6/8 - 81*p**5/8 + 1215*p**4/8 - 3*p**3 - 35*p. Let s(w) be the second derivative of k(w). Factor s(d).
-5*(d - 9)**3
Let z = -833 + 457. Let r = 2261/6 + z. Solve 0 + r*i + 5/6*i**2 = 0 for i.
-1, 0
Factor 1/4*a**5 + 0*a - 1/4*a**2 + 0 - 1/4*a**3 + 1/4*a**4.
a**2*(a - 1)*(a + 1)**2/4
Let m = -307 + 314. Let x(q) be the third derivative of 1/20*q**6 - m*q**2 + 0 + 0*q - 1/4*q**4 + 0*q**3 - 7/20*q**5 + 1/10*q**7. Factor x(z).
3*z*(z - 1)*(z + 1)*(7*z + 2)
Let q(r) be the first derivative of r**4/10 - 2*r**3/15 - r**2 - 6*r/5 - 144. Factor q(m).
2*(m - 3)*(m + 1)**2/5
Let y = 197 + -193. Let b(i) be the first derivative of -i**3 + 4 + 0*i**2 + 0*i - 1/4*i**y. Factor b(q).
-q**2*(q + 3)
Let -22/3*r + 1/3*r**2 + 121/3 = 0. What is r?
11
Let f = 76 - 73. Factor -10 - 2*a**f - 3*a**3 - a - 3*a + 19*a.
-5*(a - 1)**2*(a + 2)
Let h(t) = -t**3. Let d = -4 - -8. Let v(m) = 1 + 2*m**3 + 5*m**4 - 2*m**2 + m**3 - d*m**4 + 0*m**4. Let z(j) = 3*h(j) + v(j). Determine p so that z(p) = 0.
-1, 1
Let f(y) = -y**2 - 40*y - 204. Let v be f(-6). Factor -3/2*x**3 + 2*x**4 + v + 0*x - 1/2*x**2.
x**2*(x - 1)*(4*x + 1)/2
Suppose 4*q - 344 = -4*q. Let w = -34 + q. Suppose 9 + w*l**2 + 15*l + 1 - 4 = 0. What is l?
-1, -2/3
Let f be (-116)/290 - (-17)/5. Let g(h) be the second derivative of -1/78*h**4 + f*h - 16/13*h**2 + 0 - 8/39*h**3. Suppose g(r) = 0. Calculate r.
-4
Let f(c) be the third derivative of 0 + 27*c**2 - 2/5*c**3 - 1/20*c**5 - 1/200*c**6 + 0*c - 1/5*c**4. Find l, given that f(l) = 0.
-2, -1
Let a(t) be the third derivative of t**5/20 - 2*t**4 + 14*t**3 - 2*t**2 - 4*t. Find l such that a(l) = 0.
2, 14
Suppose -57*d = -83*d + 52. Factor 2*q**d - 4/9 + 14/9*q.
2*(q + 1)*(9*q - 2)/9
Suppose 5*f = -3 + 13. Factor -2 + 11*u**f + 21*u - 2*u**2 - 28*u.
(u - 1)*(9*u + 2)
Let y = 2/37515 + 133386/12505. Let -2/9*f**3 - y*f + 8/3*f**2 + 128/9 = 0. What is f?
4
Let y(p) = 2*p**5 + p**4 + p**3 + p + 1. Let j(w) = 7*w**5 - 4*w**4 - 59*w**3 + 140*w**2 - 79*w + 1. Let q(r) = j(r) - y(r). Factor q(z).
5*z*(z - 2)**2*(z - 1)*(z + 4)
Let v be (2/(-8))/((-9)/36)*-1. Let j be 3*v/3*-3. Let -53/3*q**j - 28/3*q**2 + 2/3 + 7/3*q + 152/3*q**4 - 80/3*q**5 = 0. Calculate q.
-1/4, 2/5, 1
Let y(p) be the first derivative of -p**2 - 1/2*p**4 + 0*p - 4/3*p**3 + 5. Suppose y(s) = 0. Calculate s.
-1, 0
Suppose 4*t - 3*n - 1 - 19 = 0, 3*t - n = 10. Let o(m) be the first derivative of -t*m - 70*m**2 - 12 + 2*m + 73*m**2 - m**3. What is q in o(q) = 0?
0, 2
Let a be (6 - 5)*3/12. Let j(h) be the first derivative of 1/12*h**3 - 1 + 1/4*h + a*h**2. Factor j(n).
(n + 1)**2/4
Solve 358*l**3 + 33*l**2 - 176*l**3 - 173*l**3 + 18*l = 0.
-3, -2/3, 0
Suppose 8 = 5*d - 4*d - 5*j, -j - 16 = -d. Let m be (d/4)/((-48)/(-16)). Factor m*t**2 + 3/2*t - 3.
3*(t - 1)*(t + 2)/2
Let v(b) be the first derivative of -b**2/2 - 5*b - 1. Let n be v(-7). Factor 5*w**n + 3*w + w - 7*w**2 + 0*w**2.
-2*w*(w - 2)
Let j(b) be the first derivative of -104/5*b**5 + 0*b + 0*b**2 + 14/3*b**6 + 20*b**4 + 32/3*b**3 + 26. Factor j(h).
4*h**2*(h - 2)**2*(7*h + 2)
Let a be 0/(-1) + (-12)/248. Let d = 71/186 + a. Factor -1/3*x**3 + 0 + 0*x**2 + d*x**4 + 0*x.
x**3*(x - 1)/3
Let r(i) = i - 7. Let z be r(10). Suppose 0 = -z*b + 2*b + 18. Solve b*h**3 - 24*h**2 + 6*h + 3*h**2 - 3*h**3 = 0 for h.
0, 2/5, 1
Let u(w) be the second derivative of w**7/42 - 7*w**6/30 + 4*w**5/5 - w**4 + 137*w. Factor u(l).
l**2*(l - 3)*(l - 2)**2
Factor -58*g - 14*g**4 + 6*g**5 - 48 - 3*g**5 - 2*g**5 + 14*g + 28*g**3 - 7*g**3 + 40*g**2.
(g - 12)*(g - 2)**2*(g + 1)**2
Let z(f) be the third derivative of -f**5/80 + f**4/16 + 3*f**3 - 2*f**2 + 2. What is x in z(x) = 0?
-4, 6
Factor -11*t + 121/2 + 1/2*t**2.
(t - 11)**2/2
Let b be (-24)/(-6) + 2 + -2. Let q(o) be the second derivative of -3/10*o**5 + 1/6*o**b + 0*o**3 + 0 + 1/12*o**6 + 0*o**2 + 5*o. Factor q(y).
y**2*(y - 2)*(5*y - 2)/2
What is n in 2/9*n**2 - 56/9*n + 50/3 = 0?
3, 25
Let m = -132 + 135. Let r(z) be the third derivative of 1/5*z**5 + 0*z**m + 3*z**2 + 1/6*z**4 + 1/10*z**6 + 2/105*z**7 + 0 + 0*z. Factor r(f).
4*f*(f + 1)**3
Let u(x) be the third derivative of x**8/784 + 3*x**7/245 + x**6/140 - 9*x**5/35 - 27*x**4/56 + 27*x**3/7 + x**2 - 112. Suppose u(l) = 0. What is l?
-3, 1, 2
Factor 5*m**2 - 23 - 17*m - 3*m - 15 + 0*m**2 + 13.
5*(m - 5)*(m + 1)
Let t(p) be the third derivative of p**7/5880 - p**6/1680 - p**5/140 + 7*p**4/24 - 7*p**2. Let x(i) be the second derivative of t(i). Factor x(r).
3*(r - 2)*(r + 1)/7
Let l(f) = -f**3 + 3*f**2 + 3*f. Let r be l(4). Let y = 7 - r. Solve y*o**2 + 2*o - 6*o**2 - 4*o**2 + 0*o = 0.
-2, 0
Let 4*z**4 + 6*z**3 + 6*z**5 - 5*z**5 + z - 55*z**2 + 29*z**2 + 30*z**2 = 0. Calculate z.
-1, 0
Let r(p) be the third derivative of 0*p**3 + 0*p + 1/25*p**5 + 1/300*p**6 + 3*p**2 + 0 + 1/12*p**4. Solve r(m) = 0 for m.
-5, -1, 0
Let f be (2 - 9)/7*2/(-1). Determine m so that -16*m**3 + 3 + 20*m + 37 - 27*m**5 - 9*m**3 + 10*m**4 + 32*m**5 - 50*m**f = 0.
-2, -1, 1, 2
Let j(m) be the second derivative of m**6/15 - 9*m**5/10 - 23*m**4 - 416*m**3/3 - 288*m**2 - 6*m - 2. Factor j(w).
2*(w - 18)*(w + 1)*(w + 4)**2
Let s be 15*(3 + 0 - 1). Suppose -5*b - 5*u + s = -40, -5*b - 2*u + 67 = 0. What is a in -2*a + b*a**2 - 3*a + 2*a**2 - 15*a**3 + 5*a**4 = 0?
0, 1
Let 616*b - 290*b - 299*b - 3*b**3 - 18*b**2 + 48 - 6 = 0. Calculate b.
-7, -1, 2
Find c, given that 588/5 + 2/5*c**3 + 8*c**2 + 266/5*c = 0.
-7, -6
Suppose -2*r + 11 = -j, -r = 2*r - 4*j - 19. Suppose 5*p = -r*w + 8 - 23, 3*w - 5*p = 31. Factor 12*d**3 - d**2 - d - d**w + 2*d**2 - d**2.
d*(3*d - 1)*(4*d + 1)
Let f(j) be the second derivative of j**6/720 + 11*j**5/120 + 121*j**4/48 - j**3/2 - 21*j. Let u(y) be the second derivative of f(y). Factor u(q).
(q + 11)**2/2
Let n(y) be the first derivative of -y**7/840 + 7*y**5/120 - y**4/4 - 7*y**3/3 - 35. Let z(h) be the third derivative of n(h). Factor z(w).
-(w - 2)*(w - 1)*(w + 3)
Let v be -2 + ((-26)/(-6) - 4)*6. Let a(c) be the first derivative of v*c - 4 - 2/39*c**3 + 3/13*c**2. What is i in a(i) = 0?
0, 3
Let i = -27 + 28. Factor -i + 7 + o**2 - 6*o**2 + 14.
-5*(o - 2)*(o + 2)
Let l = 344 - 344. Let c(t) be the third derivative of 0*t**4 + 1/735*t**7 + 0 + l*t**3 + 1/210*t**6 + 0*t**5 + 0*t + 2*t**2. Determine a so that c(a) = 0.
-2, 0
Let i(j) be the third derivative of 0*j + 0*j**3 + 2/2205*j**7 - 1/1260*j**6 + 0 + 0*j**4 + 11*j**2 - 1/3528*j**8 + 0*j**5. Suppose i(t) = 0. What is t?
0, 1
Let v = -1/811 + 11369/12165. Let -4/15 - v*n**2 + 6/5*n = 0. Calculate n.
2/7, 1
Factor 600*u + 1/2*u**3 + 30*u**2 + 4000.
(u + 20)**3/2
Let y(z) = -z - 9. Let d be y(-11). Suppose -5*v = -d*k - 13 - 4, 3*k = v - 6. Find m such that -10/7*m + 6/7*m**v - 4/7 + 8/7*m**2 = 0.
-2, -1/3, 1
Let w(t) = -4*t + 33. Let h be w(7). Let l(x) be the first derivative of -14/25*x**h + 2/5*x**2 + 0*x + 8/5*x**4 - 22/15*x**3 + 3. Let l(s) = 0. What is s?
0, 2/7, 1
Let k be (-12)/(-21) + 0 + 1599/(-3276). Let s(n) be the first derivative of 1/30*n**5 - k*n**2 - 11 + 0*n - 1/18*n**3 + 1/24*n**4. Solve s(f) = 0.
-1, 0, 1
Let w(s) be the first derivative of -s**8/2240 + s**7/280 - s**6/160 - 11*s**3 - 8. Let p(h) be the third derivative of w(h). Suppose p(u) = 0. What is u?
0, 1, 3
Let p(l) be the third derivative of -l**7/105 - 8*l**6/15 - 17*l**5/2 + 8*l**4/3 + 256*l**3/3 - 33*l**2 - 2. Find c such that p(c) = 0.
-16, -1, 1
Let g(z) be the third derivative of -z**5/480 + z**4/192 + z**3/8 - 43*z**2. Factor g(l).
-(l - 3)*(l + 2)/8
Let g(r) = 2*r**2 + 122*r + 123. Let l be g(-1). Factor -15/4*m**l + 0 - 3/4*m**5 - 3*m**4 - 3/2*m**2 + 0*m.
-3*m**2*(m + 1)**2*(m + 2)/4
Let s be (-24 + 7)*((-2)/2 - 0). Factor 19*u**2 - 21*u**2 - 55 - s + 24*u.
-2*(u - 6)**2
Factor 16*u - 43*u**2 + 10*u**2 + 13*u**2 + 15*u**2 + 9*u**2.
4*u*(u + 4)
Let j be (14 - 12)/(4/150 + 0). Let j*f - 5*f**2 - 75*f = 0. Calculate f.
0
Let u(z) be the second derivative of 1/2*z**5 + 7/3*z**3 + 31*z - 1/15*z**6 + 0 + 0*z**2 + 13/6*z**4. Find a such that u(a) = 0.
-1, 0, 7
Let g(n) be the second derivative of 0*n**3 - 6*n + 0 + 1/18*n**4 + 1/90*n**6 - 1/20*n**5 + 0*n**2. Determine k so that g(k) = 0.
0, 1, 2
Let g(w) be the second derivative of w**5/210 - w**4/28 + 5*w**2 - 6*w. Let i(p) be the first derivative of g(p). Let i(a) = 0. Calculate 