**2 - 13 - 1/66*s**4 - 1/66*s**3. Factor i(d).
-(d - 1)**3*(d + 1)**2/11
Factor 12/5 + 23/10*j - 1/10*j**2.
-(j - 24)*(j + 1)/10
Let g(o) = -o**4 - 6*o**3 + 24*o**2 - 11*o. Let h(i) = 3*i**2 - i. Let m(s) = g(s) - 3*h(s). Let m(v) = 0. What is v?
-8, 0, 1
Let t(o) = o + 11. Let y be t(-7). Suppose -8 = -y*u - 0*u. Factor 2*q**3 + 4*q + 3*q**3 + u*q**2 - 4*q**3 - 3*q**3.
-2*q*(q - 2)*(q + 1)
Let y(z) be the second derivative of z**5/40 - 3*z**4/8 + 2*z**3 - 5*z**2 - 6*z - 3. Factor y(q).
(q - 5)*(q - 2)**2/2
Let h(r) = -619*r**4 + 8012*r**3 + 1831*r**2 - 2528*r - 780. Let j(b) = b**4 + 2*b**3 + b**2 + 2*b. Let o(l) = h(l) - 6*j(l). Determine z so that o(z) = 0.
-2/5, 3/5, 13
Solve 4 - 1/2*m**2 - 7/2*m = 0 for m.
-8, 1
Let i(j) be the third derivative of j**11/8316 - j**10/5400 + j**9/15120 - j**5/5 - 13*j**2. Let r(a) be the third derivative of i(a). Factor r(l).
4*l**3*(2*l - 1)*(5*l - 1)
Factor 39*h + 54*h**2 - 3*h**5 - 91*h + 52*h + 24*h**4 - 63*h**3.
-3*h**2*(h - 3)**2*(h - 2)
Let d(y) be the first derivative of 3*y**3 + y**2/2 + 75. Find j such that d(j) = 0.
-1/9, 0
Let l(k) = 3*k**2 + 84*k - 669. Let w(h) = -2*h**2 - 85*h + 670. Suppose 2*a = -u - a + 3, 2*a + 14 = 2*u. Let q(b) = u*w(b) + 5*l(b). Factor q(m).
3*(m - 15)**2
Let c(o) be the second derivative of o**7/14 + o**6/10 - 3*o**5/20 - o**4/4 - 91*o. Let c(u) = 0. Calculate u.
-1, 0, 1
Suppose -2*k = r - 39, 2*k - 160 = -4*r + 14. Determine q, given that 59*q**2 + 52*q**4 + 20*q**4 + 27 + r*q**3 - 48*q**5 - 146*q**2 - 9*q = 0.
-3/4, 1
Let w(k) be the third derivative of k**5/27 - k**4/6 - 4*k**3/27 + 60*k**2. Factor w(b).
4*(b - 2)*(5*b + 1)/9
Let o = 9356 - 46778/5. What is m in 2/5*m - 2/5*m**3 + 0 + o*m**2 - 2/5*m**4 = 0?
-1, 0, 1
Let c be 1 + 2 + -6 + 8 + -4. Let k be 3 - (c - -5) - (0 + -13). What is h in 0*h - 8/3 - k*h**3 + 38/3*h**2 = 0?
-2/5, 2/3, 1
Solve -102/5*d**2 - 33/5*d + 0 - 108/5*d**3 - 42/5*d**4 - 3/5*d**5 = 0.
-11, -1, 0
Let q(i) = i**3 - 10*i**2 + 7*i + 19. Let k be q(8). Let f = -17 - k. Suppose -3*r**3 - 15*r**3 + 3*r**3 - 3*r**4 + 33*r**3 - 39*r**2 + f*r - 12 = 0. What is r?
1, 2
Let c(m) = -m**2 + 6*m - 3. Let z be c(2). What is t in 4 - 6*t**3 + z*t**3 + 2*t**2 - 6*t**2 - 3*t**3 + 4*t = 0?
-1, 1
Let x(g) be the third derivative of g**7/1365 - g**6/156 + 7*g**5/390 - g**4/52 + 57*g**2. Factor x(i).
2*i*(i - 3)*(i - 1)**2/13
Let i(t) be the second derivative of -t**4/30 - 44*t**3/15 - 484*t**2/5 - 77*t. Factor i(r).
-2*(r + 22)**2/5
Let a(i) be the third derivative of i**8/336 + i**7/140 + i**6/240 - i**2 - 35*i. Factor a(u).
u**3*(u + 1)*(2*u + 1)/2
Suppose -4/9*l - 16/9 + 16/9*l**2 + 4/9*l**3 = 0. What is l?
-4, -1, 1
Let p(h) = -13*h + 134. Let t be p(10). Let o(d) be the third derivative of 0*d**5 + 0*d + 0*d**3 + 0*d**t + 0 + d**2 + 1/300*d**6. Factor o(n).
2*n**3/5
Let l(w) be the second derivative of -1/6*w**4 - 2*w**2 + 0 + 7/6*w**3 + 9*w - 1/20*w**5. What is k in l(k) = 0?
-4, 1
Let l(b) = -b**3 + b**2 + b - 2. Let h(i) = -2*i**3 - 3*i**2 - 12*i + 94. Let p(t) = 2*h(t) - 6*l(t). Find x such that p(x) = 0.
-4, 5
Let p(x) = -15 - 5*x - 221*x**3 + 220*x**3 + 16*x**2 - 9*x. Let v be p(15). Determine q, given that -2/5 + v*q + 2/5*q**2 = 0.
-1, 1
Suppose -2 = -4*t + 18. Let n(h) = -7*h**3 + 7*h**2 - 5*h - 5. Let r(w) = -11*w**3 + 11*w**2 - 8*w - 8. Let p(o) = t*r(o) - 8*n(o). Solve p(j) = 0.
0, 1
Let u(l) be the second derivative of l**5/100 + l**4/10 + l**3/6 - 22*l + 1. Factor u(f).
f*(f + 1)*(f + 5)/5
Let a be (-4 - -5)/(3/3). Let l(n) = -6*n**2 + 31*n. Let h(d) = d**2 - d. Let g(v) = a*h(v) + l(v). Let g(s) = 0. What is s?
0, 6
Let j(v) = v**2 - 14*v - 3. Let k be j(15). Let n be (5/20)/(2/k). Factor 3*d - 3/2*d**3 + 0 - n*d**2.
-3*d*(d - 1)*(d + 2)/2
Suppose -31394*g = -31392*g. Determine n so that 1/2*n**2 + 0 - 1/2*n**3 + g*n = 0.
0, 1
Let j be (-74)/(-30) - (-46)/(-69). Let f = 321/70 + -39/14. Solve j*z**4 - 7/5*z**2 + f*z - 2/5 - 9/5*z**3 = 0.
-1, 1/3, 2/3, 1
Let v = -58864/1497 - 6/499. Let x = v - -40. Let 8/3 - 2*p**2 + x*p**3 + 0*p = 0. What is p?
-1, 2
Let w = 134 + -90. Let b = 398/9 - w. Factor -2/9*s**2 + b + 2/9*s - 2/9*s**3.
-2*(s - 1)*(s + 1)**2/9
Let h(c) = -c**5 - c**3 - c**2 - c. Let y be 18 - 1 - (-1 + -2). Let s(k) = -25*k**5 + 5*k**4 - 15*k**3 - 25*k**2 - 20*k. Let m(x) = y*h(x) - s(x). Factor m(g).
5*g**2*(g - 1)**2*(g + 1)
Let u(q) be the second derivative of -1/48*q**4 - 1/8*q**3 - 1/4*q**2 + 0 - 5*q. Suppose u(w) = 0. What is w?
-2, -1
Let k(g) be the second derivative of -2/3*g**3 + 0*g**2 + 1/6*g**4 - 3*g + 0. Factor k(n).
2*n*(n - 2)
Suppose 143 - 229 = -43*h. Factor 0 + 2/11*b**h - 2/11*b.
2*b*(b - 1)/11
Let j = 61 - 70. Let q be 38/9 - (-2)/j. Factor 2/7*d**q + 0 + 2/7*d**2 - 4/7*d**3 + 0*d.
2*d**2*(d - 1)**2/7
Solve 3*s**2 - 14 - 6*s + 114 - s**2 - s**2 - 14*s = 0.
10
Let t be 6 - (-2)/(-5 - -3). Suppose -p - 12 = -4*m, 1 = t*m + 3*p + 3. Factor -4*s**3 - 4*s**2 + 0*s**2 + 6 + 4*s - 2 + 0*s**m.
-4*(s - 1)*(s + 1)**2
Suppose 16 = 99*b - 97*b. Suppose -3*l - b*l = 0. Factor -1/3*t**2 + l*t + 0.
-t**2/3
Let b(h) be the second derivative of -h**6/90 + 11*h**5/15 - 175*h**4/12 + 49*h**3 + 8*h - 11. Determine w, given that b(w) = 0.
0, 2, 21
Let s(w) be the second derivative of w**4/12 - 23*w**3/2 + 67*w**2 + 253*w. What is f in s(f) = 0?
2, 67
Suppose -5*r + 2*j - 107 = -10*r, 0 = 5*r - j - 119. Let u = 28 - r. Factor -v**3 - 4*v**3 - 4*v**2 - u*v - 2*v**4 + 0*v**3 + 4*v.
-v*(v + 1)**2*(2*v + 1)
Let d = 26 + -21. Suppose d*i = r - 26, -5*r + 56 + 34 = -5*i. Factor -2*q - q**2 - 3*q - r - 3*q.
-(q + 4)**2
Let b be 686/30 - (-2)/15. Let m = b + -22. Suppose h**3 - 10*h + 2*h**3 - 5 - m + h = 0. Calculate h.
-1, 2
Determine r so that -5/4*r**5 + 0*r**2 + 0 + 0*r + 15/4*r**3 + 5/2*r**4 = 0.
-1, 0, 3
Suppose y = -2*n + 7, 3*y = -4*n - 0*y + 13. Let z(w) be the third derivative of 0*w + 0*w**n + 0 + 1/14*w**3 - 1/140*w**5 - 5*w**2. Factor z(x).
-3*(x - 1)*(x + 1)/7
Let l be -5*24/(-20) - 25. Let j be 8/10 - (1216/120)/l. Factor j*r + 16/3*r**2 - 20/3*r**3 + 0.
-4*r*(r - 1)*(5*r + 1)/3
Let y be (-99)/(-44) - 2 - 15/(-4). Let d(p) be the second derivative of -1/12*p**y + 0*p**2 + 1/20*p**5 - 1/3*p**3 - p + 0. Factor d(g).
g*(g - 2)*(g + 1)
Let i(l) be the third derivative of -l**6/270 - 4*l**5/135 + 5*l**4/54 + 34*l**2. Determine g so that i(g) = 0.
-5, 0, 1
Let p be ((-24)/44)/(((-81)/(-22))/(-9)). Factor -p*b**3 + 8/3*b**2 + 0 - 4/3*b.
-4*b*(b - 1)**2/3
Suppose t + 2*t + r = -4, 4*t - 12 = 3*r. Let k(u) be the third derivative of 5*u**2 + 0 + 0*u**4 + 0*u + 1/20*u**5 + t*u**3. Solve k(n) = 0.
0
Let z(t) be the first derivative of 3*t**4 + t**3 + 0*t**2 - 48/5*t**5 + 0*t + 29 - 32*t**6. Determine c so that z(c) = 0.
-1/4, 0, 1/4
Let r(k) = -k**3 + 15*k**2 - 13*k - 12. Let z be r(14). Find a such that -10*a**z - 4*a**5 + 8 - 3*a**5 - 4*a + 2*a**5 + a**3 + 6*a**5 + 4*a**4 = 0.
-2, 1
Let o(p) be the second derivative of -p**5/4 - 5*p**4/2 + 15*p**3/2 + 35*p**2 - 2*p + 96. Factor o(y).
-5*(y - 2)*(y + 1)*(y + 7)
Factor -16/3*m**4 + 2/3*m**5 - 16*m**2 + 44/3*m**3 + 6*m + 0.
2*m*(m - 3)**2*(m - 1)**2/3
Let x = 14 - 14. Factor -2*n + x*n**2 + n**2 + 0*n.
n*(n - 2)
Let u(z) be the second derivative of -z**4/18 + 11*z**3 + 100*z**2/3 - 64*z + 1. Determine n so that u(n) = 0.
-1, 100
Let y(t) be the third derivative of -t**7/210 + 31*t**6/60 - t**5 - 31*t**4/12 + 61*t**3/6 + 326*t**2. Find k, given that y(k) = 0.
-1, 1, 61
Suppose 0 = 143*p - 3050 - 3467 - 6353. Factor -189*z**3 + 147/2*z**4 + 0 - 12*z + p*z**2.
3*z*(z - 2)*(7*z - 2)**2/2
Let h(u) be the second derivative of 8*u**2 - 1/3*u**4 + 4*u + 0 + 0*u**3. Factor h(s).
-4*(s - 2)*(s + 2)
Let p(b) be the first derivative of b**5/50 - b**4/20 - 143*b**3/30 + 36*b**2/5 + 2592*b/5 - 306. Find l such that p(l) = 0.
-8, 9
Let x(g) be the first derivative of 23 + 3/13*g**2 + 1/26*g**4 + 2/13*g**3 + 2/13*g. Factor x(h).
2*(h + 1)**3/13
Factor 52/3 - 56/3*d + 4/3*d**2.
4*(d - 13)*(d - 1)/3
Factor -18*x**2 - 4*x**3 - 840*x + 22*x**2 - x**3 - 720 - 129*x**2.
-5*(x + 1)*(x + 12)**2
Let h = 181 - 126. Let t be h/(-25) - (-3 - 0). Determine y, given that 0*y**3 + 3/5*y**4 - 1/5*y**5 + 0*y - t*y**2 + 0 = 0.
-1, 0, 2
Let t(w) be the second derivative of -5*w**2 + 0 + 5/18*w**4 + 1/12*w**5 - 39*w