 Determine a so that r(a) = 0.
-5, -1, 0, 1/4
Let t(y) be the first derivative of 1/5*y**5 + 16/3*y**3 + 8*y**2 + 5/3*y**4 + 16/3*y + 5. Determine r so that t(r) = 0.
-2, -2/3
Let 176/21*x + 242/21*x**2 + 32/21 = 0. Calculate x.
-4/11
Factor -5 - 919*i**2 + i**3 + 967*i**2 - 3*i**3 + 5.
-2*i**2*(i - 24)
Let s(d) be the first derivative of 0*d**2 + 2/25*d**5 + 2/15*d**3 + 0*d + 9 + 1/5*d**4. Factor s(q).
2*q**2*(q + 1)**2/5
Let w(h) be the third derivative of 0*h + 7*h**2 - 1/6*h**4 + 1/15*h**5 - 1/120*h**6 + 0*h**3 + 0. Let w(i) = 0. What is i?
0, 2
Let w(g) be the third derivative of -1/132*g**4 - 1/1848*g**8 + 0*g + 0*g**3 + 1/330*g**6 + 0*g**7 + 4*g**2 + 0*g**5 + 0. Suppose w(k) = 0. What is k?
-1, 0, 1
Let x be (1 + 69/(-75))*2. Let z = x + 38/75. Factor 0 - 2/3*p - z*p**2.
-2*p*(p + 1)/3
Let c(x) = -2*x**2 + x - 1. Let k(s) = -17*s**2 - 124*s - 131. Let f(i) = -6*c(i) + k(i). Suppose f(r) = 0. What is r?
-25, -1
Let r(c) be the first derivative of 1/3*c**3 - c - 8 + 0*c**2. Factor r(b).
(b - 1)*(b + 1)
Factor -176*j**4 + j**2 - 49*j**4 + 45*j**4 - 5*j - 120*j**3 + 54*j**2.
-5*j*(j + 1)*(6*j - 1)**2
Find f, given that -106 + 3*f**2 + 3*f + 3*f**2 + 49 - 3*f**3 + 51 = 0.
-1, 1, 2
Let v(b) be the third derivative of -b**5/210 + 15*b**4/7 - 2700*b**3/7 + 176*b**2. Solve v(w) = 0 for w.
90
Let f = -31311 + 31315. Factor -24/5*r**f - 9/5*r**5 + 0*r + 0 - 16/5*r**2 + 44/5*r**3.
-r**2*(r + 4)*(3*r - 2)**2/5
Let j = 1611 - 1611. Factor 0*q - 4/5*q**2 - 12/5*q**4 + 4/5*q**5 + j + 12/5*q**3.
4*q**2*(q - 1)**3/5
Suppose 3*l + 18 = -2*c, -5*l - 2*c - 14 = -4*c. Let y be ((-8)/(-6))/(l + 10). Factor -y*t + 2/9*t**4 + 0 + 2/3*t**2 - 2/3*t**3.
2*t*(t - 1)**3/9
Let a be (-2)/(-4) + (-120)/16 + 10. Suppose a*w + 5*w = -5*w. Factor w*h - 1/10*h**2 + 1/10.
-(h - 1)*(h + 1)/10
Let l = -219/20 - -56/5. Let g(k) be the first derivative of 1 - l*k**4 + 0*k**2 + 1/5*k**5 + 0*k - 1/3*k**3 + 1/6*k**6. Determine w, given that g(w) = 0.
-1, 0, 1
Let f be (-28)/(-16) + -2 + -2 + 3. Let b = 25/12 - f. Suppose 0 - 2*x**3 + 0*x**4 + 2/3*x**5 - b*x**2 + 0*x = 0. Calculate x.
-1, 0, 2
Let v(o) = 2*o**3 + 50*o**2 - 52*o - 56. Let d(w) = -7. Let t(j) = -8*d(j) + v(j). Factor t(p).
2*p*(p - 1)*(p + 26)
Let b(s) be the second derivative of s**4/54 + 14*s**3/27 + 49*s**2/9 - 3*s + 50. Determine o, given that b(o) = 0.
-7
Let z(s) be the second derivative of s**7/5460 - s**6/156 + 21*s**5/260 - 49*s**4/156 - 4*s**3/3 - 36*s. Let m(f) be the second derivative of z(f). Factor m(q).
2*(q - 7)**2*(q - 1)/13
Let h(q) be the third derivative of -q**5/30 - q**4/3 + 5*q**3/3 + 257*q**2. Factor h(i).
-2*(i - 1)*(i + 5)
Let q be 160/33 + -2 + -27 + (-3950)/(-150). Find c such that 2*c**3 + 8/11*c**4 + 0 + 9/11*c + q*c**2 + 1/11*c**5 = 0.
-3, -1, 0
Suppose -13 = 5*s - 133. What is j in -32/7 - 240/7*j**2 - 50/7*j**3 - s*j = 0?
-4, -2/5
Factor 1/5*j**3 - 5*j - 6/5*j**2 - 18/5.
(j - 9)*(j + 1)*(j + 2)/5
Let w = -76 + 84. Let z be 2*(-4)/w - -6. Determine l, given that -3/5*l**3 + 0 - 1/5*l**2 + 1/5*l**z + 1/5*l**4 + 2/5*l = 0.
-2, -1, 0, 1
Let a(s) = -2*s**2 - 20*s + 72. Let u(h) = h**2 - h. Let b(m) = a(m) + 4*u(m). Solve b(t) = 0 for t.
6
Let y be 13 + (-77)/(-66)*-10. Factor -y*d**3 + 4/3*d**4 + 0*d + 0*d**2 + 0.
4*d**3*(d - 1)/3
Factor 4 + 2*d**2 + 1500*d**3 - 1501*d**3 + 2*d + 2*d + 3*d.
-(d - 4)*(d + 1)**2
Let v be 4 + 10/6*-3. Let w = v - -1. Determine s so that s**5 + 2*s**3 + 2 + 2*s**2 - 3*s**4 + 0*s**4 - 1 + w*s**5 - 3*s = 0.
-1, 1
Let c be -3*(4/(-10) - (-48)/(-180)). Let o(b) be the second derivative of -1/8*b**c - 6*b + 0 + 1/48*b**4 - 1/24*b**3 + 1/80*b**5. Factor o(q).
(q - 1)*(q + 1)**2/4
Suppose w = 42 - 27. Let l = 17 - w. Factor 1 - 1/3*t**l + 2/3*t.
-(t - 3)*(t + 1)/3
Suppose 0 = -3*k + 5*k + 90. Let q be 1/(-2)*36/k. Factor 1/5*p + q*p**2 + 1/5*p**3 + 0.
p*(p + 1)**2/5
Let b be (-5 + 2 + -2)*(-3)/(-3). Let p(z) = z + 5. Let a be p(b). Factor -2/9*t + 2/9*t**3 + a*t**2 + 0.
2*t*(t - 1)*(t + 1)/9
Let b(a) = -a**2 + 7*a + 20. Let c be b(9). Suppose -5 = 3*z - 5*n, -4*n - 6 = -4*z - c. Factor -36/5*k**2 + z*k**4 + 6*k**3 + 0 + 8/5*k.
k*(k + 2)*(5*k - 2)**2/5
Let c(k) = -k**2 + 2*k + 9. Let m be c(5). Let p be (-33)/m + (-3)/(-2). Suppose -12*q**5 - 10*q**4 - q + 6*q + p*q**5 + 10*q**2 = 0. Calculate q.
-1, 0, 1
Let m(l) = 13*l**2 - 13*l + 4. Let k(g) = -16*g**2 + 12*g - 5. Let n(y) = -4*k(y) - 5*m(y). Let n(c) = 0. What is c?
0, 17
Let z(k) be the first derivative of 4*k**5/5 + 2*k**4 - 4*k**3 - 27. Determine m so that z(m) = 0.
-3, 0, 1
Factor -10/7 - 18/7*d**2 - 92/7*d.
-2*(d + 5)*(9*d + 1)/7
Let r(l) be the third derivative of 16/945*l**7 + 7/180*l**6 + 3*l**2 + 0*l + 11/270*l**5 + 1/54*l**4 + 0 + 1/378*l**8 + 0*l**3. Solve r(i) = 0.
-2, -1, -1/2, 0
Suppose 25 - 28 = -q. Suppose 0*a = -2*a + 4. Factor 2/3*k**q + 2*k - 2/3 - 2*k**a.
2*(k - 1)**3/3
Let n(m) be the third derivative of 1/780*m**6 + 0*m + 0 + 7*m**2 - 1/1365*m**7 + 0*m**4 + 1/195*m**5 + 0*m**3. Factor n(s).
-2*s**2*(s - 2)*(s + 1)/13
Let v(l) be the first derivative of -5*l**3/12 - 70*l**2 - 3920*l + 325. Factor v(f).
-5*(f + 56)**2/4
Let z(f) be the third derivative of -1/3*f**3 + 1/4*f**4 + 5*f**2 + 0 + 0*f + 1/60*f**6 - 1/10*f**5. Find h such that z(h) = 0.
1
Let p be (-15)/(-75)*-15 - -5. Let 0*a**p + 0*a + 0 - 2/3*a**5 + 2*a**3 + 4/3*a**4 = 0. Calculate a.
-1, 0, 3
Let b(i) be the first derivative of 4*i - 2/3*i**6 - 19/3*i**3 + 6*i**2 + 3*i**5 - 2*i**4 - 7. Suppose b(d) = 0. Calculate d.
-1, -1/4, 1, 2
Let r(b) be the second derivative of -1/2*b**2 - 1/420*b**5 + 0*b**3 - 1/840*b**6 + 1/84*b**4 + 3*b + 0. Let d(c) be the first derivative of r(c). Factor d(s).
-s*(s - 1)*(s + 2)/7
Let c be 1 - 0 - 7/(-14 - -28). Let q(f) be the second derivative of 0 + 0*f**2 + 1/4*f**4 - f - c*f**3. Solve q(p) = 0.
0, 1
Let j(x) be the second derivative of -x**6/120 + x**5/40 + x**4/16 - 2*x + 169. Factor j(f).
-f**2*(f - 3)*(f + 1)/4
Let u(o) be the third derivative of -o**7/280 + o**6/60 - o**5/40 + 49*o**3/6 + 29*o**2. Let g(k) be the first derivative of u(k). What is b in g(b) = 0?
0, 1
Let v(u) be the third derivative of -u**8/60480 - u**7/3780 - u**6/720 - 23*u**5/60 - 24*u**2. Let d(h) be the third derivative of v(h). Factor d(t).
-(t + 1)*(t + 3)/3
Let k(o) = 4*o + 1 - 2*o + 13. Let l be k(11). Factor 96*b - 10*b**2 + 6*b**2 - l - 60*b**2.
-4*(4*b - 3)**2
Determine k, given that 5*k**3 + 0 - 19/3*k**2 - 1/3*k**5 + k**4 - 10*k = 0.
-3, -1, 0, 2, 5
Let c(j) be the second derivative of -j**8/336 + j**6/24 - j**5/12 + 11*j**3/3 + 11*j. Let i(a) be the second derivative of c(a). Suppose i(s) = 0. Calculate s.
-2, 0, 1
Let w = -91 + 135. Factor -w*r**2 + 115*r**3 + 32*r - 7*r**3 - 76*r**2 + 413*r**4 - 433*r**4.
-4*r*(r - 4)*(r - 1)*(5*r - 2)
Suppose 60*n = 54*n + 192. Factor 5*f + n + f**3 + 27*f - 1347*f**2 + 1357*f**2.
(f + 2)*(f + 4)**2
Suppose -3*g + k - 40 = 5*k, 2*g + 26 = -2*k. Let u be -1*2/6*g. Suppose 2*v**4 - 2*v**u - v**4 - 2*v**3 - v**4 = 0. What is v?
-1, 0
Let g = -13/24 - -41/24. Let n be (-20)/4*(-3)/10. Factor g*a + 1/3 - n*a**2.
-(a - 1)*(9*a + 2)/6
Let j(a) be the third derivative of -a**5/510 + 5*a**4/102 + 11*a**3/51 - 126*a**2. Factor j(c).
-2*(c - 11)*(c + 1)/17
Let s be 0*(-1 + (-30)/(-36)). Factor 0*z**2 + s*z + 0 + 4/5*z**3 - 12/5*z**4.
-4*z**3*(3*z - 1)/5
Let i = -577 + 577. Let u(r) be the third derivative of 1/120*r**6 - 2*r**2 + 0 + i*r**4 + 2/3*r**3 + 0*r - 1/20*r**5. Determine d so that u(d) = 0.
-1, 2
Suppose 5*j + 428*m = 431*m + 28, -4*j = -5*m - 38. Factor 0 - 2/9*g**j + 2/3*g.
-2*g*(g - 3)/9
Determine n, given that 11*n + 10*n**3 - 7*n**2 - 11*n - 11*n**3 - 7*n**2 = 0.
-14, 0
Let o(i) be the first derivative of -i**4/12 - 3*i**3 - 28*i**2 + 196*i/3 + 76. Factor o(p).
-(p - 1)*(p + 14)**2/3
Let b be (-130588)/(-4480) - -2*(-2)/28. Let z = b - -627/32. Determine s, given that -z*s**2 - 108/5*s - 12/5 = 0.
-2/9
Suppose 3/7*r**3 - 243/7 - 45/7*r**2 + 27*r = 0. Calculate r.
3, 9
Factor 0 + 50/13*o**3 + 2/13*o**4 + 0*o + 92/13*o**2.
2*o**2*(o + 2)*(o + 23)/13
Suppose -15*h**4 - 66*h**2 - 13*h**2 - 63*h**2 + 12*h + 94*h**2 + 51*h**3 = 0. What is h?
0, 2/5, 1, 2
Let c = 63 + 14. Let g = 83 - c. Determine s so that -s**4 + 21/4*s**3 - 1 - 37/4*s**2 + g*s = 0.
1/4, 1, 2
Let n(m) be the