.
-2, 0, 4
Let z(m) = -2*m**3 + 22*m**2 - 35*m + 3. Let v be z(9). Let l be (14/v)/((-72)/(-96)). Let 4/3 + l*x**2 + 46/9*x = 0. Calculate x.
-3, -2/7
Let 568/9*w + 4/9*w**2 + 1120/9 = 0. What is w?
-140, -2
Suppose 2429*j = 2422*j - 238. Let s = 176/5 + j. Factor -2/5*b**2 - 8/5*b - s.
-2*(b + 1)*(b + 3)/5
Let l be (-48)/(-24) - (-29 - 0/3). Factor 62*n**2 - l*n**2 - 18*n**3 - 4*n - 53*n**2.
-2*n*(n + 1)*(9*n + 2)
Suppose 4*w = 23 - 11. Let o(n) = -n**2 - n - 2*n**2 - n**2 + w*n**2. Let q(b) = -51*b + 192. Let y(l) = 3*o(l) - q(l). Factor y(s).
-3*(s - 8)**2
Suppose -t + 3*l - 18 = -2*t, -2*t + l + 29 = 0. Let k be 68/20 + (-6)/t. Determine v so that -3*v - v**k + 23*v**2 - 15*v**2 + 9 - 13*v**2 = 0.
-3, 1
Let a(r) be the third derivative of -r**7/294 - 19*r**6/105 - 19*r**5/140 + 15*r**4/28 + 2757*r**2. Solve a(m) = 0.
-30, -1, 0, 3/5
Let u(l) be the second derivative of l**5/220 + 5*l**4/22 + 29*l**3/66 - 203*l. Solve u(a) = 0.
-29, -1, 0
Let x(o) = -o**3 - 22*o**2 - 52*o + 8. Let t be x(-20). Let -8 + t*p**2 + 1 - 27*p - 5 + 2 - 2*p**3 - 263*p**2 = 0. What is p?
-5, -2, -1/2
Let t be (39/(-78))/(2/(-12)). Solve -37*d**t + d**4 - 1 - 25*d**3 + 2*d + 60*d**3 = 0 for d.
-1, 1
Let g(a) be the second derivative of -14*a + 125/2*a**3 - 95*a**2 - 15*a**4 - 1/4*a**5 + 0. Factor g(f).
-5*(f - 1)**2*(f + 38)
Let b(s) be the second derivative of -3/4*s**5 - 38 - 1/6*s**6 + 2*s + 5/2*s**3 + 95/12*s**4 - 45*s**2. Let b(y) = 0. What is y?
-6, -1, 1, 3
Suppose -52*d = 34*d + 4*d. Factor 0*w + d + 1/6*w**3 + 5/6*w**2.
w**2*(w + 5)/6
Let o(r) be the second derivative of r**7/84 - 7*r**6/60 - 27*r**5/40 + 139*r**4/24 + 163*r**3/6 + 42*r**2 - 5054*r. What is w in o(w) = 0?
-4, -1, 6, 7
Let u be 41/4 - (-3)/(-12). Suppose 9*l = u*l - 89. Find y such that -15*y**4 - 5*y**5 + 20*y**2 - 89*y**3 + l*y**3 = 0.
-2, 0, 1
Let h be (-4)/28*(-11 + 4 + 5). Solve 6/7*s**2 + 10/7*s**3 - h*s**5 + 2/7*s**4 + 0 + 0*s = 0.
-1, 0, 3
Let x(m) be the third derivative of -3*m**7/35 - 1717*m**6/60 + 391*m**5/30 + 1717*m**4/12 - 382*m**3/3 - 993*m**2. Suppose x(d) = 0. What is d?
-191, -1, 2/9, 1
Let s(y) be the first derivative of 1/4*y**5 + 0*y - 29 + 19/2*y**2 - 5/2*y**3 + 1/24*y**6 - 5/24*y**4. Let l(g) be the second derivative of s(g). Factor l(p).
5*(p - 1)*(p + 1)*(p + 3)
Let o = 4 + 2. Let q(y) = -2*y**3 + 9*y**2. Let c(f) = 2*f**3 + 0*f**3 - 4*f**3 - 67*f**2 + 77*f**2. Let x(i) = o*q(i) - 5*c(i). Factor x(s).
-2*s**2*(s - 2)
Let f = -129 + 53. Let l = f - -79. Suppose 0*n - 30*n**2 + 31*n**2 - l - 2*n = 0. Calculate n.
-1, 3
Let n(c) be the third derivative of -7/204*c**4 - 14*c**2 - 1/1020*c**6 + 0*c**3 + 5 + 0*c - 4/255*c**5. Find w, given that n(w) = 0.
-7, -1, 0
Let m(y) be the second derivative of -2*y**7/21 - 46*y**6/15 - 111*y**5/5 - 51*y**4 + 10522*y. Factor m(q).
-4*q**2*(q + 3)**2*(q + 17)
Let y(k) be the third derivative of -1/28*k**4 - 1/735*k**7 - 1/84*k**6 + 0*k + 15*k**2 + 0*k**3 - 1/30*k**5 - 4. Solve y(b) = 0 for b.
-3, -1, 0
Let o(a) = 551*a + 2207. Let w be o(-4). Solve 15/4*v + 3/2*v**w - 39/4*v**2 + 9/2 = 0.
-1/2, 1, 6
Factor 102966/5 + 524/5*y + 2/15*y**2.
2*(y + 393)**2/15
Let j(t) be the first derivative of 2/35*t**5 + 4/7*t**4 + 0*t + 58 + 16/7*t**2 + 40/21*t**3. Factor j(x).
2*x*(x + 2)**2*(x + 4)/7
Let i(y) = 36459*y + 72921. Let p be i(-2). Determine c, given that 176/3*c + 122/3*c**4 - 82/3*c**2 - 40/3 - 190/3*c**p + 14/3*c**5 = 0.
-10, -1, 2/7, 1
Let c(k) be the first derivative of -2*k**3 + 155 - 2*k**2 + 0*k**4 + 0*k + 2/5*k**5. Determine f so that c(f) = 0.
-1, 0, 2
Let m(c) = 2*c**2 - 5 - 119*c - 371*c**3 + 57*c + 58*c. Let v be m(-1). Find h, given that 108*h**5 + 268*h**2 + 16/3 + 1420/3*h**3 + v*h**4 + 64*h = 0.
-1, -2/9
Let b(m) be the third derivative of m**5/30 + 227*m**4/6 + 51529*m**3/3 - 1126*m**2. Let b(j) = 0. Calculate j.
-227
Let v be 18/(-33) + 189/(-77). Let b be 7 - ((-2)/(-1) - v). Solve 4*s - 1/2*s**b - 8 = 0.
4
Let x(i) be the first derivative of -4*i**5 - 832*i**4 - 139108*i**3/3 - 27556*i**2 + 143. Factor x(n).
-4*n*(n + 83)**2*(5*n + 2)
Factor -28702*g**3 + 5*g**5 + 210*g**4 - 541*g**2 - 5400 + 27997*g**3 - 669*g**2 + 6180*g.
5*(g - 2)**3*(g + 3)*(g + 45)
Let u(s) be the first derivative of s**6/15 + 4*s**5/5 - 5*s**4/2 - 4*s**3/3 + 24*s**2/5 - 1057. Find f, given that u(f) = 0.
-12, -1, 0, 1, 2
Let p(l) = -2*l**2 + 4*l + 3. Let h(n) = 47*n**2 + 2016*n - 18. Let c(k) = h(k) + 6*p(k). Factor c(f).
5*f*(7*f + 408)
Let t be -2 + 5/3 + (-6)/(-18). Let d(i) be the third derivative of 8/3*i**3 + 0*i + t + 7*i**2 + 8/3*i**4 + 7/15*i**5. Find k such that d(k) = 0.
-2, -2/7
Let q be 9/(-6)*24/(-9). Factor -t**3 + 7*t**3 + 3*t**3 + 107 - 9*t + 3*t**2 + 0*t**4 - 113 + 3*t**q.
3*(t - 1)*(t + 1)**2*(t + 2)
Find m, given that -17*m**2 + 650*m + 28028 + 18*m**2 + 77597 = 0.
-325
Let y(c) be the third derivative of -c**5/90 - 62*c**4/9 - 15376*c**3/9 + 1384*c**2. Factor y(d).
-2*(d + 124)**2/3
Let u = -197559 + 1382923/7. Factor -u*t**2 + 6/7 + 4/7*t.
-2*(t - 1)*(5*t + 3)/7
Suppose 0 = 5*b + 4*t - 138, -2*b + 51 = -0*b + 3*t. Suppose b*g - 12 = 27*g. Factor 44/5*m**2 + 16/5*m**3 + 48/5*m + 18/5 + 2/5*m**g.
2*(m + 1)**2*(m + 3)**2/5
Let n(r) = 21*r**3 - 13*r**2 + 8*r + 2. Let v(f) = 49*f**3 - 26*f**2 + 17*f + 5. Let o(h) = -5*n(h) + 2*v(h). Factor o(w).
-w*(w - 1)*(7*w - 6)
Factor -v**4 - 51*v + 13*v**2 - 39*v - 45*v + 125*v - 2*v**3.
-v*(v - 2)*(v - 1)*(v + 5)
Let t(o) be the third derivative of o**7/840 - o**6/10 + 27*o**5/10 + o**3/3 - 183*o**2. Let m(p) be the first derivative of t(p). Factor m(c).
c*(c - 18)**2
Factor 2/3*c**4 - 122/3*c**2 + 0 + 58/3*c**3 + 62/3*c.
2*c*(c - 1)**2*(c + 31)/3
Factor -152/3*c + 80/3 - 34/3*c**3 + 4/3*c**4 + 36*c**2.
2*(c - 2)**3*(2*c - 5)/3
Solve -2/9*l + 2/9*l**3 - 14/3*l**2 + 14/3 = 0 for l.
-1, 1, 21
Let m(y) be the first derivative of -10*y**3/9 + 1945*y**2/6 + 325*y - 5378. Determine u, given that m(u) = 0.
-1/2, 195
Let a(m) be the third derivative of m**5/60 + 2125*m**4/24 + 354*m**3 - 3145*m**2 - 3. Factor a(o).
(o + 1)*(o + 2124)
Determine a, given that 0 - 10/11*a + 9/11*a**2 + 1/11*a**3 = 0.
-10, 0, 1
Let r = -76 + 88. Suppose -r*q + 5 + 55 = 0. Factor 2*c**5 - 3*c**4 - 3*c**5 + 6*c + 9*c**3 + 15*c**2 - 2*c**q.
-3*c*(c - 2)*(c + 1)**3
Suppose 550/3*u**2 - 1/3*u**4 + 11*u**3 + 724*u + 552 = 0. Calculate u.
-6, -1, 46
Factor -4/7*s**3 - 116/7*s + 64/7*s**2 + 8.
-4*(s - 14)*(s - 1)**2/7
Suppose 21849*p = 21713*p. Factor 4/7*s**5 - 32/7*s + 20/7*s**4 + p + 24/7*s**3 - 16/7*s**2.
4*s*(s - 1)*(s + 2)**3/7
Suppose -15*w + 19*w = 12. Suppose -s - 2*z + 516 = s, -w*z = -5*s + 1266. Factor -y + y - s + 4*y**3 + 239 + 12*y**2.
4*(y - 1)*(y + 2)**2
Let a = -7445 + 7447. Let w(o) be the first derivative of 3 - 41/12*o**3 + 1/4*o**4 - 25/4*o + 55/4*o**a. Factor w(s).
(s - 5)**2*(4*s - 1)/4
Let w = 2269360/23827839 + -2/1134659. Find u, given that 8/21*u - 10/21 + w*u**2 = 0.
-5, 1
Let l(x) = x**2 + x - 1255. Let g be l(-36). Let n(b) be the first derivative of 21 + 0*b - 1/9*b**3 - 1/15*b**g + 1/6*b**4 + 0*b**2. Factor n(a).
-a**2*(a - 1)**2/3
Let y(r) be the third derivative of -r**8/1176 - 58*r**7/735 - 781*r**6/420 + 58*r**5/7 - 75*r**4/7 + 3*r**2 + 3*r + 35. Solve y(m) = 0 for m.
-30, 0, 1
Let o(w) be the second derivative of 7 + 4*w**4 + 0*w**3 - 1/6*w**6 - 1/42*w**7 - w + 2/5*w**5 + 0*w**2. Factor o(s).
-s**2*(s - 3)*(s + 4)**2
Let k(c) be the third derivative of 5/12*c**4 + 0*c**3 - 1/60*c**6 + 6*c**2 + 0*c + 5 + 1/60*c**5. Suppose k(s) = 0. What is s?
-2, 0, 5/2
Determine j so that 2406/7*j + 3582/7*j**2 + 222*j**3 + 402/7 - 24/7*j**4 = 0.
-1, -1/4, 67
Suppose 0 = -4*b - 4*t + 128, 0 = -b - 2*t + 36 - 7. Let q be (40/b)/((-6)/(-21)). Factor 3 - 2*k**2 - q*k**2 + 3*k**4 + 0*k**4.
3*(k - 1)**2*(k + 1)**2
Let a(i) be the third derivative of 0*i + 0 + 0*i**3 + 1/30*i**6 + 1/84*i**8 + 30*i**2 + 1/5*i**5 - 2/35*i**7 - 1/3*i**4. Factor a(g).
4*g*(g - 2)*(g - 1)**2*(g + 1)
Suppose 723*n = 730*n + 7. Let l be n/7 + (-4137)/(-1176). Suppose -3/4*o**3 + 9/8*o**4 + 9/2*o - 3/2 - l*o**2 = 0. Calculate o.
-2, 2/3, 1
Suppose -3*p = 4*o - 20, 0 = 18*p - 22*p - 4*o + 24. Solve -30*c**2 + 40*c - 14*c + 28 - 17*c**p - 26*c**3 + 19*c**4 = 0 for c.
-1, 1, 14
Let i(a) = -a**2 + 365*a + 5310. Let k be i(-14). Le