let d(u) be the first derivative of -2/5*u**l - 2/5*u**2 - 1/10*u**4 + 0*u + 3. Solve d(v) = 0 for v.
-2, -1, 0
Let 4/3*t**5 + 400/3*t + 132*t**2 - 132*t**4 + 0 - 404/3*t**3 = 0. What is t?
-1, 0, 1, 100
Suppose 20 - 61/3*j + 1/3*j**2 = 0. What is j?
1, 60
Let c be (-90738)/1420*(-13)/((-234)/(-8)). Factor 2888/15 - 68/15*p**3 + 2/15*p**4 + 2584/15*p + c*p**2.
2*(p - 19)**2*(p + 2)**2/15
Let j = -58691 + 763003/13. Factor 0 - 2/13*x**5 - 64/13*x**3 + 0*x + j*x**4 + 64/13*x**2.
-2*x**2*(x - 4)**2*(x - 2)/13
Solve 88*q + 2/9*q**2 + 0 = 0.
-396, 0
Let n(w) be the second derivative of w**6/30 + 7*w**5/30 + 19*w**4/36 + 2*w**3/9 - 2*w**2/3 - 16*w - 35. Let n(b) = 0. Calculate b.
-2, -1, 1/3
Suppose 2*g + 2*t + 4 = -2*g - g, -68 = 4*t. Factor -1/2*s**2 + 4*s - g.
-(s - 6)*(s - 2)/2
Let b = 221069 + -221065. Factor -1/2*k**b - k**3 + 0 - 1/2*k**2 + 0*k.
-k**2*(k + 1)**2/2
Let d(p) be the first derivative of -p**6/2 + 12*p**5 - 84*p**4 - 64*p**3 + 3072*p**2 - 12288*p - 4884. Determine i so that d(i) = 0.
-4, 4, 8
Factor -5/3*w**3 - 149/3*w + 62/3*w**2 - 72.
-(w - 8)*(w + 1)*(5*w - 27)/3
Let h(r) be the first derivative of 0*r + 0*r**2 - r**4 + 0*r**3 + 51 - 2/5*r**5. Find s, given that h(s) = 0.
-2, 0
Solve 16/3*g**5 + 158/3*g**2 - 40/3*g**4 - 47/3*g**3 - 68/3*g + 8/3 = 0 for g.
-2, 1/4, 2
Let w(r) be the first derivative of 2*r**6/57 - 42*r**5/95 + 37*r**4/19 - 64*r**3/19 + 32*r**2/19 + 2036. Determine m, given that w(m) = 0.
0, 1/2, 2, 4
What is d in -6069*d**2 + 3129*d**2 + 2941*d**2 + 1302*d + 423801 = 0?
-651
Let q(z) be the third derivative of -z**5/90 - 77*z**4/36 + 196*z**3/3 - 3810*z**2. Factor q(c).
-2*(c - 7)*(c + 84)/3
Let t(n) be the second derivative of n**4/3 + 2732*n**3/3 - 1215*n - 1. Factor t(r).
4*r*(r + 1366)
Let l(h) be the first derivative of -69*h**5/10 - 153*h**4/2 - 433*h**3/2 + 45*h**2 - 4948. Find d such that l(d) = 0.
-5, -4, 0, 3/23
Let r(b) = -b**5 - 62*b**2 - 219*b**3 + 220*b**3 - b**4 + 63*b**2. Let z(j) = 20*j**5 - 25*j**4 + 9*j**3 + 5*j**2. Let y(l) = 5*r(l) - z(l). Factor y(m).
-m**3*(5*m - 2)**2
Let f(y) be the third derivative of -1/20*y**6 - 6/35*y**7 - 205*y**2 + 1/14*y**8 + 11/20*y**5 + 1/2*y**3 + 0 - 3/4*y**4 + 0*y. Factor f(q).
3*(q - 1)*(q + 1)*(2*q - 1)**3
Let -6452*g + 19*g**2 - 36*g**2 + 19*g**2 - 1340861 + 3590859 + 2953540 = 0. What is g?
1613
Suppose 5*v - 4*d + 6 = -0*d, 0 = -4*v - 5*d + 28. Factor -76*i**2 + 4 + 29*i**2 + 26*i**2 + 6*i + 23*i**v.
2*(i + 1)*(i + 2)
Suppose 72 = 59*n - 50*n. Let g be (40/n + -9)/(-1). Factor 8/15*f**2 + 0 + 0*f - 2/5*f**g + 0*f**3 + 2/15*f**5.
2*f**2*(f - 2)**2*(f + 1)/15
Factor z**2 - 31 - 278/3*z.
(z - 93)*(3*z + 1)/3
Suppose -9*m - 1339 = -5929. Suppose 4*c - 518 + m = 0. Factor 1/2*g**c - 1 - 1/2*g.
(g - 2)*(g + 1)/2
Suppose -11*o = 54 - 10. Let t(j) = 5*j**3 - 4*j**2 + j + 2. Let s(w) = 6*w**3 - 5*w**2 + 2*w + 2. Let r(n) = o*s(n) + 5*t(n). Factor r(v).
(v - 1)**2*(v + 2)
Let k(x) be the second derivative of -x**4/42 - 88*x**3/7 - 263*x**2/7 + 1106*x. Factor k(c).
-2*(c + 1)*(c + 263)/7
Let r(z) be the first derivative of 9/2*z**2 - 14*z + 35 - 1/3*z**3. Factor r(a).
-(a - 7)*(a - 2)
Let r = -147 - -152. Let y(f) = 7*f**2 - 5*f + 20. Let a(t) = -4*t**2 + 3*t - 12. Let n(o) = r*a(o) + 3*y(o). What is u in n(u) = 0?
0
Factor 473344 + 4*t**4 - 467840*t - 25*t**3 + 1145*t**3 + 360*t**3 - 120*t**3 + 112848*t**2.
4*(t - 2)**2*(t + 172)**2
Let p = -3850 + 3852. Let q(h) = 5*h - 17. Let b be q(4). Factor p*n**2 + 4/3*n**b + 4/3*n + 1/3 + 1/3*n**4.
(n + 1)**4/3
Let g(d) be the second derivative of d**4/66 + 98*d**3/11 + 293*d**2/11 + 1032*d. Factor g(c).
2*(c + 1)*(c + 293)/11
Suppose -23*c + 25*c = 0. Suppose c = -3*r + 6. Factor -25 + 4*n + 14 + 17 - n**r - 3*n.
-(n - 3)*(n + 2)
Solve -2*x + 1/2*x**3 - 1/2*x**4 + 3*x**2 - 4 = 0 for x.
-2, -1, 2
Let w = 1091591/92144 + -3/7088. Let p = -115363/13 - -8879. Determine y, given that 98/13*y**3 + p*y - w*y**2 - 8/13 = 0.
2/7, 1
Let k(l) be the first derivative of 2*l**3/33 - 46*l**2/11 + 1076. Solve k(a) = 0 for a.
0, 46
Let c = -73 - -98. Let j be ((-160)/c + 7)/(18/500). Factor j*h - 10/3*h**2 + 2/9*h**3 - 250/9.
2*(h - 5)**3/9
Suppose 5*h + 3*p = 4*p + 23, -7*p = -h + 93. Determine d so that 2/3*d**h - 28/3*d + 26/3 = 0.
1, 13
Find l such that 30*l**2 + 0 + 3/2*l**4 - 32*l + 26*l**3 = 0.
-16, -2, 0, 2/3
Suppose -96*m - 100/3*m**3 + 104*m**2 + 0 + 4/9*m**5 + 16/9*m**4 = 0. What is m?
-12, 0, 2, 3
Let i(c) be the third derivative of 1/30*c**5 + 28/3*c**3 + 0 - 4/3*c**4 - 132*c**2 + c. Factor i(z).
2*(z - 14)*(z - 2)
Let o be 5/50*(-10)/(-2)*133/(43 + -24). Factor o*b - 3 - 1/2*b**2.
-(b - 6)*(b - 1)/2
Let i = -14257 + 14267. Let u(g) be the first derivative of 15/2*g**2 - i*g + 0*g**3 - 5/4*g**4 - 5. Determine v so that u(v) = 0.
-2, 1
Let q(c) = 17*c**2 + 170*c + 320. Let d(r) = 36*r**2 + 340*r + 640. Let a(h) = 6*d(h) - 13*q(h). Solve a(n) = 0 for n.
-32, -2
Let t = 45509/24 - 1896. Let j(h) be the second derivative of 5*h**3 - t*h**4 + 0 - 6*h - 45*h**2. Solve j(x) = 0 for x.
6
Let -9558/5*t**2 + 0 + 94/5*t**4 - 8748/5*t - 2/5*t**5 - 714/5*t**3 = 0. What is t?
-6, -1, 0, 27
Factor -582/23*r - 576/23*r**2 - 146/23 + 8/23*r**3.
2*(r - 73)*(2*r + 1)**2/23
Suppose 0 = -3*j + t - 4*t + 24, -5*j + 25 = 2*t. Suppose -7*w = -24 + j. Factor -1/4*u**4 + 0*u**w + 0*u**2 - 1/4*u**5 + 0 + 0*u.
-u**4*(u + 1)/4
Suppose 2420/3*o**4 + 2/3*o**5 + 34297420960/3*o + 1659995174464/3 + 283449760/3*o**2 + 1171280/3*o**3 = 0. What is o?
-242
Let l = 244 + -241. Suppose 16*i**4 - 78*i**3 + 348*i - 256*i**2 + 176*i**3 - 4*i**5 - 58*i**l - 144 = 0. What is i?
-4, 1, 3
Let x(d) = 4247*d**3 - 547*d**2 + 13*d. Let y(f) = 8497*f**3 - 1093*f**2 + 25*f. Let q(o) = 11*x(o) - 5*y(o). Factor q(w).
2*w*(46*w 