m - 20 = j. Factor 5*t**4 + 0*t**3 + 82*t**m - 5*t**3 - 5*t**2 - 77*t**5.
5*t**2*(t - 1)*(t + 1)**2
Let d(y) = -2*y**4 + 3*y**3 + 4*y - 5. Suppose 0*j + 4 = j. Let u(f) = f**j + 7 - f**3 + 4 - 2*f - 9. Let k(r) = 3*d(r) + 7*u(r). Find v, given that k(v) = 0.
-1, 1
Let y be 4/(-26) + 441/1092. Suppose -3*o + 2 = -h, -3*o - 4*h + 6 = -8*o. Factor 0 - 1/2*k - y*k**o.
-k*(k + 2)/4
Let h be -1 - -1 - 2/6*-3. Let m be 3*(-124)/60*h*-9. What is a in -81/5*a**5 - 71*a**3 - 4/5 - 48/5*a - 201/5*a**2 - m*a**4 = 0?
-1, -2/9
Suppose 4*d + 20 = 0, g + d + 3*d = -20. Suppose 4*c = g, 2*t + 4*c = t + 4. Factor 6 + 3*f**2 - 3*f - 6*f + t - 4.
3*(f - 2)*(f - 1)
Let j(m) = m**3 - 10*m**2 + 14*m + 18. Let y be j(8). Let t(f) be the second derivative of -f**3 - 7/10*f**5 + 0 - 2*f**4 - 11*f + y*f**2. Factor t(k).
-2*(k + 1)**2*(7*k - 2)
Let b(v) = -4*v**2 - 7*v**2 + v**3 + 2 - v + 13*v**2. Let g be b(0). Factor -22 + g*n**2 + 22 - 2*n.
2*n*(n - 1)
Let p(j) be the second derivative of 0*j**2 + 0 + 1/7*j**4 + 3/14*j**3 - 4*j + 3/140*j**5. Factor p(s).
3*s*(s + 1)*(s + 3)/7
Let x = 6 - 4. Factor 21 + 16 - x*t**3 - 4*t - 44*t - 5 + 18*t**2.
-2*(t - 4)**2*(t - 1)
Determine q, given that 4/5*q**2 - 8/5*q**3 + 2/5*q**4 + 8/5*q - 6/5 = 0.
-1, 1, 3
Let o = -1/1924 + 3851/5772. Suppose l**3 - 5/6*l**4 + 1/6*l**5 + o*l**2 + 0 - 4/3*l = 0. What is l?
-1, 0, 2
Let f(b) be the first derivative of -b**4/4 + 2*b**3/3 - b**2/2 - 108. Let f(y) = 0. Calculate y.
0, 1
Let l = 1045/6 - 347/2. Factor -4/3*k - 2/3 - l*k**2.
-2*(k + 1)**2/3
Let i(w) = w**4 + 15*w**3 + 24*w**2 + 10*w + 6. Let o(a) = a**3 - a + 1. Let f(s) = i(s) - 6*o(s). Factor f(n).
n*(n + 1)*(n + 4)**2
Suppose -27 = -4*z - 5*t, 22*z + 12 = 25*z + t. Let m(p) be the second derivative of 0 - 1/4*p**4 - 3/20*p**5 + 4*p + p**z + 0*p**2. Factor m(d).
-3*d*(d - 1)*(d + 2)
Let o = -110 - -109. Let z be (16/20)/((-6)/15 - o). Let -5/6*p**3 - 1/6*p**4 - 2/3*p - z*p**2 + 0 = 0. What is p?
-2, -1, 0
Let j = -584 - -584. Let n(t) be the first derivative of 0*t - 1/5*t**5 + 1/3*t**3 - 6 + 0*t**2 + j*t**4. Factor n(a).
-a**2*(a - 1)*(a + 1)
Let 16*w**2 - 24*w**2 - 7*w**2 - 10*w + 15*w**4 + 5*w**5 + 5*w**3 = 0. Calculate w.
-2, -1, 0, 1
Let z = 356/7 + -1773/35. Solve 1/5*c**4 + z*c - 1/5*c**3 - 1/5*c**2 + 0 = 0 for c.
-1, 0, 1
Let q = 37/5 - 7. Let s(p) be the first derivative of -5 - q*p**3 + p**2 - 4/5*p. Factor s(c).
-2*(c - 1)*(3*c - 2)/5
Let l(a) be the first derivative of -6*a**5/55 - 21*a**4/22 - 18*a**3/11 + 81*a**2/11 + 324*a/11 - 138. Factor l(w).
-6*(w - 2)*(w + 3)**3/11
Let q be 22/(-18) + 1 + 16/72. Let y(h) be the third derivative of -1/360*h**6 - 1/1260*h**7 - 1/360*h**5 + 0 + 0*h + 5*h**2 + 0*h**3 + q*h**4. Factor y(a).
-a**2*(a + 1)**2/6
Let l(s) = -s**3 - 2*s**2 - s + 3. Let h be l(-2). Determine c, given that h*c**3 + 20*c**2 - 3*c - c**3 + 19*c = 0.
-4, -1, 0
Let t = -4616 + 9533/2. Let a = t - 128. What is l in -a*l**3 + 0 - 6*l**5 + 39/2*l**4 + 21/2*l**2 - 3/2*l = 0?
0, 1/4, 1
Let t(i) be the first derivative of -3*i**3 - 33*i**2/2 - 18*i - 383. Suppose t(c) = 0. Calculate c.
-3, -2/3
Find q, given that 578/7*q + 1/7*q**2 + 83521/7 = 0.
-289
Let z(f) = 1 + 55*f - 55*f - f**4 + f**2. Let y(j) = 2*j**3 + 4*j**2 - 2*j - 6. Let v(p) = -y(p) - 2*z(p). Determine l so that v(l) = 0.
-1, 1, 2
Suppose 4*w - 40 = -w. Suppose -w*p = -2*p - 18. Suppose d**2 - 8*d + 19*d - 11*d - d**p = 0. Calculate d.
0, 1
Let o(a) = -36*a**3 + 75*a**2 - 48*a - 3. Let s(i) = 37*i**3 - 74*i**2 + 49*i + 4. Let p(v) = 4*o(v) + 3*s(v). Factor p(w).
-3*w*(w - 1)*(11*w - 15)
Let b = -1/648 - -2599/4536. Determine m so that 0 - 2/7*m**2 + b*m = 0.
0, 2
Let q be (-1)/(-8)*-2 - (-18)/(-24). Let t be ((-2)/(-5))/(-1*q/5). Determine a, given that -1/2 + 5/4*a + 1/4*a**3 - a**t = 0.
1, 2
Let r(k) = k**3 - 4*k**2 - k + 8. Let w be r(2). Let v be (-11 + 11)*w/6. Suppose 4/7 + v*o + 1/7*o**3 - 3/7*o**2 = 0. What is o?
-1, 2
Let v be 3 + (-4 - -1 - -1). Suppose l + v = 0, -4*c + 3*l + 15 = -0. Solve -1/5*d**2 + 0 - 1/5*d**c + 1/5*d + 1/5*d**4 = 0.
-1, 0, 1
Let u = 439/318 + -5/106. Let x(k) be the second derivative of 0 - 4/9*k**3 - 6*k + u*k**2 + 1/18*k**4. Let x(m) = 0. Calculate m.
2
Factor -i**2 + 5/2*i**3 + 0*i - 2*i**4 + 1/2*i**5 + 0.
i**2*(i - 2)*(i - 1)**2/2
Let c(j) be the first derivative of -2*j**5/5 - 9*j**4/2 - 14*j**3/3 + 9*j**2 + 16*j - 231. Factor c(a).
-2*(a - 1)*(a + 1)**2*(a + 8)
Let u = -18401 - -128816/7. Factor u*w + 2/7*w**2 - 8/7*w**3 - 1/7*w**5 - 6/7*w**4 + 4/7.
-(w - 1)*(w + 1)**3*(w + 4)/7
Let j(t) be the second derivative of -t**7/280 + t**6/30 - 3*t**5/40 + 17*t**3/6 - 17*t. Let h(r) be the second derivative of j(r). Factor h(d).
-3*d*(d - 3)*(d - 1)
Suppose 0 = -60*h + 50*h - 360. Let o be 8/h - (-14)/63. Determine j, given that 8/7*j**2 + 2/7*j + o = 0.
-1/4, 0
Let a(i) be the first derivative of -i**5/5 + 7*i**4/3 - 10*i**3 + 18*i**2 + 10*i - 30. Let k(f) be the first derivative of a(f). Factor k(j).
-4*(j - 3)**2*(j - 1)
Let l(n) be the second derivative of 1/36*n**4 + 2*n + 0 + 0*n**2 - 1/18*n**3. Factor l(v).
v*(v - 1)/3
Let a = 26 - 3. Suppose a*u**2 + 21*u**3 + 11*u**4 + 3*u - 2*u**4 - 8*u**2 = 0. Calculate u.
-1, -1/3, 0
Let m(a) be the second derivative of -1/2*a**3 + 0*a**2 - 1/8*a**4 + 0 + 1/360*a**6 - 2*a + 1/60*a**5. Let d(o) be the second derivative of m(o). Factor d(y).
(y - 1)*(y + 3)
Let t(s) = -4*s - 50. Let r be t(-13). Let o be 18/45 + r/20. What is k in -1/2*k**3 - k**4 - o*k**5 + 0*k + 0*k**2 + 0 = 0?
-1, 0
Let a(y) be the first derivative of 8*y + 6*y**2 + 4 + 4/3*y**3. Factor a(q).
4*(q + 1)*(q + 2)
Let w(u) = -u**3 + 91*u**2 + 314*u + 302. Let d(y) = 12*y**3 - 912*y**2 - 3141*y - 3021. Let n(c) = 2*d(c) + 21*w(c). Factor n(k).
3*(k + 2)**2*(k + 25)
Suppose -5*q - o = -3*o - 24, -5*q + 14 = 3*o. Let z be (10 - 2 - 4) + 0. Factor -8*g**4 + 4*g**q - g**5 + 0*g**5 + 3*g**z.
-g**4*(g + 1)
Determine z, given that -176/9*z**2 + 10/3*z**3 + 8/9*z**4 + 14/3*z + 0 = 0.
-7, 0, 1/4, 3
Let m(b) = -b**3 + 3*b**2 - 2*b. Let i be m(2). Factor i*p - 15*p**2 + p + 0*p + 16*p**2.
p*(p + 1)
Let m be (-4)/(-2) + 748/(-910) + -3. Let d = -2/91 - m. Factor 3/5*u**3 + d*u - 12/5*u**2 + 0.
3*u*(u - 3)*(u - 1)/5
Let b(n) be the second derivative of 0*n**2 + 0*n**3 + 0 - 1/75*n**6 + 0*n**4 + 4*n + 1/50*n**5. Factor b(u).
-2*u**3*(u - 1)/5
Let t = 302 + -454. Let v = t - -766/5. Factor 3/5*w + 3/5*w**3 - v*w**2 + 0.
3*w*(w - 1)**2/5
Solve 1/3*y**3 - 2/3*y**4 - 1/2*y + 0 + 1/6*y**5 + 2/3*y**2 = 0.
-1, 0, 1, 3
Let a(m) be the first derivative of 2*m**3/27 - 11*m**2/9 + 20*m/9 + 44. Solve a(n) = 0.
1, 10
Let d(f) be the second derivative of -f**5/90 - 11*f**4/54 - 8*f**3/27 + 20*f**2/9 - 7*f + 6. Solve d(w) = 0 for w.
-10, -2, 1
Suppose -9 = 50*c - 9. Let l(b) be the first derivative of -4*b**2 + c*b + 5 - 2/3*b**3. Factor l(n).
-2*n*(n + 4)
Determine i, given that -3/2*i**5 + 185/2*i**4 - 2528*i - 6849/2*i**2 - 512 - 2629/2*i**3 = 0.
-1, -1/3, 32
Suppose -5*v - 36 = 99. Let b be ((-104)/(-20) - 5) + v/(-15). Factor -2/5 - 4/5*g**3 + 0*g**b + 4/5*g + 2/5*g**4.
2*(g - 1)**3*(g + 1)/5
Let j be 5/(-1 - (-52)/50). Solve 1900*z**3 + 576*z**5 + j*z**2 + 27 + 472*z**2 - 7*z**2 + 445*z**2 + 270*z + 1680*z**4 = 0 for z.
-3/4, -1/3
Let a = -1182 - -1182. Factor -1/9*m**3 - 2/9*m + a + 1/3*m**2.
-m*(m - 2)*(m - 1)/9
Let c(y) be the first derivative of -2*y**3/3 + 158*y**2 - 12482*y - 287. Factor c(d).
-2*(d - 79)**2
Let o(b) be the first derivative of 2/65*b**5 + 0*b**4 + 0*b**2 + 0*b**3 + 32 + 0*b. Find k such that o(k) = 0.
0
Let r(m) be the first derivative of 5*m**2 + 32 + 0*m + 1/3*m**3. Factor r(p).
p*(p + 10)
Factor 334*m**2 - 3*m**3 - 295*m**2 - 96*m + 56 + 4.
-3*(m - 10)*(m - 2)*(m - 1)
Find h such that -10 + 65*h**4 + 20*h**5 - 114*h + 59*h - 34*h**3 - 55*h**2 + 69*h**3 = 0.
-2, -1, -1/4, 1
Let b be 112/18 + (-144)/648. Let n(r) be the first derivative of 0*r + 2 - 1/10*r**5 + 1/36*r**b + 1/24*r**4 + 1/6*r**3 - 1/6*r**2. Let n(p) = 0. What is p?
-1, 0, 1, 2
Let f = -291 - -296. Let k(m) be the first derivative of 5/12*m**4 + f + 7/6*m**2 + 2/3*m + m**3 + 1/15*m**5. Determine a so that k(a) = 0.
-2, -1
Let d(x) be the third derivative of x**8/1176 - 2*x**7/245 - 2*x**6/105 + x**5/35 + x**4/12 + 116*x**2. What is h in d(h) = 0?
