
1, 283
Let s(m) = -24*m**2 + 725*m + 21595. Let r(o) = -15*o**2 + 363*o + 10797. Let g(x) = -5*r(x) + 3*s(x). What is l in g(l) = 0?
-60
Find k, given that -5043/2 - 3/8*k**2 - 123/2*k = 0.
-82
Let 196*k + 66 + 60*k**3 - 787*k**4 - 15*k**2 + 785*k**4 + 207*k**2 = 0. What is k?
-1, 33
Suppose -83*b = -1056 + 890. Determine u so that -2/9*u**b + 20/9 + 2/3*u = 0.
-2, 5
Let b(l) = -8*l**2 - 13*l - 1. Let f be b(-2). Let m be (476/f - -2)/(-14). Determine r, given that 9/7*r**3 - 12/7 + m*r**2 + 0*r - 9/7*r**5 - 3*r**4 = 0.
-2, -1, 2/3, 1
Let k be (61002/72)/((-33)/12) - 0. Let b = k + 309. Factor b*d + 8/11 + 2/11*d**2.
2*(d + 1)*(d + 4)/11
Suppose 543*p = 35*p + 1081 + 951. Factor -2/9*g**5 - 2*g - 32/9*g**2 - 4/9 - 4/3*g**p - 28/9*g**3.
-2*(g + 1)**4*(g + 2)/9
Suppose 4*t - 128 = -2*k, -5*k - 135 + 420 = 3*t. Factor 52*g + 1341*g**2 - 1335*g**2 + k - 22.
2*(g + 8)*(3*g + 2)
Let q be 162/729 - (-4)/(-18). Let p(y) be the first derivative of q*y - 7 + 10/57*y**3 + 0*y**2 + 2/95*y**5 + 3/19*y**4. Factor p(n).
2*n**2*(n + 1)*(n + 5)/19
Suppose 12*m - 29*m + 1344 = 25*m. Let b(y) be the first derivative of 0*y**2 + 1/8*y**6 + 0*y - 3/4*y**4 - m - y**3 + 3/20*y**5. What is f in b(f) = 0?
-2, -1, 0, 2
Let s = -41 - -43. Let p be -4 - (3 + -63)/s. Solve -38*k + 5*k**4 + p*k**2 - 11*k**2 + 63*k - 20 - 25*k**3 = 0.
-1, 1, 4
Let r be 9/((-135)/(-80))*114/8. Factor -u**2 - 4*u**2 + r - 166 - 55*u.
-5*(u + 2)*(u + 9)
Let p = -4957 + 4961. Let y(x) be the second derivative of 0 - 10*x + 1/6*x**3 + 1/24*x**p - 3/40*x**5 + 0*x**2. Factor y(s).
-s*(s - 1)*(3*s + 2)/2
Suppose 5*f + 10 = o, o - f + 230 = 232. Solve o + 1/6*n**3 + n**2 + 0*n = 0 for n.
-6, 0
Suppose -5*n = 136 - 536. Let q be (n/(-15))/(2/(-36)). Suppose -q*v + 4*v**5 + 120*v**4 + 72*v**4 - 188*v**2 + 144 + 92*v**3 - 148*v**4 = 0. Calculate v.
-6, -1, 1
Let h(p) be the second derivative of -p**4/3 + 138*p**3 + 836*p**2 + 1764*p. Factor h(v).
-4*(v - 209)*(v + 2)
Let j(x) be the first derivative of x**5/20 + 3*x**4/8 - 14*x**3/3 - 147*x**2/4 + 343*x/4 + 1751. Determine n so that j(n) = 0.
-7, 1, 7
Let h(i) be the second derivative of i**5/45 - 55*i**4/27 + 1886*i**3/27 - 1058*i**2 + 5958*i. Suppose h(s) = 0. What is s?
9, 23
Let h(w) be the first derivative of -4*w**3/21 - 2*w**2/7 + 288*w/7 - 4439. Find a such that h(a) = 0.
-9, 8
Let w = -591 - -307. Let m = w + 288. Factor 0*h - 1/2*h**2 - 1/8*h**m + 0 - 1/2*h**3.
-h**2*(h + 2)**2/8
Let a(u) be the third derivative of 91*u**2 + 1/336*u**8 - 2/15*u**5 + 0 + 0*u**3 + 1/70*u**7 + 0*u**4 - 1/20*u**6 + 0*u. Solve a(l) = 0.
-4, -1, 0, 2
Let h(z) be the first derivative of 3/2*z + 67 - z**2 + 1/8*z**4 + 1/24*z**3 - 1/40*z**5. Find m, given that h(m) = 0.
-2, 1, 2, 3
Let s(x) = -15*x - 2*x + 2*x + 95 - 25*x**2 + 5*x. Let f(z) = z**3 - 24*z**2 - 11*z + 94. Let o(h) = -5*f(h) + 4*s(h). Factor o(c).
-5*(c - 3)**2*(c + 2)
Let g(l) = 34*l**2 - 4 - 188*l - 2 + 0 - 20 + 42*l. Let r(b) = 6*b**2 - 29*b - 5. Let m(n) = 3*g(n) - 14*r(n). Factor m(x).
2*(x - 2)*(9*x + 2)
Let j(k) = -5*k**2 + 54*k - 533. Suppose 8*d = -19 - 5. Let c(t) = -t**2 + 2*t - 1. Let a(m) = d*j(m) + 12*c(m). Factor a(h).
3*(h - 23)**2
Let i(o) be the third derivative of o**7/3360 + o**6/144 + 5*o**5/96 + 221*o**3/6 - 10*o**2 + 6. Let l(u) be the first derivative of i(u). Factor l(j).
j*(j + 5)**2/4
Let a(x) = 3*x**2 - 3*x. Suppose 0*y + 4*y = -20. Let b = 2634 - 2637. Let n(u) = u**4 - 6*u**2 + 5*u. Let s(q) = b*n(q) + y*a(q). Solve s(p) = 0 for p.
-1, 0, 1
Let k be 30/(-18) - (5 + (-102)/18). Let y be ((k - -5) + -4)*(-4)/8. Find i such that 0*i**2 + 2/7*i + y - 2/7*i**3 = 0.
-1, 0, 1
Let w(i) = 40*i - 715. Let r be w(32). Let k = r + -563. Suppose 6/5*q + 27/5*q**k + 0 = 0. What is q?
-2/9, 0
Let c = -105777 + 105779. Find h such that 32/5*h - 6 - 2/5*h**c = 0.
1, 15
Let d(m) be the third derivative of -m**5/240 + 73*m**4/32 + 55*m**3/6 - 1589*m**2. Factor d(z).
-(z - 220)*(z + 1)/4
Let v(r) = -2*r**2 + 12*r + 29. Let f be v(7). Suppose 0 = 3*x + 2*h + 2, f*x + 2*h = 19*x - 16. Suppose 22/3*u - 4 - 4*u**x + 2/3*u**3 = 0. Calculate u.
1, 2, 3
Let d(s) be the third derivative of s**8/1680 - 53*s**7/350 - s**6/600 + 53*s**5/100 - 12*s**2 + 42*s - 3. Solve d(c) = 0.
-1, 0, 1, 159
Let p(m) be the second derivative of m**4/36 - 2791*m**3/9 + 7789681*m**2/6 + 792*m. Factor p(s).
(s - 2791)**2/3
Let u = -1/2613797 + 2613805/20910376. Factor 0 - u*o**5 + 0*o**2 + 0*o + o**3 + 7/8*o**4.
-o**3*(o - 8)*(o + 1)/8
Let u(m) = 0*m + 0*m + m + 1. Suppose -12 = -2*k + 5*k. Let y(p) = -p**2 + 5*p + 4. Let n(j) = k*u(j) + y(j). Find d, given that n(d) = 0.
0, 1
Suppose 174*b - 12*b = 0. Let l(g) be the second derivative of 15*g + b + 2*g**3 + 1/25*g**5 + 3/5*g**4 - 10*g**2. Factor l(u).
4*(u - 1)*(u + 5)**2/5
Let n(u) be the second derivative of 20/3*u**3 + 35/2*u**2 + 5/12*u**4 + 0 - 25*u. Find f such that n(f) = 0.
-7, -1
Let m(l) be the first derivative of -l**3 + 177*l**2 + 720*l - 368. Find b such that m(b) = 0.
-2, 120
Factor -98*s + 620*s**3 - 9*s**4 - 96*s + 5*s**4 + 194*s.
-4*s**3*(s - 155)
Let b(m) = m**3 - 8*m**2 + 11*m + 1. Let k be b(7). Let o = k + 17. Factor -o*f + 46*f + 3*f**3.
3*f**3
Let x(g) be the third derivative of g**7/280 - 11*g**6/480 + g**5/48 + g**4/32 - 2*g**2 - 10*g + 25. What is v in x(v) = 0?
-1/3, 0, 1, 3
Let h(u) be the third derivative of 0 + 11/24*u**6 + 0*u**3 + 8*u + 75/8*u**4 + 13/4*u**5 + 1/42*u**7 + 3*u**2. Suppose h(p) = 0. Calculate p.
-5, -3, 0
Let s(h) be the first derivative of 2*h**5/5 - 121*h**4/10 + 296*h**3/5 - 484*h**2/5 + 32*h + 656. Solve s(w) = 0 for w.
1/5, 2, 20
Let -48/7*v**2 - 2*v**3 + 44/7 + 2*v + 4/7*v**4 = 0. What is v?
-2, -1, 1, 11/2
Suppose 27/2*o**4 + 117/2*o**3 + 363 - 693/2*o - 177/2*o**2 = 0. What is o?
-11/3, 1, 2
Suppose 1416133*j - 164 = 1416051*j. Factor 49/2*u**3 - 28*u**j - 75/2*u - 9.
(u - 2)*(7*u + 3)**2/2
Suppose 1 = 5*w - 9. Suppose -w*h - 14 + 24 = 0. Find l such that 3*l**4 - h*l**4 + 4*l**4 + 2*l**4 = 0.
0
Let i(j) be the third derivative of -j**8/336 + j**7/210 + j**6/40 - j**5/12 + j**4/12 - 630*j**2. Factor i(v).
-v*(v - 1)**3*(v + 2)
Factor -1/4*m**2 - 36 + 25/4*m.
-(m - 16)*(m - 9)/4
Let f be 162/12*4/3*1. Suppose -16*a**4 + f*a**5 - 64*a**3 - 14*a**4 + 8*a**2 - 32*a**2 = 0. Calculate a.
-2/3, 0, 3
Let p(r) be the third derivative of 23/96*r**4 + 0 + 1/2*r**3 - 1/480*r**6 + 1/24*r**5 + 0*r - 38*r**2. Factor p(q).
-(q - 12)*(q + 1)**2/4
Let g(r) be the third derivative of 0*r + 0*r**6 + 0*r**3 + 1/15*r**5 - 1/12*r**4 + 1/168*r**8 - r**2 - 2/105*r**7 + 2. Determine a so that g(a) = 0.
-1, 0, 1
Let q = -95544/67 - -1426. Let n = q + 81/469. Find b such that -n*b**2 - 1/7 + 2/7*b = 0.
1
Let q(f) be the third derivative of -f**7/945 - 11*f**6/540 - 4*f**5/45 + f**4/3 - 1442*f**2. Determine z, given that q(z) = 0.
-6, 0, 1
Let l be 99/2 + (-15)/10*-1. Let v(u) = 3*u**3 + 5*u**2 - 8. Let r(p) = -25*p**3 - 40*p**2 + p + 64. Let a(n) = l*v(n) + 6*r(n). Factor a(b).
3*(b - 1)*(b + 2)*(b + 4)
What is m in -204/7 + 177/7*m**2 - 96*m + 15*m**3 = 0?
-17/5, -2/7, 2
Let y(u) be the second derivative of u**4/15 - 20*u**3/3 + 282*u**2/5 + 778*u. Find h such that y(h) = 0.
3, 47
Let r(c) be the first derivative of -c**4 + 1004*c**3/3 - 31750*c**2 + 62500*c - 1527. Factor r(u).
-4*(u - 125)**2*(u - 1)
Let m(g) be the second derivative of g**4/12 - 11*g**3 + 1089*g**2/2 - 5*g + 83. Solve m(q) = 0.
33
Let w(o) be the third derivative of -5*o**5/12 + 5*o**4 + 25*o**3/6 + 146*o**2 + 5*o. Factor w(x).
-5*(x - 5)*(5*x + 1)
Let z(d) be the first derivative of d**4 + 22/3*d**3 - 28*d - 23*d**2 + 81. Factor z(l).
2*(l - 2)*(l + 7)*(2*l + 1)
Let r(k) be the first derivative of -4*k**5/5 - 10*k**4 + 44*k**3/3 + 3299. Determine j, given that r(j) = 0.
-11, 0, 1
Suppose -73 = -9*c + 17. Let f(j) be the first derivative of 20*j**2 + c - 80*j - 5/3*j**3. Solve f(x) = 0 for x.
4
Let b be (-6*(-13)/(-936))/(5/(-15)). Let j(y) be the second derivative of -b*y**2 + 13/24*y**3 - 7/16*y**4 + 0 - 8*y. Factor j(a).
-(3*a - 1)*(7*a - 2)/4
Let h be 155/55 - 3 - (-35182)/22. Let i = h - 1595. Let -5/11*n**2 + 0 - 1/11*n**i - 2/11*n - 4/11*n**3 = 0. What is n?
-2, -1, 0
Let q be -1*(96/(-44) - 2/(-11)). Let i be (q/(-28))/(38/(-399)). Find n, given that 0 - i*n - n*