 13*g**6/210 - 18*g**5/35 - 46*g**4/21 - 16*g**3/3 - 559*g**2. What is m in t(m) = 0?
-7, -2
Factor 3/4*b**3 - 57/4*b - 21/2 - 3*b**2.
3*(b - 7)*(b + 1)*(b + 2)/4
Factor -14/3*c**4 - 8/3*c - 10*c**3 - 26/3*c**2 + 0 - 2/3*c**5.
-2*c*(c + 1)**3*(c + 4)/3
Factor 2/7*b**3 - 6/7*b**2 + 16/7 - 12/7*b.
2*(b - 4)*(b - 1)*(b + 2)/7
Let n = 70/39 - 178/273. Let c(l) be the second derivative of -28/5*l**6 - 219/20*l**5 - 43/4*l**4 + 11*l + 0 - n*l**7 - 11/2*l**3 - 3/2*l**2. Factor c(h).
-3*(h + 1)**3*(4*h + 1)**2
Let j(g) = -8*g**2 - 107*g - 114. Let u(l) = 39*l**2 + 534*l + 567. Let d(h) = 24*j(h) + 5*u(h). Find q such that d(q) = 0.
-33, -1
Find b, given that -1161 - 1151 + 2312 + 3*b**4 = 0.
0
Let d(s) be the second derivative of s**7/5040 - s**6/360 + s**5/60 - 13*s**4/12 - 11*s. Let h(z) be the third derivative of d(z). Solve h(i) = 0 for i.
2
Let j = 45 - 18. What is x in -6*x + 15*x**4 - 27*x**5 - j*x**3 + 0*x + 24*x**5 + 21*x**2 = 0?
0, 1, 2
Suppose 3*l - 7 + 1 = 0. Suppose -3*r = -8*r + 15, -24 = -2*b + 2*r. Factor -5*p**2 + b*p**4 - 12*p**3 + 3*p**5 - 9*p**5 + 8*p**l.
-3*p**2*(p - 1)**2*(2*p - 1)
Suppose 3*x + z + 2*z + 9 = 0, 2*z = 4*x + 6. Let s be x/(3 - 1)*-3. Determine l so that 18*l**3 - 30*l**3 + 5*l**2 + 19*l**s - 2*l = 0.
-1, 0, 2/7
Suppose 4*m - 4*d = 12, -4*m - 17 = -8*m - d. Let s(z) be the third derivative of -1/12*z**m + 0 + 0*z + 5*z**2 + 2/9*z**3 + 1/90*z**5. Factor s(f).
2*(f - 2)*(f - 1)/3
Find z, given that -12/5*z**4 - 2/5*z**5 + 22/5*z + 12/5 - 4*z**3 + 0*z**2 = 0.
-3, -2, -1, 1
Let h(q) be the second derivative of 5*q**4/12 + 65*q**3/6 + 55*q**2 - 12*q + 7. Factor h(k).
5*(k + 2)*(k + 11)
Factor -164/7*u - 12/7*u**2 + 8.
-4*(u + 14)*(3*u - 1)/7
Suppose -5*u + 5*i - 10 = 0, -710*u - i + 2 = -705*u. Let 0*q - 1/8*q**4 + u*q**3 + 1/4*q**2 - 1/8 = 0. Calculate q.
-1, 1
Let w(f) be the second derivative of -f**6/30 + 13*f**5/80 - f**4/16 - 93*f. Find u such that w(u) = 0.
0, 1/4, 3
Let j(s) be the third derivative of 3/70*s**7 + 0 - 26*s**2 + 1/6*s**4 + 1/5*s**5 - 5/24*s**6 + 0*s**3 + 0*s. Let j(p) = 0. What is p?
-2/9, 0, 1, 2
Let h(b) = -b - 1. Let u(t) = -4*t**2 + 282*t + 286. Let c(o) = 2*h(o) - u(o). Factor c(p).
4*(p - 72)*(p + 1)
Suppose 3*d - 153 = -144. Let j(w) = w + 12. Let i be j(-10). Factor -3*n**d + 3*n**4 + 6*n**3 + 2*n**i + 6*n**3 - 4*n**3.
n**2*(n + 1)*(3*n + 2)
Let y = 43 + -38. Factor -y*p + 16*p**4 + 2 - 31*p**4 - 2 - 25*p**2 - 35*p**3.
-5*p*(p + 1)**2*(3*p + 1)
Let t(c) be the first derivative of 11*c**3/4 - 105*c**2/8 + 9*c/2 + 23. Find n such that t(n) = 0.
2/11, 3
Let z(o) be the second derivative of 1/3*o**3 + o**2 - 35*o + 0 - 13/24*o**4 + 1/8*o**5. Solve z(u) = 0 for u.
-2/5, 1, 2
Let m(x) be the first derivative of -3*x**5/20 + x**4/4 - 18*x + 21. Let b(i) be the first derivative of m(i). Factor b(r).
-3*r**2*(r - 1)
Let o(s) be the third derivative of -s**7/1260 + s**5/45 - 4*s**3/9 + 42*s**2 + s. Factor o(f).
-(f - 2)**2*(f + 2)**2/6
Let a(h) be the third derivative of h**6/360 + h**5/20 + 23*h**4/72 + 5*h**3/6 - 200*h**2. Suppose a(r) = 0. What is r?
-5, -3, -1
Solve 8*h - 1/2*h**3 - 1/2*h**2 + 8 = 0.
-4, -1, 4
Let a be 62*((-25)/(-10) + -3). Let l be (a/(-9) - 2) + -1. Suppose -4/9 + 14/9*j + l*j**4 - 2/9*j**3 - 4/3*j**2 = 0. What is j?
-2, 1/2, 1
Let i = 56231/20 - 2811. Let t(l) be the first derivative of 1/8*l**2 + i*l**5 + 1/2*l**3 - 7/8*l**4 - 1 - 1/4*l - 1/8*l**6. Factor t(h).
-(h - 1)**4*(3*h + 1)/4
Factor -8*z**2 + 10 - 2*z**3 + 3*z**3 - 2 - z.
(z - 8)*(z - 1)*(z + 1)
Let t = -137 - -2467/18. Let g(s) be the second derivative of 0 - 4*s - t*s**3 + 0*s**2 + 1/36*s**4. Let g(o) = 0. What is o?
0, 1
Let a(o) be the third derivative of -o**5/60 - o**4/8 + 14*o**3/3 + 133*o**2. Factor a(y).
-(y - 4)*(y + 7)
Factor -15*q**2 - 2523 + 29*q**2 - 17*q**2 + 174*q.
-3*(q - 29)**2
Let w(q) be the first derivative of -q**6/135 + q**5/30 + 8*q - 14. Let l(b) be the first derivative of w(b). Factor l(f).
-2*f**3*(f - 3)/9
Suppose -3*n = -12*n + 72. Suppose -2*y = 2*k - 8, -2*k - n + 1 = -3*y. Suppose 8/7 + 16/7*u + 10/7*u**2 + 2/7*u**y = 0. Calculate u.
-2, -1
Suppose 0*i + g = 5*i - 30, 3*g = -15. Let q be 5 - 24/i - 6/(-70). Determine n, given that 0*n**2 - q*n**3 + 0 + 2/7*n = 0.
-1, 0, 1
Let x = 22 - 10. Factor 10 + 25*k**2 - 21*k - x*k + 68*k.
5*(k + 1)*(5*k + 2)
Suppose 675*c - 364*c + 64 = 343*c. Factor -15 + 5/2*h**c + 5/2*h.
5*(h - 2)*(h + 3)/2
Let h(g) be the second derivative of 1/5*g**5 + 3/35*g**7 + 1/5*g**4 - 1/5*g**2 + 0 + 11*g - 7/25*g**6 - 1/5*g**3. Solve h(k) = 0 for k.
-1/3, 1
Let f = -48083/4 - -12023. Factor f*z - 3/4*z**2 + 3.
-3*(z - 4)*(z + 1)/4
Let n(p) = p**3 + 28*p**2 + 27*p + 3. Let s be n(-27). Let d(w) be the first derivative of 3/4*w**4 + s*w + 5 - w**3 - 3/2*w**2. What is t in d(t) = 0?
-1, 1
Let x be 1 - -1*8/(-10). Let t be (63/84)/((-15)/(-12)). Solve -t*k**3 - 1/5*k**4 - x*k + 0 - 3/5*k**2 = 0.
-1, 0
Let f(w) = 0*w - w**2 - 5 + 3 - 5*w. Let r be f(-3). Solve 6*o**2 - 3*o**2 + 4*o**3 - o**3 - 6*o**3 + 3*o - 3*o**r = 0 for o.
-1, 0, 1
Let f(u) be the second derivative of 0*u**3 + 0*u**4 + 0 - 1/200*u**5 + 0*u**2 - 14*u. Determine q so that f(q) = 0.
0
Suppose -336 = 6*o + 696. Let v = o + 1206/7. Determine n, given that -50/7 - v*n**2 - 20/7*n = 0.
-5
Let f(i) be the first derivative of i**4/26 + 32*i**3/39 + 77*i**2/13 + 196*i/13 + 143. Factor f(a).
2*(a + 2)*(a + 7)**2/13
Let a(s) be the third derivative of -s**7/140 + s**6/10 - s**5/8 - 25*s**4/8 - 66*s**2. Solve a(u) = 0.
-2, 0, 5
Determine d so that 1280 - 160*d**2 - 13024*d**4 + 4*d + 13029*d**4 - 4*d = 0.
-4, 4
Factor 493 + 493 + 491 - 1469 - 28*r - 16*r**2.
-4*(r + 2)*(4*r - 1)
Suppose 29*z - 78 - 67 = 0. Let d(a) be the first derivative of a**2 - 8/3*a**3 + z + 3*a**4 + 1/3*a**6 + 0*a - 8/5*a**5. Suppose d(n) = 0. Calculate n.
0, 1
Factor 22*x + 28*x - 63*x + x**3 + 5*x**2 + 7.
(x - 1)**2*(x + 7)
Factor -41*n**2 + 12 + 34*n - 6*n**2 + 78 + n + 5*n**3 - 3*n**2.
5*(n - 9)*(n - 2)*(n + 1)
Let b(p) = -7*p**5 - 6*p**4 - 10*p**3 - 8*p**2 - 15*p - 2. Let r(v) = -v**5 - v**4 - v**3 - v. Let y(i) = -3*b(i) + 24*r(i). Determine h so that y(h) = 0.
-1, 2
Let z = -5046 + 5050. Factor -32*m - 64/3 - 4/3*m**z - 4/3*m**2 + 8*m**3.
-4*(m - 4)**2*(m + 1)**2/3
Let r(p) be the first derivative of -p**7/315 + p**6/225 + p**5/150 - p**4/90 + 5*p + 2. Let u(x) be the first derivative of r(x). Factor u(v).
-2*v**2*(v - 1)**2*(v + 1)/15
Let b(r) be the first derivative of -r**5/25 - 3*r**4/20 + 2*r**3/15 + 6*r**2/5 + 8*r/5 - 6. Factor b(p).
-(p - 2)*(p + 1)*(p + 2)**2/5
Let u = -5003 + 5003. Solve 0*a - 2/7*a**3 + u + 0*a**2 = 0.
0
Solve -1/10*p**4 - 3/10*p**2 + 2/5*p - 2/5*p**3 + 2/5 = 0.
-2, -1, 1
Let y(q) = -7*q**2 + 432*q - 11655. Let a(x) = 20*x**2 - 1296*x + 34968. Let k(o) = -3*a(o) - 8*y(o). Suppose k(j) = 0. What is j?
54
Let c(h) = -3*h**4 + 51*h**3 + 94*h**2 - 4. Let r(z) = 7*z**4 - 154*z**3 - 281*z**2 + 11. Let p(g) = 11*c(g) + 4*r(g). Suppose p(x) = 0. Calculate x.
-9, -2, 0
Suppose r - 5 = -2*i, -6*r + r - i = -16. Find g such that 14*g**r - 13*g**3 - 13*g**3 - 8*g**5 + 2*g**2 + 18*g**4 = 0.
0, 1/4, 1
Let r(f) be the first derivative of 7/20*f**5 + 0*f**3 + 0*f + 1/4*f**4 - f**2 + 1. Let q(l) be the second derivative of r(l). Factor q(s).
3*s*(7*s + 2)
What is q in -152*q**3 + 19*q**2 - 175*q**2 + 48*q**5 - 16*q - 5*q**4 + 10*q**4 + 16 + 15*q**4 = 0?
-1, -2/3, 1/4, 2
Let n be (-2 - (0 + 0))/(80/840*-7). Factor -p + 0*p**2 + 1/3*p**n + 2/3.
(p - 1)**2*(p + 2)/3
Suppose 5*f - 4*m - 14 = 8, 0 = -3*f + 4*m + 10. Find k, given that -k**3 + 21*k + 16*k**3 - 6 - f*k**2 + 18*k**4 - 21*k**2 - 21*k**4 = 0.
1, 2
Let m(n) = -30*n**4 + 16*n**3 - 10*n**2 - 6*n. Let a(k) = 90*k**4 - 49*k**3 + 29*k**2 + 17*k. Let i(g) = 6*a(g) + 17*m(g). Determine q, given that i(q) = 0.
0, 1/3, 2/5
Let m(u) be the first derivative of -8/7*u**2 + 8 + 32/7*u + 2/21*u**3. Let m(y) = 0. Calculate y.
4
What is y in -4/13*y**2 + 4/13 + 2/13*y - 2/13*y**3 = 0?
-2, -1, 1
Suppose -2*w - 4 = 2*u, -5*u - 4*w + 2*w = -2. Find b, given that -106*b - b**3 - u + 210*b - 101*b + 0 = 0.
-2, 1
Suppose -2*x = 2*s - 6, -3*x = -2*s - 3 - 11. Determine u, given that -104*u**3 - 288*u**2 + 108 + 5*u**x + 0*u**4 + u**4 - 216*u - 18*u**4 = 0.
-3, 1/3
Let 8/3*x**3 + 4/3*x*