k + 1)/3
Let r = -3/5 - -21/10. Factor -1/2*t**2 - 1/2*t**4 - r*t + 3/2*t**3 + 1.
-(t - 2)*(t - 1)**2*(t + 1)/2
Let q(v) be the second derivative of -1/120*v**6 + 11*v + 0*v**3 + 0 - 2*v**2 + 0*v**4 - 1/20*v**5. Let r(z) be the first derivative of q(z). Factor r(j).
-j**2*(j + 3)
Let p(f) = 80*f + 7. Let o be p(-1). Let a = o + 75. Find y such that 0 + 4/3*y + 2/3*y**a - 2/3*y**3 = 0.
-1, 0, 2
Suppose 48 = -48*p + 144. Factor 368/15*t**p - 256/15*t + 32/15 + 192/5*t**3 + 54/5*t**4.
2*(t + 2)**2*(9*t - 2)**2/15
Let y(w) = -w**3 - 19*w**2 - 17*w + 30. Let j be y(-18). What is m in 15*m + 2 + j - 5*m**2 - 4 - 5*m**4 - 15*m**3 = 0?
-2, -1, 1
Let h = -5676 - -3065041/540. Let f(t) be the third derivative of 0*t + 1/135*t**5 - t**2 + h*t**6 + 0*t**3 + 0 + 0*t**4. Factor f(w).
2*w**2*(w + 2)/9
Suppose -q + 6 = 5*l + 2, 3*q + 5*l = 2. Let p(b) = -4*b - 2. Let o be p(q). Determine k, given that 2*k**4 + 4*k - 5*k**2 + 4 + 2*k**o - 3*k**4 - 4*k**3 = 0.
-2, -1, 1
Let r(n) be the second derivative of -n**6/900 - 2*n**5/75 - 4*n**4/15 + 3*n**3/2 + n. Let j(o) be the second derivative of r(o). Suppose j(s) = 0. What is s?
-4
Let u = -3779 - -3782. Solve 0 - 1/4*g**u + 0*g**2 - 3/8*g**4 + 0*g = 0.
-2/3, 0
Let c(b) = 2*b**2 - 58*b + 408. Let r be c(12). Factor r*g**3 - 4/3*g**2 + 0 + 4/3*g**4 + 2/3*g**5 - 2/3*g.
2*g*(g - 1)*(g + 1)**3/3
Let 8*p**2 - 6*p + 3/2*p**3 + 0 - 2*p**4 = 0. What is p?
-2, 0, 3/4, 2
Let i = 95/1896 + -2/237. Let a(j) be the first derivative of 5 + 1/4*j**2 - i*j**6 + 0*j + 1/20*j**5 - 5/12*j**3 + 3/16*j**4. Factor a(y).
-y*(y - 1)**3*(y + 2)/4
Suppose -4*x + 2 = 5*y, -y + 2*x = -0*x - 6. Factor 5*r**2 - 11*r**y + 2*r**2.
-4*r**2
Let p(j) be the third derivative of -j**6/40 + j**5/2 - 3*j**4 - 159*j**2. Let p(z) = 0. Calculate z.
0, 4, 6
Let f be 143/195*3 + 13/(-65). Suppose 4*g + 8/3*g**4 - 32/9*g**3 + 0 - 4/9*g**5 - 8/3*g**f = 0. Calculate g.
-1, 0, 1, 3
Let f = -1 + 3. Factor -2*v**2 + 9*v + 5*v**f + 2*v**2 - 14*v.
5*v*(v - 1)
Let y(r) be the third derivative of -r**8/84 - 2*r**7/35 + 4*r**5/15 + 5*r**2. Let y(s) = 0. What is s?
-2, 0, 1
Suppose -1/7*y**5 - 18/7*y**2 - 26/7*y**3 - 9/7*y**4 + 27/7*y + 27/7 = 0. Calculate y.
-3, -1, 1
Let u(z) = 34*z**2 - 338*z + 188. Let g(i) = -11*i**2 + 113*i - 62. Let n(y) = -14*g(y) - 5*u(y). Factor n(c).
-4*(c - 6)*(4*c - 3)
Suppose 0 = -3*v - 6, -5*v - 9 - 1 = -f. Let b(a) be the second derivative of -12*a + 0*a**2 - 1/6*a**6 + f - 1/3*a**3 + 3/10*a**5 + 3/4*a**4. Factor b(u).
-u*(u - 2)*(u + 1)*(5*u - 1)
Let f(d) be the second derivative of 0 - 1/105*d**6 + 2/35*d**5 - 16/21*d**3 + 16/7*d**2 + 0*d**4 + 5*d. Solve f(b) = 0 for b.
-2, 2
Suppose 32 - 141*r + 0*r**2 + 3 + 171*r - 5*r**2 = 0. What is r?
-1, 7
Let o(q) be the third derivative of q**5/210 + 5*q**4/84 + 4*q**3/21 + 58*q**2. Factor o(n).
2*(n + 1)*(n + 4)/7
Factor 8/3 + 32/9*q - 22/9*q**2.
-2*(q - 2)*(11*q + 6)/9
Let z be (4/(-21))/((-3 + 1)*165/5940). Find a, given that -z*a - 12/7*a**3 + 8/7 + 26/7*a**2 + 2/7*a**4 = 0.
1, 2
Suppose -4 + 12 = -2*c. Let z be -4 + 3 + 37/1. Let y(h) = -h**3 + 13*h**2 - 3*h. Let s(v) = v**2. Let n(a) = c*y(a) + z*s(a). Determine r, given that n(r) = 0.
0, 1, 3
Let g(m) be the first derivative of 5*m**4/12 - 10*m**3/3 + 15*m**2/2 - 6*m + 2. Let a(l) be the first derivative of g(l). Solve a(t) = 0.
1, 3
Factor 6*u - 2/3*u**2 + 20/3.
-2*(u - 10)*(u + 1)/3
Solve 5*v**2 + 7410*v - 7410*v - 5 = 0 for v.
-1, 1
Let s(g) be the third derivative of -g**9/756 - g**8/210 + g**6/45 + g**5/30 - 7*g**3/2 + 23*g**2. Let z(j) be the first derivative of s(j). Factor z(u).
-4*u*(u - 1)*(u + 1)**3
Let i(k) be the first derivative of k**4/18 - 38*k**3/9 - 58*k**2/9 + 462. Factor i(d).
2*d*(d - 58)*(d + 1)/9
Let h(o) be the second derivative of 0 - 1/24*o**4 - 3/4*o**2 - 1/3*o**3 - 41*o. Find b such that h(b) = 0.
-3, -1
Suppose 2*g = -4, 2 = -i + 2*g + 2*g. Let y be (i/(-4) - 4)*24/(-9). Factor -1/3*w**5 + 2/3*w**y + 2/3*w**3 + 7/3*w - 8/3*w**2 - 2/3.
-(w - 1)**4*(w + 2)/3
Let p(j) = 4*j**2 - 2*j + 4. Let g = 22 - 8. Let h(s) = 9*s**2 - 4*s + 9. Let q(z) = g*p(z) - 6*h(z). Find l such that q(l) = 0.
1
Let u(f) = -11*f**3 - f**2 + f + 1. Let y be u(-1). Suppose -9*x = -y*x + 3. Let k**4 - 10*k**x + 2 + 6*k**3 - 3*k**4 + 4*k = 0. Calculate k.
-1, 1
Solve -4*q**3 + 6*q - 4*q - 30 + 29*q + 2*q**2 - 12*q**2 + 5*q**3 = 0 for q.
2, 3, 5
Let h(p) be the first derivative of p**5/15 - 27*p**4/4 + 533*p**3/3 + 1681*p**2/6 - 175. Factor h(j).
j*(j - 41)**2*(j + 1)/3
Let c(t) = -55*t**4 + 1355*t**3 - 7710*t**2 + 4235*t + 13355. Let s(i) = 5*i**4 - 123*i**3 + 701*i**2 - 385*i - 1214. Let y(p) = 4*c(p) + 45*s(p). Factor y(n).
5*(n - 11)**2*(n - 2)*(n + 1)
Let o(j) = 3*j**2 - 16*j + 10. Suppose 6*a - a - 15 = 0, -5*g = -4*a - 13. Let y be o(g). Factor 4/13*b**2 + 4/13*b**3 - 6/13*b - 6/13*b**4 + 2/13 + 2/13*b**y.
2*(b - 1)**4*(b + 1)/13
Factor 540 + 502*k**3 - 40*k**5 + 227*k**4 - 858*k**3 - 1057*k - 563*k - 794*k**3 + 113*k**4 + 1935*k**2.
-5*(k - 2)**2*(2*k - 3)**3
Let r be 3/(-4)*(-2)/6. Let g(n) be the first derivative of 4/3*n**3 + r*n**4 + 5 + 2*n + 5/2*n**2. Factor g(k).
(k + 1)**2*(k + 2)
Let q = 113/2 - 1412/25. Let h(a) be the second derivative of 5*a + 0*a**2 - q*a**5 + 1/45*a**4 + 0*a**3 + 0. Factor h(l).
-2*l**2*(3*l - 2)/15
Let d(z) be the third derivative of 1/72*z**4 - 1/210*z**7 - z**2 + 0*z - 1/9*z**3 - 1/360*z**6 + 1/36*z**5 + 0. Solve d(c) = 0 for c.
-1, 2/3, 1
Suppose -173*y + 70*y = 0. What is t in 2/7*t**3 + 0*t**2 + y*t + 0 = 0?
0
Let a(q) be the third derivative of -q**7/945 - q**6/270 + q**5/270 + q**4/54 - 99*q**2. Solve a(u) = 0.
-2, -1, 0, 1
Let b(l) be the first derivative of 2*l**3/21 - 11*l**2/7 + 48*l/7 + 41. Factor b(k).
2*(k - 8)*(k - 3)/7
Suppose -4*j - j = 60. Let r be (j/(-27))/(2/9). Factor -m - 7 + r*m + 9 - m**2.
-(m - 2)*(m + 1)
Determine o so that -9*o - 18 + 2*o**2 - 12 + 0*o**2 + 3*o + 10*o = 0.
-5, 3
Let r(q) be the second derivative of -q**5/90 - 5*q**4/54 - 4*q**3/27 + 5*q - 1. Factor r(l).
-2*l*(l + 1)*(l + 4)/9
Suppose 4*s = -2*r + 24, -5*s - 2*r + 39 - 11 = 0. Let d be 4*(0/13 - (-6)/4). Factor -4*m**5 - 7*m**4 + 8*m + 20*m**2 - d*m**4 + 12*m**3 + 9*m**s + 0*m.
-4*m*(m - 2)*(m + 1)**3
Suppose -2/7*d**2 + 12*d - 126 = 0. Calculate d.
21
Let y(w) be the first derivative of 1/7*w**2 - 1/21*w**3 - 3/28*w**4 + 0*w - 3. Let y(n) = 0. What is n?
-1, 0, 2/3
Let k(w) be the second derivative of 2*w**6/45 - 6*w**5 + 225*w**4 + 76*w. Determine x, given that k(x) = 0.
0, 45
Let l be (-30)/2 - (-1 + -14). Suppose 1/2*k**2 + 0*k + l - 1/2*k**3 = 0. What is k?
0, 1
Let v(w) be the third derivative of w**8/6720 - w**7/1680 - w**6/40 + w**5/2 + 15*w**2. Let o(m) be the third derivative of v(m). What is s in o(s) = 0?
-2, 3
What is l in -2/3*l - 1/3*l**3 + 1/3*l**4 + 1/9*l**5 + 0 - 11/9*l**2 = 0?
-3, -1, 0, 2
Let l(t) be the first derivative of -t**7/560 + t**5/160 + t**2 + 5. Let v(b) be the second derivative of l(b). Let v(h) = 0. What is h?
-1, 0, 1
Let y be (51/(-17))/((-6)/4). Factor 4*u**y - 3*u**2 - 3*u + 0*u + 5*u.
u*(u + 2)
Let w(r) = 6*r**4 - 47*r**3 - 83*r**2 + 431*r + 472. Let n(i) = 3*i**4 - 24*i**3 - 42*i**2 + 216*i + 237. Let q(f) = 11*n(f) - 6*w(f). Factor q(v).
-3*(v - 5)**2*(v + 1)*(v + 3)
Factor 8/7*m**2 - 2/7*m**4 + 0 + 12/7*m**3 - 48/7*m.
-2*m*(m - 6)*(m - 2)*(m + 2)/7
Let s(j) be the third derivative of j**5/210 + 37*j**4/42 + 1369*j**3/21 - 205*j**2. Let s(h) = 0. What is h?
-37
Let c(s) = -2*s**3 - 14*s**2 - 6*s - 40. Let h be c(-7). Suppose 2/3*w**h - 4/3*w + 0 + 2/3*w**3 = 0. What is w?
-2, 0, 1
Let r be (2 - (-26)/(-10))/(707/56 + -13). Determine u so that -7/5 - r*u - 1/5*u**2 = 0.
-7, -1
Let r(n) be the first derivative of -1/4*n**4 + 1/2*n**2 - 30 - 3*n + n**3. Factor r(b).
-(b - 3)*(b - 1)*(b + 1)
Determine g so that -360*g**3 - 30*g - 40 + 54*g**2 + 17*g**4 + 241*g**2 + 28*g**4 + 55*g**3 + 35*g**5 = 0.
-4, -2/7, 1
Let p(g) be the first derivative of -1 - 1/6*g**4 - 1/3*g**2 - 4/9*g**3 + 0*g. Factor p(f).
-2*f*(f + 1)**2/3
Let h(n) = n**3 + n**2. Let s(x) = -8*x**4 - 18*x**3 + 4*x**2 + 24*x - 8. Let a(p) = 12*h(p) - 2*s(p). Factor a(v).
4*(v + 2)**2*(2*v - 1)**2
Suppose 2*h + 80 = 6*h. Let c = h - 17. Let 2*m**5 - 2*m**2 - 103*m + 2*m**4 + 107*m - 7*m**c + m**3 = 0. Calcul