. Let s be (-1 - r)*(5 - -3)/4. Factor -1/3*j + 1/3*j**3 + 1/3*j**s - 1/3.
(j - 1)*(j + 1)**2/3
Let q(t) be the third derivative of -t**5/540 - 83*t**4/216 - 41*t**3/27 + 7*t**2 - 7*t. Determine n so that q(n) = 0.
-82, -1
Let t(d) be the first derivative of -d**6/8 - 33*d**5/20 - 21*d**4/4 + 9. Factor t(y).
-3*y**3*(y + 4)*(y + 7)/4
Let x(j) = -12*j + 58. Let s be x(15). Let m = s + 124. Determine b so that 0*b**m + 0 - 2/11*b**3 + 8/11*b = 0.
-2, 0, 2
Suppose 2*v - 8 = -5*w, 4*w + 3*v = w + 3. Suppose 8/7*b + 0 + 1/7*b**w = 0. What is b?
-8, 0
Suppose -1/2*d**5 + 0*d**2 + 2*d**4 + 0 + 21/2*d**3 + 0*d = 0. Calculate d.
-3, 0, 7
Let z be 3/5 + 99/(-3465). What is q in 0*q**3 + 2/7*q**4 - 6/7*q**2 + 0 - z*q = 0?
-1, 0, 2
Let s(t) be the second derivative of t**6/15 - 11*t**4/6 - 6*t**3 - 8*t**2 - t + 194. What is z in s(z) = 0?
-2, -1, 4
Let f(i) be the second derivative of i**7/168 + i**6/60 - 3*i**5/80 - i**4/12 + i**3/6 + 103*i. Factor f(g).
g*(g - 1)**2*(g + 2)**2/4
Let x(s) be the first derivative of -s**7/1820 + s**6/468 - s**5/780 - s**4/156 + 32*s**3/3 + 28. Let c(y) be the third derivative of x(y). Factor c(l).
-2*(l - 1)**2*(3*l + 1)/13
Let v(l) = 2*l + 3*l**2 - 17 + 9*l - l**2. Let s be v(-7). Find y such that -3/4*y**3 + 0*y + 0*y**s + 0 + 1/2*y**2 + 1/4*y**5 = 0.
-2, 0, 1
Let s(x) = -12*x**2 + 2*x. Suppose 5*w + 16 = 13*w. Let m(i) = -i**3 + 25*i**2 - 5*i. Let f(a) = w*m(a) + 5*s(a). Factor f(g).
-2*g**2*(g + 5)
Suppose 0 = -7*c - c + 48. Suppose q - 17 = -c*z + z, -4*q - z = -11. Solve -2/9*y**3 + 2/9*y + 2/9 - 2/9*y**q = 0.
-1, 1
Let m be 6 - -3*(-4)/(-6). Let q = m - 3. Suppose 2*i**3 + 2*i**q + 3*i**4 - 3*i**4 + 4*i**4 = 0. Calculate i.
-1, 0
Determine m so that -8/3*m**2 + 0 - 1/3*m**3 - 16/3*m = 0.
-4, 0
Suppose -4*c = c - 10. Factor 3*g**c - 6*g**2 - 58 - 30*g - 17.
-3*(g + 5)**2
Suppose -4*g - 2 = -22. Find s, given that 3*s**3 - 8*s**3 - g*s**4 + 5*s**2 - 9*s + 14*s = 0.
-1, 0, 1
Let q(w) be the third derivative of -w**7/4200 - 11*w**6/600 - 121*w**5/200 - w**4/8 - 13*w**2 - w. Let n(x) be the second derivative of q(x). Factor n(z).
-3*(z + 11)**2/5
Let k = -125 - -128. Let b(y) be the third derivative of -1/150*y**6 + 2/75*y**5 + 0*y**k + 0*y - 2/525*y**7 + 0 + 0*y**4 + 2*y**2. Factor b(q).
-4*q**2*(q - 1)*(q + 2)/5
Let t(m) be the second derivative of 0 - 1/10*m**3 + 3/100*m**5 - m + 0*m**2 + 1/20*m**4 - 1/50*m**6. Factor t(j).
-3*j*(j - 1)**2*(j + 1)/5
Let j(q) be the third derivative of q**6/120 + 53*q**5/240 - 43*q**4/96 - 7*q**3/12 + 511*q**2. What is k in j(k) = 0?
-14, -1/4, 1
Let o(l) be the first derivative of 5*l**6/6 - l**5 - 5*l**4/2 + 10*l**3/3 + 5*l**2/2 - 5*l - 58. What is y in o(y) = 0?
-1, 1
Let h(g) be the second derivative of -g**5/10 - 7*g**4/6 - 16*g**3/3 - 12*g**2 - 112*g + 2. Factor h(t).
-2*(t + 2)**2*(t + 3)
Let z(g) = g + 82. Let w be z(0). Let o = -82 + w. Factor 0*c**2 + 0*c**4 - 5/3*c**3 + o*c + 5/3*c**5 + 0.
5*c**3*(c - 1)*(c + 1)/3
Let h = -8 - -12. Suppose -14 = -5*o + h*o. Factor 6*m**2 - 24*m + 20*m**3 + 29*m**3 + m**2 + 4 + o*m**2.
(m + 1)*(7*m - 2)**2
Determine t, given that 2/19*t - 48/19 - 2/19*t**3 + 48/19*t**2 = 0.
-1, 1, 24
Find p such that -4/3*p**2 + 2/9*p**3 - 80/9 - 8*p = 0.
-2, 10
Let y be (-22347)/1337 - (0 - 17). Let -4/7*d + 2/7*d**3 + 1/7 + 4/7*d**2 - 5/7*d**4 + y*d**5 = 0. Calculate d.
-1, 1/2, 1
Let g(o) be the second derivative of 81/2*o**2 - 81/2*o**3 + 0 + 9*o - 2/5*o**6 - 21/4*o**5 - 99/4*o**4. Let g(z) = 0. What is z?
-3, 1/4
Suppose 2*o - 10 = 4*v, 0 = -4*o - 3*v + v + 10. Suppose -o*j - 16 = -7*j. Suppose -32*c**2 + 16*c**3 + 32*c - j*c**4 + 2/5*c**5 - 64/5 = 0. Calculate c.
2
Suppose -5*h - 3*d = 2, 5*d + 7 = 2*h - 17. Factor -10*s**h - 6*s**5 + 235*s**4 - 255*s**4 - 25*s**3 + s**5.
-5*s**2*(s + 1)**2*(s + 2)
Suppose -27*t**4 - 9*t**4 - 75*t**3 + 15062*t**2 - 15068*t**2 = 0. What is t?
-2, -1/12, 0
Let f(i) be the first derivative of -i**5/10 - 21*i**4/8 - 27*i**3 - 135*i**2 - 324*i - 79. Find j such that f(j) = 0.
-6, -3
Factor 2114 - 2146 - r**2 - 3*r**2 - 4*r + 28*r.
-4*(r - 4)*(r - 2)
Factor -10*s**2 - 7*s**2 - 10*s**2 + 5*s**3 + 2*s**2.
5*s**2*(s - 5)
Let g(w) = 2*w**2 + 12*w + 20. Let y be g(-2). Let u(v) be the second derivative of -2/15*v**2 + 1/45*v**3 + 0 + 5*v + 1/90*v**y. Factor u(o).
2*(o - 1)*(o + 2)/15
Solve -2/3*h**2 - 22/3*h - 16 = 0.
-8, -3
Let f(y) = y**2 - 6. Let x be f(-3). Find i such that 8*i**4 + i**x + i**2 - 9*i**4 - 2*i + i**3 = 0.
-1, 0, 1, 2
Factor 72 + 78*s + 71 + 63 - 206 + 3*s**2.
3*s*(s + 26)
Let g(s) be the second derivative of 1/84*s**4 + 0 + 1/7*s**2 - 1/14*s**3 + 16*s. Suppose g(o) = 0. What is o?
1, 2
Let i = -65 + 76. Factor 282 - 4*h - 4*h**4 - i*h**2 + 19*h**3 - 282.
-h*(h - 4)*(h - 1)*(4*h + 1)
Suppose -8*l + 24 = 8. Let h(p) be the first derivative of 5 + 36/5*p**5 + 2*p**3 + 0*p**l - 27/4*p**4 + 0*p - 5/2*p**6. Let h(z) = 0. Calculate z.
0, 2/5, 1
Let b = 2341/2637 + 1/879. Let f = -175417/9 - -19491. Let 8/9*c + 0 + f*c**3 - b*c**2 = 0. Calculate c.
0, 2
Let f(j) be the first derivative of -j**4/24 - 10*j**3/9 - 53*j**2/12 - 17*j/3 - 215. Solve f(r) = 0 for r.
-17, -2, -1
Let b(k) = k - 2. Let t be b(4). Find h, given that -38*h**2 - 24 + 17*h**3 - 340*h**t + 130*h**3 + 180*h = 0.
2/7, 2
Factor 20/3 + 1/6*i**2 + 13/6*i.
(i + 5)*(i + 8)/6
Factor 2*l**3 + 247 - 4*l**2 - 247.
2*l**2*(l - 2)
Let -407/6*v**3 - 2*v + 121/6*v**4 + 0 + 68/3*v**2 = 0. What is v?
0, 2/11, 3
Factor -9/2*p**2 + 0 + 0*p - 6*p**3 - 21/8*p**4 - 3/8*p**5.
-3*p**2*(p + 2)**2*(p + 3)/8
Let u(d) be the first derivative of -4*d**4 - 4*d**3/3 + 22*d**2 - 24*d - 150. Suppose u(l) = 0. What is l?
-2, 3/4, 1
Let r(j) be the third derivative of -j**5/90 - j**4/9 + 91*j**2. Find g such that r(g) = 0.
-4, 0
Let t(n) = -5*n**5 - 85*n**4 - 25*n**3 + 130*n**2 - 25*n + 25. Let k(y) = y**5 + 21*y**4 + 6*y**3 - 32*y**2 + 6*y - 6. Let d(f) = 25*k(f) + 6*t(f). Factor d(w).
-5*w**2*(w - 2)**2*(w + 1)
Let s(x) be the second derivative of x**4/66 + 32*x**3/11 + 316*x + 2. Factor s(r).
2*r*(r + 96)/11
Let r be 122/(-18) + 2/(-9). Let a = -5 - r. Determine k, given that -82*k**a + 3*k + 3*k**5 + 82*k**2 - 6*k**3 = 0.
-1, 0, 1
Let b(s) be the first derivative of s**3/4 - 63*s**2/4 + 1323*s/4 - 310. Factor b(y).
3*(y - 21)**2/4
Let u be ((-1)/6)/((-8)/24). Let o(l) be the first derivative of u*l**4 + 0*l - 4 - 1/3*l**6 + 0*l**5 + 0*l**2 + 0*l**3. Find j such that o(j) = 0.
-1, 0, 1
Factor -15/4*v + 7/2 + 1/4*v**2.
(v - 14)*(v - 1)/4
Let l(o) be the first derivative of o**4 - 104*o**3/3 + 280*o**2 + 1568*o + 6. Find i, given that l(i) = 0.
-2, 14
Let l(i) be the first derivative of i**6/27 - 8*i**5/45 + 2*i**4/9 + 4*i**3/27 - 5*i**2/9 + 4*i/9 - 615. Find q, given that l(q) = 0.
-1, 1, 2
Let m(k) be the second derivative of -3*k**6/55 + 147*k**5/110 + 101*k**4/66 + 17*k**3/33 + 3*k - 65. Factor m(v).
-2*v*(v - 17)*(3*v + 1)**2/11
Let l be ((-4)/(-8) + 0)*4. Let y(x) = 3*x - 19. Let h be y(8). Factor -g**h + 11*g - g**2 - 1 - 8*g - g**l - 2*g**3 + 3*g**4.
-(g - 1)**4*(g + 1)
Let a(p) be the third derivative of 5*p**2 + 0*p**3 + 3/14*p**8 + 0*p**4 + 0 + 0*p + 19/35*p**7 + 2/15*p**5 + 7/15*p**6. Factor a(o).
2*o**2*(3*o + 2)**2*(4*o + 1)
Determine l so that -3/5*l**2 - 258/5*l - 51 = 0.
-85, -1
Let t(j) be the first derivative of 15/4*j**4 - 3/5*j**5 - 12*j**2 + 12*j + j**3 - 19 - 1/2*j**6. Factor t(g).
-3*(g - 1)**3*(g + 2)**2
Let v be 2/12 - 188/(-24). Suppose -4*x = -v*x + 164. What is q in 26*q + 2*q**5 - 10*q**5 + 22*q**3 - x*q**2 - 2 + 10*q**4 - 2 - 5*q**2 = 0?
-2, 1/4, 1
Suppose -10 = -5*m + 5*k, k + 4*k + 25 = 0. Let b be (12/(-8))/(m/4). Determine w so that 9*w**2 - 3*w**2 - 12*w**3 + 2*w**2 + 3*w**4 - 12 + 12*w + w**b = 0.
-1, 1, 2
Find q such that 500/3 + 5/3*q**4 + 10*q**3 - 100*q - 55/3*q**2 = 0.
-5, 2
Let y(o) be the second derivative of -o**7/3080 - o**6/1980 + o**5/440 + o**4/132 - 14*o**3/3 + 34*o. Let q(k) be the second derivative of y(k). Factor q(c).
-(c - 1)*(c + 1)*(3*c + 2)/11
Let t(q) be the third derivative of -7*q**6/30 + q**5/3 + q**4/3 + 7*q**2 - 5. Solve t(y) = 0.
-2/7, 0, 1
Solve 40*w**4 + 4*w**3 + 43*w**2 + 30*w**2 - 85*w**2 + 24*w**3 = 0 for w.
-1, 0, 3/10
Let m be 0*(19 - 0 - 20). Determine d, given that m - 8/5*d + 2/5*d**2 = 0.
0, 4
Factor -1