 -56 + 17. Factor -2*k**4 + 441*k + 12*k**3 - 153*k + z + 24*k**3 - 167 - 194*k**2.
-2*(k - 8)**2*(k - 1)**2
Let q(l) be the first derivative of -l**4/12 + l**3/6 - 8*l - 18. Let t(o) be the first derivative of q(o). What is u in t(u) = 0?
0, 1
Factor -1/3*q**5 + 34/3*q**3 + 0 - 5*q**4 + 0*q + 0*q**2.
-q**3*(q - 2)*(q + 17)/3
Let j = -2493 + 5001/2. Solve 9/4*n**4 + 27/4*n**2 - j*n**3 - 3/2*n + 0 = 0 for n.
0, 1/3, 1, 2
Let p(i) be the second derivative of 1/45*i**6 - 4/3*i**2 + 4/9*i**3 - 2/15*i**5 - 6*i + 1/6*i**4 + 0. Let p(u) = 0. Calculate u.
-1, 1, 2
What is r in 9/2*r + 0 - 7/2*r**2 = 0?
0, 9/7
Let f be (-4)/(11 - 15)*2. Factor 0 + 10/11*l**f - 6/11*l**3 - 4/11*l.
-2*l*(l - 1)*(3*l - 2)/11
Suppose -18414*n + 105*n**3 + 20*n**2 + 18414*n + 17*n**4 + 88*n**4 + 20*n**5 = 0. Calculate n.
-4, -1, -1/4, 0
Suppose -3*g + 80 = 2*g. Let d(x) be the first derivative of -2*x**5 - 20*x**2 + 17/2*x**4 + g*x - 2 - 4*x**3. Solve d(w) = 0.
-1, 2/5, 2
Factor -15*x**4 - 7158 - 3466 + 1175*x**2 + 8*x**5 - 3*x**5 + 6000*x - 345*x**3 - 11876.
5*(x - 5)**3*(x + 6)**2
Let v(w) = -15*w**3 - 124*w**2 - 214*w - 94. Let s(x) = -3*x**3 - 25*x**2 - 43*x - 19. Let y be (-2 - -3)/1*-2. Let u(n) = y*v(n) + 11*s(n). Factor u(q).
-3*(q + 1)**2*(q + 7)
Let p(m) be the third derivative of m**7/105 - m**6/20 - m**5/15 + m**4 - 8*m**3/3 - 254*m**2. Determine z, given that p(z) = 0.
-2, 1, 2
Suppose -2*u - 3*u - 5*f = -25, 0 = 5*f - 25. Let d(y) be the first derivative of 1/10*y**5 + u*y**3 + 4 + 0*y**2 - 1/4*y**4 + 0*y. What is w in d(w) = 0?
0, 2
Suppose 3*r - 14 = -5*z + 12, 2*z = -2*r + 16. Suppose -r*w = -5*w - 10. Factor -4*q**4 + 3*q**4 + 5*q**w + 5*q**3 + 11*q**4.
5*q**3*(q + 1)**2
Let p(d) be the first derivative of 12 + 57/28*d**4 + 19/21*d**3 + 0*d + 1/7*d**2 + 8/21*d**6 + 8/5*d**5. Let p(j) = 0. Calculate j.
-2, -1, -1/4, 0
Suppose -8*i + 2 = -7*i. Factor 5*k**4 - 7*k**3 + 94*k**2 + k**4 + 3*k + 1 - 97*k**i.
(k - 1)**2*(2*k + 1)*(3*k + 1)
Let t be 3/(12/10)*90/75. Let n(l) be the second derivative of 0*l**2 + 0*l**4 + t*l + 0*l**3 + 0*l**5 + 1/120*l**6 + 0. Factor n(x).
x**4/4
Suppose 29*l = 4*l. Let p(k) be the third derivative of -2*k**2 + 1/4*k**4 + 0*k**3 + 1/20*k**5 + 0 - 1/40*k**6 + l*k. Suppose p(d) = 0. What is d?
-1, 0, 2
Let m = 233 - 233. Let z(t) be the third derivative of -1/140*t**5 + 0*t**4 + 8*t**2 + m + 1/1470*t**7 + 0*t**3 + 1/420*t**6 + 0*t. Factor z(r).
r**2*(r - 1)*(r + 3)/7
Let d(v) be the third derivative of -v**6/60 - 27*v**5/10 - 729*v**4/4 - 6561*v**3 - v**2 + 54*v. What is m in d(m) = 0?
-27
Let p(w) = -w**3 - w**2 - 2*w + 1. Let l(b) = -5*b**4 - 51*b**3 - 46*b**2 - 12*b + 6. Let r(j) = l(j) - 6*p(j). Factor r(i).
-5*i**2*(i + 1)*(i + 8)
Factor 161*m + 2*m**3 + 114*m**2 + 424 - 80*m + 351*m.
2*(m + 2)**2*(m + 53)
Let h(a) = 3*a**3 - a + 16*a + 3*a**3 - 6*a**4. Let l(j) = -j**4 + j**3 + 2*j. Suppose -3*q - 59 = -14. Let w(p) = q*l(p) + 2*h(p). Factor w(n).
3*n**3*(n - 1)
Suppose 33*z = 27*z + 12. Let k(i) be the first derivative of i**5 + 0*i - 1 + 1/4*i**z + 1/4*i**6 + 3/2*i**4 + i**3. Solve k(q) = 0 for q.
-1, -1/3, 0
Suppose -15*d + 87*d**2 + 1 - 27 - 88*d**2 = 0. What is d?
-13, -2
Let l(z) be the third derivative of -z**6/480 - z**5/120 - z**4/96 - 41*z**2. Find u, given that l(u) = 0.
-1, 0
Let l(r) = -2*r**3 + 6*r**2 + 2. Let b be l(3). Let o be -1*6*(-3)/12. Suppose 1/2 - 2*k + 2*k**3 + o*k**2 - b*k**4 = 0. What is k?
-1, 1/2, 1
Determine o, given that -132*o**2 - 107*o**5 - 185*o**4 + 60*o**3 - 45 + 906*o**3 - 456*o + 8*o**4 + 2*o**5 - 51 = 0.
-4, -2/5, -2/7, 1, 2
Let z(s) be the second derivative of 1/40*s**5 + 11/12*s**3 + 5/4*s**2 - 7*s + 0 + 7/24*s**4. Factor z(v).
(v + 1)**2*(v + 5)/2
Suppose -3*u - 112 = -k, 5*u - u + 218 = 2*k. Let j = k + -102. Suppose 139/4*i**3 + 8*i - 95/4*i**4 - j - 97/4*i**2 + 25/4*i**5 = 0. Calculate i.
2/5, 1
Suppose 7*f + 206 - f**2 - 416 + 204 = 0. Calculate f.
1, 6
Let f(w) be the third derivative of w**7/945 + w**6/54 + 14*w**5/135 + 2*w**4/9 + 36*w**2. What is l in f(l) = 0?
-6, -2, 0
Suppose 2*s + 0*x + 8 = 3*x, 4 = 4*s - x. Suppose -s*v + 2 = -v. Let -u**v - 1/3 + u + 1/3*u**3 = 0. Calculate u.
1
Let p(u) be the second derivative of u**10/6048 + u**9/1512 - u**7/252 - u**6/144 + 7*u**4/6 - 21*u. Let o(a) be the third derivative of p(a). Factor o(w).
5*w*(w - 1)*(w + 1)**3
Factor 43 + 16 + 8 + 2*k**2 + 13 - 82*k.
2*(k - 40)*(k - 1)
Let u be ((-3)/(-9))/(4/18)*8. Let z be ((-42)/54 - -1)/(1/u). Factor 1/6*w**2 - 4/3*w + z.
(w - 4)**2/6
Let h be (2/(-10)*1)/(-12*28/4410). Determine t, given that 3/4*t**3 + 3/4 + h*t + 21/8*t**2 = 0.
-2, -1, -1/2
Suppose 4*f - 14 = -18. Let q be ((-51)/(-45) + f)/((-2)/(-3)). Factor -1/5*v**2 + 1/5 - 1/5*v + q*v**3.
(v - 1)**2*(v + 1)/5
Let r(q) be the first derivative of 0*q**2 + 1/14*q**4 - 28 + 0*q - 1/35*q**5 + 1/7*q**3. Let r(v) = 0. What is v?
-1, 0, 3
Let s be 23085/35 - (24/28)/(-2). Let x be 444/s - (-3)/5. Solve 28/11*h**3 + 4/11 + 4/11*h**4 - x*h - 14/11*h**5 - 8/11*h**2 = 0 for h.
-1, 2/7, 1
Factor -144*b**2 + 0*b + 3/4*b**5 + 12*b**3 + 0 + 39/4*b**4.
3*b**2*(b - 3)*(b + 8)**2/4
Factor 90*r**2 - 93*r**2 + 27*r - 108 + 9*r.
-3*(r - 6)**2
Let t(n) = 14*n**2 + n**4 - 7*n**4 + 0*n**2 + 8 + 16*n**5 - 22 + 18*n**3. Let r(w) = w**5 + w**3 + w**2 - 1. Let p(d) = 28*r(d) - 2*t(d). What is m in p(m) = 0?
0, 1, 2
Let u(q) be the first derivative of -q**3 - 6*q**2 + 15*q + 118. Solve u(r) = 0 for r.
-5, 1
Factor -323/4*a**2 - 467/8*a + 93/4 + 7/8*a**3.
(a - 93)*(a + 1)*(7*a - 2)/8
Let f be (0 - 2/(-1))/(77 + -76). Let l(h) be the first derivative of 3/2*h**2 + 1/3*h**3 + 0*h - f. Factor l(s).
s*(s + 3)
Let g(t) be the first derivative of -2*t**5/25 - 7*t**4/10 + 6*t**3/5 + 7*t**2/5 - 16*t/5 + 147. Solve g(l) = 0.
-8, -1, 1
Let n(b) be the first derivative of 4*b**3/15 + 68*b**2/5 + 1156*b/5 - 22. What is j in n(j) = 0?
-17
Find k such that 0 + 0*k - 32/7*k**2 - 2/7*k**4 - 16/7*k**3 = 0.
-4, 0
Let y(l) be the first derivative of -55*l**4/2 + 196*l**3/3 - 192*l**2/11 - 576*l/11 + 244. Factor y(h).
-2*(5*h + 2)*(11*h - 12)**2/11
Let l(t) be the first derivative of 0*t**2 + 16 - 3/10*t**5 + 1/12*t**6 - 1/8*t**4 + 7/6*t**3 - 2*t. Suppose l(v) = 0. What is v?
-1, 1, 2
Let i(f) be the third derivative of -5*f**8/112 + 31*f**7/35 - 249*f**6/40 + 17*f**5 - 25*f**4/2 + 472*f**2. What is r in i(r) = 0?
0, 2/5, 2, 5
Let l(f) be the second derivative of -f**6/270 + 11*f**5/180 - 2*f**4/9 - 2*f**3/3 + f - 6. Solve l(i) = 0.
-1, 0, 6
Let z(q) = 13*q**3 - 3*q**2 - 2*q + 3. Let l be z(1). Suppose 2*b - l*b = -0*b. Find x, given that b - 3/2*x - 3/2*x**2 = 0.
-1, 0
Solve 246/13*m**2 + 8/13 + 112/13*m + 46/13*m**4 + 188/13*m**3 = 0 for m.
-2, -1, -2/23
Let t(o) = -4*o**3 - 6*o**2 + 10*o + 6. Let u(r) = 16*r**3 + 25*r**2 - 43*r - 25. Let s(i) = -9*t(i) - 2*u(i). Find f such that s(f) = 0.
-1, 1
Let -99/5 - 3/5*k**2 + 42/5*k = 0. What is k?
3, 11
Let y(k) be the first derivative of k**4/26 + 44*k**3/39 + 21*k**2/13 - 3. Let y(z) = 0. What is z?
-21, -1, 0
Suppose -l - 2*l + 6 = 0. Let o = -23 + 29. Suppose 7*a**2 - o*a + 8*a + 8*a**3 + l*a**4 + a**4 = 0. What is a?
-1, -2/3, 0
Let l = 215 + -859/4. Factor -i**2 + l*i**3 - 1/2 + 5/4*i.
(i - 2)*(i - 1)**2/4
Let i be (6 + (-4 - -3))*(-6)/15. Let a be 6/(12/i)*-3. Factor -1/2*c**2 + 0 - 1/2*c + c**a.
c*(c - 1)*(2*c + 1)/2
Let r(t) be the third derivative of t**6/300 - t**5/75 + t**4/60 - t**2 + 11*t. Determine c, given that r(c) = 0.
0, 1
Suppose 0*o + 2*d + 262 = -4*o, 3*o - d + 209 = 0. Let m = o + 68. Factor 1/2*u**3 - 1/4*u + 0 + 0*u**4 + m*u**2 - 1/4*u**5.
-u*(u - 1)**2*(u + 1)**2/4
Let b(t) be the third derivative of -t**8/6720 + t**7/1260 - t**6/720 - t**4/6 + 10*t**2. Let m(p) be the second derivative of b(p). Factor m(n).
-n*(n - 1)**2
Let d(o) = 6*o**2 + 20*o + 8. Let v = -19 - -27. Let m(u) = -2*u**2 - 7*u - 3. Let j be (-15)/(-6) - 5/(-4 - 6). Let i(z) = j*d(z) + v*m(z). Factor i(h).
2*h*(h + 2)
Let f(o) be the second derivative of 1/10*o**6 + 0 - 12*o + 3/10*o**5 + 0*o**3 + 0*o**4 + 0*o**2. Let f(b) = 0. Calculate b.
-2, 0
Let b(r) = 7*r**2 - 10*r - 42. Let s(u) be the first derivative of -12*u**3 + 25*u**2 + 211*u + 15. Let l(m) = -11*b(m) - 2*s(m). Find p such that l(p) = 0.
-2, 4
Let q(u) = u**2 - 2*u - 1. Let a(g)