- c**2 - 12 + 7*c + 8*c. Let m(h) = w(h) - 2*x(h). Factor m(g).
-3*(g - 2)**2
Let p be (-118 - -114) + (-18)/(-4). Let a(s) be the second derivative of -1/8*s**4 + p*s**3 + 0*s**2 + 0 - 9*s. Let a(q) = 0. Calculate q.
0, 2
Let k be (600 - 599)/(2/4). Suppose y**5 + 7/3*y**4 - 1/3*y**3 - 7/3*y**k + 0 - 2/3*y = 0. What is y?
-2, -1, -1/3, 0, 1
Let r(v) be the second derivative of -3*v**5/80 + 15*v**4/32 + 9*v**3/16 - 3*v**2/2 + 47*v. Factor r(u).
-3*(u - 8)*(u + 1)*(2*u - 1)/8
Let w(t) be the first derivative of -t**3/15 - 9*t**2/10 + 52*t/5 - 120. Factor w(i).
-(i - 4)*(i + 13)/5
Let u(y) be the second derivative of y**10/60480 - y**9/10080 + y**8/4480 - y**7/5040 + y**4 - 13*y. Let o(b) be the third derivative of u(b). Factor o(r).
r**2*(r - 1)**3/2
Let t = 17713/14164 - 2/3541. Factor -1/4*y**5 - y**4 + 1/2 - y**3 + 1/2*y**2 + t*y.
-(y - 1)*(y + 1)**3*(y + 2)/4
Suppose -3*d = 15*d - 54. Let c(x) be the first derivative of -1/8*x**4 + 0*x**2 + 1/6*x**d + 2 + 0*x. Let c(b) = 0. What is b?
0, 1
Let m(q) be the second derivative of -q**9/22680 + q**8/5040 - q**7/3780 + 5*q**4/6 + 5*q. Let o(b) be the third derivative of m(b). Factor o(h).
-2*h**2*(h - 1)**2/3
Factor -1/7*h**2 - 5/7*h**3 - h**4 - 3/7*h**5 + 0*h + 0.
-h**2*(h + 1)**2*(3*h + 1)/7
Let t be 3 + (-2)/(7 - 3)*-66. Suppose o + 34 = t. Determine x so that -2/7*x**o + 2/7*x + 0 = 0.
0, 1
Factor 74/19 - 4*u + 2/19*u**2.
2*(u - 37)*(u - 1)/19
Let d be 10/165*11*11022/(-14). Let j = -524 - d. Factor -2*k + j - 2/7*k**3 + 10/7*k**2.
-2*(k - 3)*(k - 1)**2/7
Let f(b) = 3 - 10*b - 1 + 3*b**2 + 6*b**2 + b**3 + 0*b**3. Let t be f(-10). Let c + 2*c + 3*c**t - 2*c**2 = 0. Calculate c.
-3, 0
Let c = 4736 - 4733. Factor -8/5*r**c + 2/5*r**2 + 0 - 4/5*r**5 + 0*r + 2*r**4.
-2*r**2*(r - 1)**2*(2*r - 1)/5
Let l = 2081/11 - 189. Factor 30/11*i**3 + 8/11*i**5 - 14/11*i**2 - 26/11*i**4 + l*i + 0.
2*i*(i - 1)**3*(4*i - 1)/11
Let d = -2262 + 2264. Solve -3/8*x**d + 3/4*x - 3/8 = 0 for x.
1
Let g(n) be the third derivative of n**8/84 - 29*n**7/210 + 17*n**6/40 - 31*n**5/60 + 5*n**4/24 + 204*n**2. Factor g(k).
k*(k - 5)*(k - 1)**2*(4*k - 1)
Let t(l) be the first derivative of l**4/4 - 5*l**3 - 9*l**2 + 32*l - 161. Factor t(d).
(d - 16)*(d - 1)*(d + 2)
Factor -1/2*o**3 - 3 - 2*o**2 + 11/2*o.
-(o - 1)**2*(o + 6)/2
Let s = 33385/7 - 4769. Factor 2/7*z + 0 + 2/7*z**2 - s*z**4 - 2/7*z**3.
-2*z*(z - 1)*(z + 1)**2/7
Let z(u) be the first derivative of -5*u**4/4 + 20*u**3 - 120*u**2 + 320*u - 71. Determine i, given that z(i) = 0.
4
Let j(a) = -6*a**2 - 6*a. Let u be j(0). Factor 0*c**3 - 7/6*c**5 + 0 + 1/3*c**4 + 0*c + u*c**2.
-c**4*(7*c - 2)/6
Let y(n) = 36*n - 360. Let s be y(10). Let d(f) be the second derivative of -1/10*f**6 + 0*f**3 + 0*f**5 + 1/4*f**4 - 2*f + 0 + s*f**2. Factor d(a).
-3*a**2*(a - 1)*(a + 1)
Let g(c) be the first derivative of c**8/1512 - c**7/315 + c**6/180 - c**5/270 - 11*c**2/2 - 3. Let q(o) be the second derivative of g(o). Factor q(f).
2*f**2*(f - 1)**3/9
Let m(g) be the first derivative of g**7/42 - g**6/10 + 3*g**5/20 - g**4/12 - 4*g - 10. Let l(j) be the first derivative of m(j). Let l(f) = 0. Calculate f.
0, 1
Factor -45*v**3 + 49*v**3 - 42*v - 78*v**2 + 31 + 9.
2*(v - 20)*(v + 1)*(2*v - 1)
Suppose 0 = -63*t + 67*t - 16. Suppose -2*d + 2 = -t. Factor -3/2*b**d - 3/2*b + 0 + 3*b**2.
-3*b*(b - 1)**2/2
Let j(t) be the second derivative of -t**4/15 - 2*t**3 - 88*t**2/5 - 230*t. Determine w, given that j(w) = 0.
-11, -4
Let t(u) be the first derivative of -u**4/12 - 8*u**3/9 - 7*u**2/2 - 6*u - 100. Determine k, given that t(k) = 0.
-3, -2
Let y(c) = -8*c**3 + 58*c**2 - 35*c - 91. Let d(w) = 12*w**3 - 88*w**2 + 52*w + 136. Let p(b) = -5*d(b) - 8*y(b). Factor p(j).
4*(j - 4)*(j - 3)*(j + 1)
Let r(y) = 8*y**5 + 66*y**4 + 102*y**3 - 37*y**2 - 112*y - 31. Let t(c) = c**5 + c**2 + c + 1. Let z(x) = -r(x) - t(x). Find s, given that z(s) = 0.
-5, -2, -1, -1/3, 1
Let b be (4 + -9 - -12)*-1. Let d = b - -9. Factor 0 + 0*j + 2/5*j**d - 2/5*j**3.
-2*j**2*(j - 1)/5
Suppose -232 = -3*q - q - 4*z, 3*q - 174 = -2*z. Let w be (-33)/88 + q/112. Solve 0*o**2 + 0*o + 1/7*o**5 + 0*o**4 - w*o**3 + 0 = 0.
-1, 0, 1
Suppose 10 = 5*q - 0*q. What is w in w**4 - 5*w**2 + 10*w + w**q + 3*w**4 - 2*w - 8*w**3 = 0?
-1, 0, 1, 2
Let u(i) be the second derivative of -1/20*i**6 + 0*i**4 - 4*i - 3/80*i**5 + 0 + 0*i**2 - 1/56*i**7 + 0*i**3. Suppose u(f) = 0. Calculate f.
-1, 0
Let r(y) = 2*y**2 - 7*y + 31. Let a(u) = -u**2 + 4*u - 15. Let x(z) = -14*a(z) - 6*r(z). Factor x(p).
2*(p - 4)*(p - 3)
What is v in -10*v**2 + 35*v + 8*v + 8*v**2 + v - 42 = 0?
1, 21
Suppose 5*r - 5*j - 41 = r, -r - 5*j = 21. Suppose -2*s = -r*s + 4. Factor 28*a + 3*a**s - 28*a - 3.
3*(a - 1)*(a + 1)
What is j in 16/3*j - 46/9*j**3 - 94/9*j**2 + 22/9*j**4 - 2/9*j**5 + 8 = 0?
-1, 1, 6
Let u(q) be the third derivative of q**5/20 + q**4/8 - 3*q**3 + 397*q**2. Find d such that u(d) = 0.
-3, 2
Let l(q) = 4*q**3 + 12*q**2 - 23. Let t(h) = 2*h**3 + 6*h**2 - 11. Let s = -9 - -3. Let n(r) = s*l(r) + 14*t(r). Factor n(d).
4*(d - 1)*(d + 2)**2
Let j(p) = 52 + 3*p + 0*p**2 - 2*p + p**2. Let n be j(0). Factor a**2 - 5*a**3 - a**4 + 4 + 0*a**4 - 51*a**5 + n*a**5 + 8*a.
(a - 2)**2*(a + 1)**3
Let p(r) be the first derivative of -r**9/13608 + r**8/7560 + r**7/1890 - r**3/3 + 15. Let y(z) be the third derivative of p(z). Factor y(m).
-2*m**3*(m - 2)*(m + 1)/9
Let o(b) be the third derivative of b**8/336 + b**7/6 + 44*b**6/15 + 64*b**5/5 - 81*b**2 - b. Factor o(a).
a**2*(a + 3)*(a + 16)**2
Let m(t) be the second derivative of -t**5/80 + 19*t**4/48 - 33*t**3/8 + 81*t**2/8 - 46*t. Solve m(f) = 0 for f.
1, 9
Let s(z) = -6*z**2 - 14*z + 4. Let n(k) = k**3 - 5*k**2 - 11*k + 3. Let f(y) = 4*n(y) - 3*s(y). Factor f(x).
2*x*(x - 1)*(2*x + 1)
Suppose -11 = x - 5*j, 7 = -3*x + 2*j + 26. Solve -x + 10*u**3 - 8*u**2 - 18*u**3 - u**4 - 24*u + 0*u**2 - 14*u**2 = 0 for u.
-3, -1
Let x(l) be the second derivative of -l**4/18 - l**3/3 - 2*l**2/3 - 27*l + 1. Find r, given that x(r) = 0.
-2, -1
Let f(a) = a**3 + 4*a**2 + a + 7. Let w be f(-4). Factor -17*k**3 - 7 - 25 + 24*k**3 - 12*k**w - k**4 + 6*k**2 + 32*k.
-(k - 2)*(k - 1)*(k + 4)**2
Factor 125 + 3280*w - 3*w**2 - 2*w**2 - 3160*w.
-5*(w - 25)*(w + 1)
Let u(f) be the first derivative of 9*f - 1/6*f**4 + 1/3*f**3 + 0*f**2 - 1. Let d(w) be the first derivative of u(w). Let d(j) = 0. Calculate j.
0, 1
Let v(h) be the first derivative of 0*h + 1/780*h**6 + 0*h**5 + 0*h**3 - 1/156*h**4 + 1 - 1/2*h**2. Let o(g) be the second derivative of v(g). Factor o(n).
2*n*(n - 1)*(n + 1)/13
Let a be 76/(-285)*(-70)/28. What is m in -a - m - 1/3*m**2 = 0?
-2, -1
Let o(b) be the first derivative of -b**3/18 + 13*b**2/3 + 53*b/6 + 134. Factor o(u).
-(u - 53)*(u + 1)/6
Let q(h) be the first derivative of 343*h**6/13 + 13328*h**5/65 - 3815*h**4/26 - 12*h**3 + 412*h**2/13 - 112*h/13 - 308. Let q(p) = 0. Calculate p.
-7, -1/3, 2/7
Let j = 19 - 16. Let b(n) = -44*n**2 + j*n - 2*n**3 - 7*n - 8*n + 60 + 6*n**3. Let d(h) = h**2 + h - 1. Let g(w) = -b(w) - 24*d(w). Solve g(s) = 0 for s.
-1, 3
Let i(j) be the first derivative of 2 + 1/9*j**3 + 0*j**2 - 1/12*j**4 + 0*j. Factor i(y).
-y**2*(y - 1)/3
Let g = 942 + -940. Factor -3/5*j**4 + 81/5*j**g + 87/5*j + 6 + 21/5*j**3.
-3*(j - 10)*(j + 1)**3/5
Let w be (55/(-30) - (-3)/(-18))*-1. Factor -2*g**4 + 0*g**2 + 87*g**5 + w*g**3 - 89*g**5 + 2*g**2.
-2*g**2*(g - 1)*(g + 1)**2
Suppose -3*n - 22 = -3*h - h, h + 2*n = 0. Let t be ((-14)/70)/(1/17) + h. Factor 3/5*o**2 - 6/5*o + t.
3*(o - 1)**2/5
Let n(f) be the second derivative of -f**8/280 + f**7/105 - f**6/180 + 4*f**3/3 + 9*f. Let y(x) be the second derivative of n(x). Factor y(t).
-2*t**2*(t - 1)*(3*t - 1)
Let y(a) be the third derivative of -a**5/60 - 7*a**4/24 - 5*a**3/3 - 12*a**2. Let v be y(-4). Factor u**4 + 2/3*u - 4/3*u**3 - 1/3*u**v + 0.
u*(u - 1)**2*(3*u + 2)/3
Find z, given that 21/2 - 17/4*z + 1/4*z**2 = 0.
3, 14
Let p(o) = 6*o**2 - 2*o - 1. Let j be p(-2). Factor -3*v**3 - 18*v**2 - j*v - 15 - 4 + 7.
-3*(v + 1)**2*(v + 4)
Let d(u) = -11*u**3 + 84*u**2 + 308*u - 78. Let p(l) = 10*l**3 - 86*l**2 - 310*l + 80. Let v(g) = 2*d(g) + 3*p(g). Determine t so that v(t) = 0.
-3, 1/4, 14
Let t = -85579/3 + 28541. Factor 0 + 4*z**4 + 16/3*z + 32/3*z**2 - t*z**3.
4*z*(z -