*p**2 - m*p - 6*p - 43.
-4*(p - 1)*(p + 3)
Suppose -133*v = -144*v + 22. Let m(q) be the first derivative of 0*q - 1/3*q**3 + v + 3/2*q**2. Solve m(b) = 0.
0, 3
Factor 0 - 29/2*q + 1/2*q**2.
q*(q - 29)/2
Factor 102/5*p**3 + 0 + 8/5*p - 208/5*p**2.
2*p*(p - 2)*(51*p - 2)/5
Let m(u) = 11*u**2 - 118*u + 1562. Let o(y) = 41*y**2 - 470*y + 6250. Let h(x) = -22*m(x) + 6*o(x). Let h(j) = 0. What is j?
28
Let q(g) be the second derivative of -5/6*g**3 + g + 1/240*g**5 + 1/1440*g**6 + 0*g**2 + 1/96*g**4 + 0. Let l(b) be the second derivative of q(b). Factor l(y).
(y + 1)**2/4
Let u(s) = 2*s**3 + 2*s - 1. Let v(m) = 14*m**3 + 86*m**2 + 178*m + 76. Let z(o) = 12*u(o) - 2*v(o). Factor z(k).
-4*(k + 1)**2*(k + 41)
Let y(t) be the second derivative of -1/10*t**5 + 0*t**2 + 1/8*t**4 + 1/60*t**6 - 14*t + 0*t**3 + 0. Determine k, given that y(k) = 0.
0, 1, 3
Let -3*p**3 + 0 + 57/8*p**2 + 3/8*p**4 - 9/2*p = 0. What is p?
0, 1, 3, 4
Factor 366*o + 0*o**3 + 3*o**3 + o**3 - 370*o - 12 + 12*o**2.
4*(o - 1)*(o + 1)*(o + 3)
Suppose -x + 10 = x. Suppose -2*u + 1 + x = 0. Factor 9*h**5 + 24*h**2 - 4*h - 12*h**4 - 6*h**3 + h**u - 12*h**2.
h*(h - 1)*(h + 1)*(3*h - 2)**2
Let o be (-33)/9*42*4/8. Let y be -3 + 0 - (7 + 803/o). Factor 0 + 6/7*w - 3/7*w**3 + y*w**2.
-3*w*(w - 2)*(w + 1)/7
Let g(l) be the second derivative of 0 - 1/4*l**4 - 4*l**3 - 24*l**2 + 3*l. Let g(y) = 0. What is y?
-4
Determine q so that -116*q**3 + 185*q**3 + 266*q**2 - 6*q**4 + 73*q**3 + 4*q**4 + 2*q**5 + 32*q**4 + 216*q + 64 = 0.
-8, -4, -1
Let z(t) be the second derivative of 0 + 25/2*t**3 - 2*t + 0*t**2 + 3/20*t**5 - 5/2*t**4. Determine i so that z(i) = 0.
0, 5
Factor -4*t**2 - 29*t + 10*t + 8*t + 15*t + t**3.
t*(t - 2)**2
Let t = -9205 + 174897/19. Suppose -2/19 - 4/19*r - t*r**2 = 0. Calculate r.
-1
Let o(n) = -n**3 + 4*n**2 - 4*n + 3. Let j be o(3). Suppose -2*z + z = j. Solve v + 0*v**2 - v**2 + z*v**2 = 0 for v.
0, 1
Let m be (8/(-6))/(8/(-12)). Factor -20*g**4 - 1539*g**3 + 2 - m - 25*g**2 + 1644*g**3.
-5*g**2*(g - 5)*(4*g - 1)
Let d(h) be the first derivative of 5*h**5/4 + 5*h**4/4 - 10*h**3 + 10*h**2 + 8*h + 13. Let k(q) be the first derivative of d(q). Factor k(l).
5*(l - 1)*(l + 2)*(5*l - 2)
Solve -34*g + 4*g - 12*g**2 + 0*g - 6*g**2 + 2*g**2 - 2*g**3 = 0.
-5, -3, 0
Let x = 2213/8355 - -1/557. Let y(o) be the second derivative of -1/50*o**5 + 0*o**2 + 0 + x*o**3 + 4*o + 0*o**4. Solve y(t) = 0 for t.
-2, 0, 2
Let n(m) = 6*m - 12*m**2 + 5 + 2*m**2 - m + 12*m**2. Let s(v) = v**2 + 2*v + 2. Let a(z) = -2*n(z) + 5*s(z). Find y, given that a(y) = 0.
0
Let m be ((20/6)/2)/(5/6). Let f(u) be the third derivative of 2*u**m + 1/240*u**5 + 0*u - 1/24*u**3 + 0 + 0*u**4. Suppose f(t) = 0. What is t?
-1, 1
Factor -16 + 35*r**4 - 25*r**3 - 20*r**4 + 16 - 80*r**2 + 60*r.
5*r*(r - 3)*(r + 2)*(3*r - 2)
Factor 21*l**3 + 0*l**4 - 17*l**3 + l**4.
l**3*(l + 4)
Let q(j) = 54*j - 3184. Let f be q(59). Suppose 32/3 + 4*b**3 + 2/3*b**f - 16*b + 2/3*b**4 = 0. What is b?
-4, 1
Factor 18*m**2 + 18*m**2 - 38*m**2 + 2*m**4.
2*m**2*(m - 1)*(m + 1)
Let l be 0/2 - (2 + -20 + 2). Solve -98*o**4 - 22*o**3 + 24*o - 65*o**3 - 74*o**3 - 133*o**3 - 188*o**2 + l = 0.
-2, -1, -2/7, 2/7
Suppose 10*h - 101 = -101. Factor 0*q + 0 + 1/2*q**3 + 0*q**2 - 1/2*q**5 + h*q**4.
-q**3*(q - 1)*(q + 1)/2
Let c(i) be the third derivative of i**5/270 + 2*i**4/27 - i**3/3 + 92*i**2 + 2*i. Factor c(p).
2*(p - 1)*(p + 9)/9
Let s = -2777 + 13887/5. Let i be 0/4*(-1)/(-1). Factor s*o**2 + i - 2/5*o.
2*o*(o - 1)/5
Let p(t) be the second derivative of -t**4/42 + 13*t**3/21 + 2*t**2 - 323*t. Solve p(y) = 0 for y.
-1, 14
Let s(a) be the second derivative of a**8/9240 - a**6/660 - a**5/330 - a**3/2 - 8*a. Let w(n) be the second derivative of s(n). Factor w(g).
2*g*(g - 2)*(g + 1)**2/11
Factor -20*a + 0*a**2 + 4 + 0*a**2 + 15*a**2 + 0 + 1.
5*(a - 1)*(3*a - 1)
Let z(m) be the third derivative of 0 - 4/15*m**5 + 1/30*m**6 + 0*m - 10*m**2 - 4/3*m**3 + 5/6*m**4. Find k, given that z(k) = 0.
1, 2
Let d(n) be the first derivative of n**4/28 - 16*n**3/21 + 120. What is i in d(i) = 0?
0, 16
Suppose -144*p + 0*p**2 - 84*p + 60*p + 2*p**2 + 3528 = 0. What is p?
42
Let b be 5/((2 + -3)*(-395)/237). Factor 6/5*p**2 + 0*p - 8/5 + 2/5*p**b.
2*(p - 1)*(p + 2)**2/5
Let j(y) be the third derivative of y**7/2520 - y**6/360 - y**5/40 - y**4/8 - 23*y**2. Let u(p) be the second derivative of j(p). Factor u(c).
(c - 3)*(c + 1)
Let x(h) be the first derivative of 3*h**4/4 - 29*h**3 + 39*h**2 + 168*h + 302. Solve x(u) = 0.
-1, 2, 28
Let n = -109/8 + 455/24. Factor 1/3*l**2 + n - 8/3*l.
(l - 4)**2/3
Let c = -9/44 + 89/220. Solve 0*z + z**3 + 0 - c*z**2 - 4/5*z**4 = 0 for z.
0, 1/4, 1
Factor 0 + 0*v + 2/7*v**3 - 2/7*v**4 + 4/7*v**2.
-2*v**2*(v - 2)*(v + 1)/7
Let k(b) be the third derivative of b**10/75600 + b**9/25200 - b**7/12600 + b**4/24 - 11*b**2. Let h(f) be the second derivative of k(f). Factor h(d).
d**2*(d + 1)**2*(2*d - 1)/5
Let p(r) be the first derivative of -29 - 1/4*r**3 + 1/16*r**4 + r + 0*r**2. Let p(k) = 0. What is k?
-1, 2
Suppose 3*s = -4*m + 6, -4*s + 8 + 0 = -2*m. What is h in 2*h**s + 32 - 10*h + 2*h + 24*h = 0?
-4
Let z(y) be the second derivative of 2*y**7/21 - 4*y**6/15 - 3*y**5/5 - 28*y. Factor z(d).
4*d**3*(d - 3)*(d + 1)
Let 8/7*k**3 - 2/7*k**4 + 0 - 8/7*k + 2/7*k**2 = 0. What is k?
-1, 0, 1, 4
Let j(m) be the first derivative of m**6/480 + 11*m**5/240 + m**4/3 + 7*m**3/6 + 2*m**2 - 26. Let n(v) be the second derivative of j(v). What is k in n(k) = 0?
-7, -2
Find s such that 5/2*s**3 + 10 + 15*s**2 + 45/2*s = 0.
-4, -1
Let l(x) = -20*x + 1202. Let k be l(60). What is n in 2/3*n**3 - 10/3*n**k - 8/3 + 16/3*n = 0?
1, 2
Let -14/3*w + 148/15 - 2/15*w**2 = 0. Calculate w.
-37, 2
Let b(x) be the second derivative of -x**6/3600 - x**5/300 - x**4/60 + x**3/2 - 6*x. Let f(s) be the second derivative of b(s). Factor f(d).
-(d + 2)**2/10
Let o be (5/((-500)/(-56)))/(2832/1370). Let t = -1/236 + o. Solve 2/15*g**4 + 0*g + t*g**3 + 2/15*g**2 + 0 = 0.
-1, 0
Let z(n) be the third derivative of n**6/240 + 3*n**5/80 - 7*n**3/6 - 12*n**2. Let g(w) be the first derivative of z(w). Factor g(k).
3*k*(k + 3)/2
Let k(n) be the first derivative of 2*n**3/15 - n**2 + 121. Let k(b) = 0. What is b?
0, 5
Let g(i) = i**3 + 4*i**2 - i - 1. Suppose 2 = -x - 2. Let s be g(x). Find w such that 3*w**4 + 4*w**2 + 9*w**s + 3*w - 6*w**4 - 13*w**2 = 0.
0, 1
Let m(j) be the second derivative of j**6/360 - j**5/120 + 5*j**3/3 - 7*j. Let g(o) be the second derivative of m(o). Suppose g(v) = 0. Calculate v.
0, 1
Let v(z) be the third derivative of z**5/135 - 5*z**4/6 + 88*z**3/27 + 436*z**2. Factor v(d).
4*(d - 44)*(d - 1)/9
Factor 50/3 + 20/3*v + 2/3*v**2.
2*(v + 5)**2/3
Suppose 5*v = 1 + 29. Let f(c) be the first derivative of 2*c - 1/2*c**4 - 2/3*c**3 + c**2 - v. Determine r so that f(r) = 0.
-1, 1
Let x(r) be the second derivative of -3/4*r**2 + 20*r + 3/20*r**5 + 0 + 5/6*r**3 - 1/60*r**6 - 1/2*r**4. Let x(t) = 0. What is t?
1, 3
Let u(x) be the second derivative of -x**6/40 + x**5/20 + x**4/8 - x**3/2 - 19*x**2/2 + 16*x. Let z(w) be the first derivative of u(w). Factor z(f).
-3*(f - 1)**2*(f + 1)
Let w(n) be the second derivative of -n**7/2520 + n**6/240 - n**5/60 - 29*n**4/12 + 3*n. Let i(g) be the third derivative of w(g). Find l such that i(l) = 0.
1, 2
Suppose -70*o = -58*o - 24. Let t(i) be the first derivative of -5/6*i**6 - 11 + 0*i + i**5 + 5/4*i**4 - 5/3*i**3 + 0*i**o. Determine n so that t(n) = 0.
-1, 0, 1
Let k(r) be the second derivative of -r**3/6 + 13*r**2/2 - 48*r. Let c be k(10). Find h, given that 2/5 - 2/5*h + 2/5*h**c - 2/5*h**2 = 0.
-1, 1
Let o(c) be the first derivative of -3*c**5/5 - 633*c**4/4 - 14910*c**3 - 536550*c**2 - 1029000*c + 8. Factor o(u).
-3*(u + 1)*(u + 70)**3
Let a(s) be the second derivative of s**6/285 + 12*s**5/95 + 199*s**4/114 + 208*s**3/19 + 448*s**2/19 + 163*s. Determine q, given that a(q) = 0.
-8, -7, -1
Let t(u) = -u - 63. Let k be t(-65). Factor 1 - 4/3*j**3 + 7/3*j**k + 14/3*j.
-(j - 3)*(j + 1)*(4*j + 1)/3
Let v(m) be the third derivative of 3*m**2 + 0*m**3 - 19/60*m**6 + 1/15*m**5 + 1/4*m**4 + 2/35*m**7 + 0 - 4*m. Let v(n) = 0. Calculate n.
-1/3, 0, 1/2, 3
Suppose m = -3*m + 52. Factor -15*t**3 - 9*t**2 + 9*t - m*t + 10*t.
-3*t*(t + 1)*(5