vative of -s**9/120960 + s**7/3360 + s**6/720 - 3*s**5/20 + 19*s**2. Let g(t) be the third derivative of k(t). Factor g(f).
-(f - 2)*(f + 1)**2/2
Suppose -96*n - 84 = 46*n - 510. Let l(f) be the first derivative of -1/2*f**4 + 1/5*f**5 - f**n + 0*f**2 - 16 + 0*f. Solve l(x) = 0.
-1, 0, 3
Let q = 115844 + -115841. Factor -18 + q*n - 1/8*n**2.
-(n - 12)**2/8
Let g = 190 + -188. Find w, given that 7*w**3 - 7*w**2 + 0*w**3 + w**g - w**4 = 0.
0, 1, 6
Let u(m) be the third derivative of m**5/150 - 401*m**4/30 + 267*m**3/5 + m**2 - 93. Factor u(w).
2*(w - 801)*(w - 1)/5
Suppose 5*l - 6 = 4. Let j(h) be the first derivative of 14 - 3*h**2 + 5*h**l - h**4 + 0*h**2 + 0*h**4. Let j(m) = 0. What is m?
-1, 0, 1
Factor 446/3*r + 48*r**2 + 100 - 2/3*r**3.
-2*(r - 75)*(r + 1)*(r + 2)/3
Let l be -14 + (-2139)/(-598)*4. Suppose -4/13*o**4 + 2/13*o**5 + 0 + 6/13*o - 8/13*o**3 + l*o**2 = 0. What is o?
-1, 0, 1, 3
Let r(o) be the third derivative of -2*o**2 + 1/5*o**5 + 3/8*o**4 + 0*o - 38 - 7/40*o**6 + 0*o**3. Factor r(d).
-3*d*(d - 1)*(7*d + 3)
Let w(v) be the third derivative of v**6/120 - 163*v**5/30 + 643*v**4/8 - 480*v**3 - 410*v**2 + 4. Factor w(r).
(r - 320)*(r - 3)**2
Factor -224/5 - 548/15*m - 34/5*m**2 + 2/15*m**3.
2*(m - 56)*(m + 2)*(m + 3)/15
Let s(w) be the third derivative of -w**7/6300 + w**6/1800 + w**5/25 - 19*w**4/8 + 91*w**2. Let f(v) be the second derivative of s(v). Factor f(i).
-2*(i - 4)*(i + 3)/5
Let u(h) be the third derivative of 28 + 0*h + 15*h**3 - 3*h**2 - 29/8*h**4 - 1/20*h**5. Factor u(m).
-3*(m - 1)*(m + 30)
Let t = -918977 - -918980. Suppose 0*y + 1/6*y**t + 0 + 43/6*y**2 = 0. What is y?
-43, 0
Let x(t) be the first derivative of -13/2*t**4 - 5 - 2/5*t**5 + 0*t - 46/3*t**3 - 11*t**2. Find c, given that x(c) = 0.
-11, -1, 0
Let p = 35 - 32. Let h(w) be the second derivative of 0 + 1/3*w**p - 1/6*w**4 + 0*w**2 + 12*w. Determine r so that h(r) = 0.
0, 1
Let f(s) be the third derivative of -9/40*s**6 + 0*s + 0 + 20*s**3 + 70*s**2 + 29/2*s**4 + 39/10*s**5. Factor f(g).
-3*(g - 10)*(3*g + 2)**2
Let r(f) be the first derivative of -f**5/40 + 19*f**4/4 - 361*f**3 - 15*f**2/2 + 3*f + 119. Let x(c) be the second derivative of r(c). Solve x(w) = 0.
38
Suppose -10*y + 116 = 48*y. Let f(l) be the second derivative of 1/4*l**4 + 0*l**3 + 8*l + 0 - 6*l**y. Factor f(k).
3*(k - 2)*(k + 2)
Let t(b) be the first derivative of -b**6/36 - 13*b**5/90 - b**4/9 + 4*b**3/9 - 183*b**2/2 - 169. Let f(k) be the second derivative of t(k). Factor f(l).
-2*(l + 1)*(l + 2)*(5*l - 2)/3
Let d be (-570)/(-171) - 6/9. Let w = 143/3 - 47. Find h such that d - w*h - 1/3*h**2 = 0.
-4, 2
Let j(h) be the first derivative of 3/20*h**4 - 3/10*h**2 + 3/25*h**5 - 1/5*h**3 + 0*h + 87. Factor j(f).
3*f*(f - 1)*(f + 1)**2/5
Let o = 319453 - 319453. Let u be (4/6)/(7/3). What is s in 2/7*s**2 + 2/7*s**5 + o*s - 2/7*s**4 + 0 - u*s**3 = 0?
-1, 0, 1
Let f(l) be the first derivative of 1/3*l**3 + 7*l**2 + 39 + 24*l. Determine v, given that f(v) = 0.
-12, -2
Let u(p) = 8*p**2 - 32*p - 10. Let s be u(5). Let d be 1/((6 + 0)*s/270). Factor -d*v**2 + 9 + 3/2*v.
-3*(v - 3)*(v + 2)/2
Suppose -5*o + 5*b = 15, -8*b + 24 = -62*o + 64*o. Let -2/9*v**2 + 8/9*v + 2/9*v**4 + o - 8/9*v**3 = 0. Calculate v.
-1, 0, 1, 4
Factor -892/5*t**3 + 4/5*t**4 + 12544/5 + 49952/5*t + 49281/5*t**2.
(t - 112)**2*(2*t + 1)**2/5
Let j(a) = 14*a**3 + 700*a**2 - 2908*a + 2859. Let y(n) = 6*n**3 + 350*n**2 - 1448*n + 1430. Let d(w) = -4*j(w) + 10*y(w). Let d(t) = 0. What is t?
-179, 2
Let x(r) be the second derivative of r**4/16 + 3*r**3/2 - 724*r. Solve x(g) = 0.
-12, 0
Let k(t) be the second derivative of -t**6/6 - 107*t**5/4 - 324*t + 3. Factor k(x).
-5*x**3*(x + 107)
Let j be 1 + 0 + 6/2. Let o(t) = t**2 - 1. Suppose 21*h - 7 = -13*h + 27. Let c(f) = -2*f**3 - 2*f**2 + 4*f + 4. Let x(a) = h*c(a) + j*o(a). Factor x(s).
-2*s*(s - 2)*(s + 1)
Factor -15*u**3 - 211*u - 2*u**4 + 240*u**2 + 1563*u - 23*u**3 + 1472.
-2*(u - 8)*(u + 2)**2*(u + 23)
Let r be (-2)/4 + (-2)/((-20)/45). Let s be (36/(-8) - -4) + 10/r. Factor -30*i**2 + 59*i**s - 32*i**2.
-3*i**2
Let o(d) be the first derivative of 2*d**3/27 - 23*d**2 - 140*d + 8652. Find p such that o(p) = 0.
-3, 210
Let p(y) be the second derivative of y**7/4410 - y**6/45 + 14*y**5/15 + y**4/6 + 14*y**3/3 + y + 18. Let g(s) be the third derivative of p(s). Factor g(m).
4*(m - 14)**2/7
Let z(m) be the first derivative of m**8/1680 + m**7/140 + m**3 + 2*m**2 - 72. Let a(j) be the third derivative of z(j). Factor a(t).
t**3*(t + 6)
Let s be 1*(-17 - -17)/33. Suppose s + 16/7*m**2 - 15/7*m - 1/7*m**3 = 0. What is m?
0, 1, 15
Let z = -63 - -93. Let l be 6/z - (-36)/20. Factor -3/4*x**l + 0*x + 0 + 3/4*x**3.
3*x**2*(x - 1)/4
Suppose 4572 - 390 = -b + 5*s, -15 = 5*s. Let d be 0 + b/(-63) + (-23)/69. Factor -128*i**2 - d*i - 28*i**3 - 64/7.
-4*(i + 4)*(7*i + 2)**2/7
Let z(w) be the third derivative of w**6/72 - 7*w**5/9 + 1015*w**4/72 - 440*w**3/9 + w**2 - 1499*w. Find q, given that z(q) = 0.
1, 11, 16
Factor 98/9*z + 2/9*z**3 - 44/3 + 32/9*z**2.
2*(z - 1)*(z + 6)*(z + 11)/9
Let k be (-13 + 15)*458/567. Let j = k - -8/81. Factor -2/7 - j*b**2 + 8/7*b - 2/7*b**4 + 8/7*b**3.
-2*(b - 1)**4/7
Solve 0*o + 3/5*o**4 - 471/5*o**3 - 954/5*o**2 + 0 = 0 for o.
-2, 0, 159
Let y(k) be the first derivative of -5*k**4 - 75*k**3 - 435*k**2/2 + 680*k - 11272. Suppose y(n) = 0. What is n?
-8, -17/4, 1
Suppose 8*d - 996 = -484. Let w(z) be the first derivative of -112*z**2 + d*z + 44/5*z**5 - 7 - 43*z**4 + 292/3*z**3 - 2/3*z**6. Factor w(j).
-4*(j - 4)**2*(j - 1)**3
Suppose 17388 + 68494 = 46*t. Let 1867*i + 0*i**4 - t*i - 5*i**4 - 5*i**3 = 0. What is i?
-1, 0
Suppose 24*t + 6 = 23*t. Let z(s) = -2*s**2 + 10*s. Let a(y) = 8*y**2 - 40*y. Let r(o) = t*a(o) - 22*z(o). Solve r(i) = 0 for i.
0, 5
Let t(c) = 13*c + 94. Let j be t(-7). Determine v so that -6 - 20*v**j - 38*v**2 - 21 + 35 - 32*v + 10*v**3 = 0.
-2, 1/5
Find a, given that 6/7*a**2 - 370/7 + 1108/7*a = 0.
-185, 1/3
Let q(j) be the third derivative of 146*j**2 + 4/105*j**7 + 0 - 59/30*j**5 + 0*j - 1/15*j**6 - 8*j**4 - 15*j**3. Factor q(c).
2*(c - 5)*(c + 1)*(2*c + 3)**2
Let x(s) be the third derivative of -182*s**2 + 1/3*s**5 - 1/105*s**7 + 2/3*s**4 - 2/15*s**6 + 0*s - 3*s**3 + 0. Factor x(m).
-2*(m - 1)**2*(m + 1)*(m + 9)
Let p(r) be the second derivative of r**7/21 - 18*r**6/5 + 31*r**5/2 - 17*r**4 - 11364*r. Determine m, given that p(m) = 0.
0, 1, 2, 51
Let s be (-1 - (-5 + 3))*10. Determine l, given that 42 - l**2 - s - 4 + 19*l - 8 = 0.
-1, 20
Let t(s) be the second derivative of s**4/4 + 136*s**3 + 27744*s**2 + 8050*s. Factor t(d).
3*(d + 136)**2
Suppose 159*o + 65*o = -44*o + 804. Factor 0 + 0*u**o + 2/3*u - 1/3*u**4 + u**2.
-u*(u - 2)*(u + 1)**2/3
Let j = -35216 - -35220. Find b, given that -8/9*b + 0 + 8/9*b**3 - 2/9*b**j + 2/9*b**2 = 0.
-1, 0, 1, 4
Let c(j) be the third derivative of -j**6/15 - 77*j**5/10 + 49*j**4/2 - 59*j**3/3 - 1298*j**2. Factor c(f).
-2*(f - 1)*(f + 59)*(4*f - 1)
Let b(w) = -3*w**2 + 11*w + 8. Let k be b(4). Factor -2*q**2 - 12*q**2 + 6*q**k + 2*q**4 - 12*q - 6*q**4.
2*q*(q - 3)*(q + 1)*(q + 2)
Let y be -4 + (3054/16)/(-48 + 78). Let i(d) be the second derivative of 0*d**2 + 16*d + 0 + 17/8*d**4 + 1/2*d**3 + y*d**5 - 81/80*d**6. Factor i(m).
-3*m*(m - 2)*(9*m + 2)**2/8
Let t(m) be the second derivative of 0 - 17*m + 1/12*m**5 + 0*m**3 + 0*m**4 - 1/2*m**2 - 1/24*m**6. Let f(w) be the first derivative of t(w). Solve f(x) = 0.
0, 1
Let i(b) be the first derivative of -2*b**5/55 + 5*b**4/11 - 40*b**3/33 - 10*b**2/11 + 42*b/11 - 994. Suppose i(x) = 0. Calculate x.
-1, 1, 3, 7
Let a(t) be the third derivative of t**6/20 - t**4/12 - 47*t**2. Let x be a(1). Determine o so that 0 + x*o**3 + 8/3*o**2 - 4/3*o = 0.
-1, 0, 1/3
Let c(g) be the third derivative of g**6/200 - g**5/4 + 35*g**4/8 - 75*g**3/2 + 10179*g**2. Find l such that c(l) = 0.
5, 15
Let k(n) be the second derivative of -1/16*n**4 + 5/24*n**3 + 0 + 1/2*n**2 + 43*n - 1/16*n**5 - 1/120*n**6. Factor k(a).
-(a - 1)*(a + 1)**2*(a + 4)/4
Let c(r) be the first derivative of 2*r**5/45 + 25*r**4/9 + 1250*r**3/27 + 2384. Factor c(t).
2*t**2*(t + 25)**2/9
Let y(g) be the first derivative of 0*g - 159 + 31/5*g**2 - 2/15*g**3. Factor y(j).
-2*j*(j - 31)/5
Factor 0 + 0*c 