 - 27*t**2 + 112*t - 110. Let h(d) = -5*y(d) + 14*z(d). Factor h(i).
2*(i - 2)**2*(i + 15)
Let d(f) be the second derivative of f**6/20 - 3*f**5/20 + 326*f. Suppose d(k) = 0. What is k?
0, 2
Suppose 5*h - 69 + 110 = 56. Suppose -32/7*j**2 + 8/7 + 12/7*j + 12/7*j**h = 0. Calculate j.
-1/3, 1, 2
Let b = -1 - -6. Suppose -3*k + t + 21 = 0, 4*t - b*t = 3. Factor -q + 3*q**2 - k + 6*q + 3*q**2 - 2*q - 3*q**3.
-3*(q - 2)*(q - 1)*(q + 1)
Let k(t) = t**2 + t - 1. Let d be ((-21)/(-14))/(9/84). Let x(g) = 5*g**2 + 23*g - 39. Let f(l) = d*k(l) - 2*x(l). Solve f(u) = 0.
4
Solve 5*r**5 + 2005*r - 12*r**4 + 40 + 35*r**2 - 35*r**3 - 1915*r - 3*r**4 = 0 for r.
-1, 2, 4
Let y(v) be the third derivative of -v**7/1995 - v**6/228 - 7*v**5/570 - v**4/76 - v**2 - 37*v. Factor y(g).
-2*g*(g + 1)**2*(g + 3)/19
Let y(t) = -10*t**2 - 42*t - 40. Let g(r) = -9*r**2 - 42*r - 35. Let h(n) = -8*g(n) + 7*y(n). Let h(i) = 0. Calculate i.
-21, 0
Let o = 30 - 26. Let g be -6*(0 + (-1)/2). Factor y**4 - o*y**2 - 3*y**4 - 6*y**g - 2*y**5 - 4*y**4 + 2*y**2.
-2*y**2*(y + 1)**3
What is w in -2*w**3 - 308*w**4 + 2*w**5 - 4*w**2 + 0*w**3 + 312*w**4 = 0?
-2, -1, 0, 1
Let t be (-3)/(-60)*(1 - 0). Let o(r) be the third derivative of 1/120*r**6 + 0*r - t*r**5 - 1/6*r**3 + 0 + 1/8*r**4 + 3*r**2. Determine v, given that o(v) = 0.
1
Let j = -1527 - -1527. Factor 2/7*a - 2/7*a**3 + j + 0*a**2.
-2*a*(a - 1)*(a + 1)/7
Factor 23*i**2 - 192 + 5*i**2 - 12553*i + 12489*i.
4*(i - 4)*(7*i + 12)
Let v(x) be the third derivative of x**6/40 - 9*x**5/5 + 357*x**4/8 - 289*x**3 - 533*x**2. Determine r so that v(r) = 0.
2, 17
Let j(g) be the first derivative of -14 - 1/34*g**4 - 4/17*g**3 - 12/17*g**2 - 16/17*g. Suppose j(w) = 0. What is w?
-2
Let q(w) be the first derivative of -2*w**5/75 + w**4/30 - 501. Let q(c) = 0. Calculate c.
0, 1
Suppose -14/23 - 16/23*z - 2/23*z**2 = 0. Calculate z.
-7, -1
Let i(p) = -5*p + 21. Let x be i(7). Let r = 16 + x. Solve 4*g + 2/3*g**r + 6 = 0.
-3
Let v(t) be the first derivative of t**6/10 - 3*t**5/5 + t**4 - 28*t - 21. Let q(u) be the first derivative of v(u). Suppose q(s) = 0. Calculate s.
0, 2
Let g(k) be the third derivative of -3*k**8/56 + 41*k**7/35 - 547*k**6/60 + 173*k**5/6 - 103*k**4/3 + 20*k**3 + 18*k**2 + 11*k. What is a in g(a) = 0?
1/3, 2, 5, 6
Solve 4/3*a**3 + 0*a - 2/9*a**5 - 2/3*a**4 + 16/9*a**2 + 0 = 0 for a.
-4, -1, 0, 2
Determine k so that 0 + 13/5*k**3 - 1/5*k**5 + 12/5*k**2 + 0*k + 0*k**4 = 0.
-3, -1, 0, 4
Let j(s) = -3*s - 2. Let c(t) = -3*t**2 - 39*t - 81. Let q(n) = -c(n) + 3*j(n). Find x, given that q(x) = 0.
-5
Let u(r) be the second derivative of 1/2*r**4 + 0*r**5 - 8*r - 1/2*r**3 + 0*r**2 + 0 - 1/5*r**6 + 1/14*r**7. Factor u(x).
3*x*(x - 1)**3*(x + 1)
Factor 288/5 - 624/5*i - 3/5*i**5 + 528/5*i**2 - 216/5*i**3 + 42/5*i**4.
-3*(i - 6)*(i - 2)**4/5
Let y(t) be the second derivative of -t**4/24 - 25*t**3/12 - 6*t**2 + 2*t - 101. Determine a, given that y(a) = 0.
-24, -1
Suppose -1 = -5*y + 29. Factor -6*i + y*i**3 - 144 + 144 - 21*i**4 + 21*i**2.
-3*i*(i - 1)*(i + 1)*(7*i - 2)
Let s(t) = -7*t**4 + 13*t**3 - 2*t**2 - t. Let x(h) = -13*h**4 + 26*h**3 - 4*h**2 - 2*h. Let d(z) = 7*s(z) - 3*x(z). Suppose d(y) = 0. What is y?
-1/5, 0, 1/2, 1
Let a(n) = 3*n**5 + 3*n**4 - 30*n**3 + 30*n**2 - 18*n + 3. Let b(u) = 3*u**5 + 3*u**4 - 31*u**3 + 29*u**2 - 20*u + 4. Let d(w) = -4*a(w) + 3*b(w). Factor d(c).
-3*c*(c - 1)**3*(c + 4)
Let k(r) be the first derivative of 4*r**5/15 + 7*r**4/3 + 8*r**3/3 + 225. Solve k(w) = 0 for w.
-6, -1, 0
Let a(r) be the third derivative of r**8/448 - 27*r**7/280 + 21*r**6/20 + 49*r**5/20 - 62*r**2. Factor a(n).
3*n**2*(n - 14)**2*(n + 1)/4
Let h = 46 + -17. Suppose 0 = -2*i - 4*s - h + 89, 15 = 2*i - 5*s. Find o, given that 2*o**3 - 49 + i - 2*o**2 + 29 = 0.
0, 1
Let s(k) be the first derivative of k**6/3 + 28*k**5/5 + 32*k**4 + 76*k**3 + 63*k**2 - 465. Factor s(v).
2*v*(v + 1)*(v + 3)**2*(v + 7)
Let u(a) = 5*a**4 + 40*a**3 + 104*a**2 + 84*a. Let q(d) = 5*d**4 + 40*d**3 + 105*d**2 + 85*d. Let f(k) = 4*q(k) - 5*u(k). Factor f(i).
-5*i*(i + 2)**2*(i + 4)
Let q(h) be the first derivative of 11 + 176/39*h**3 + 2/39*h**6 + 28/13*h**4 + 34/65*h**5 + 64/13*h**2 + 32/13*h. Factor q(w).
2*(w + 2)**4*(2*w + 1)/13
Solve 48*r - 3/5*r**5 + 24/5*r**4 - 48/5*r**2 - 48/5*r**3 - 192/5 = 0 for r.
-2, 2, 4
Let b be (-367236)/(-2106) - (-2)/(-13). Let k = -174 + b. Solve -k*s**2 + 4/3*s - 2 = 0.
3
Let z(k) = -2*k**3 - 4*k**2 + 3*k. Let y be z(3). Let s be (-3)/((3 - 0)/y). Determine p, given that 81*p**4 - 8 - 54*p**2 - 28*p + s*p**3 - 16 - 56*p = 0.
-2/3, 1
Let w be (-4)/(-16)*7 + (-1)/4. Let i(q) be the first derivative of -3*q**2 + w*q**4 + 2/3*q**3 + 2/5*q**5 + 4 - 4*q. Factor i(p).
2*(p - 1)*(p + 1)**2*(p + 2)
Let p(u) be the first derivative of -2*u**3/3 + 118*u**2 - 6962*u - 171. Solve p(q) = 0 for q.
59
Let c be ((-39)/(-195))/(2/15) + -1. Find v such that -c*v**5 + 1/2*v**3 + 0*v + 0*v**2 + 0 + 0*v**4 = 0.
-1, 0, 1
Suppose 0 = -h + 22 - 18. Factor -3*g**3 + 4*g**3 + 6*g**3 + 11*g**3 - 10*g**h + 4*g - 14*g**2 + 2*g**5.
2*g*(g - 2)*(g - 1)**3
Let w(b) be the first derivative of 3*b**6/7 - 132*b**5/35 + 67*b**4/14 + 4*b**3 - 76*b**2/7 + 48*b/7 - 109. Determine j so that w(j) = 0.
-1, 2/3, 1, 6
Let b be (-14 + 10 - (-2)/(-2))*(-2)/5. Let 1/2*w**5 - 3/4*w**4 + 0*w - 3/4*w**3 + 0 + 1/2*w**b = 0. What is w?
-1, 0, 1/2, 2
Find g such that 32/13*g**2 + 160/13 + 2/13*g**3 - 152/13*g = 0.
-20, 2
Let r(y) be the third derivative of y**5/24 + 3*y**4/16 + y**3/3 - 76*y**2 + 1. Factor r(s).
(s + 1)*(5*s + 4)/2
Let x(r) be the third derivative of r**6/270 + 4*r**5/45 + 5*r**4/6 + 100*r**3/27 + 214*r**2. Suppose x(s) = 0. What is s?
-5, -2
Let w(g) = 4*g - 3 - 6*g**2 + 3 + 2 + 2*g + g**3. Let y be w(6). Find n such that n - y - n**2 + 38 = 0.
0, 1
Let k(m) be the first derivative of -m**5/6 + 5*m**4/4 - 5*m**3/18 - 10*m**2 - 40*m/3 + 214. Let k(t) = 0. What is t?
-1, 4
Let y(r) = -4*r**2 - 1088*r + 47526. Let p(a) = 7*a**2 + 1634*a - 71289. Let f(q) = 5*p(q) + 8*y(q). Factor f(k).
3*(k - 89)**2
Find z, given that 147 + 3/7*z**3 + 9*z**2 + 63*z = 0.
-7
Determine c so that 230*c**2 + 28*c - 16*c**5 + 37*c - 150 - 80*c**4 + 11*c**5 - 60*c**3 = 0.
-15, -2, -1, 1
Let c = 5297/540 + -49/5. Let p(t) be the third derivative of c*t**4 + 0 - 1/540*t**6 + 4*t**2 + 1/270*t**5 - 1/27*t**3 + 0*t. Let p(w) = 0. What is w?
-1, 1
Let p(c) be the first derivative of 2/5*c**5 + 24 + 0*c + 8/3*c**3 + 0*c**2 + 5/2*c**4. Factor p(g).
2*g**2*(g + 1)*(g + 4)
Let r be (42/(-11907)*18)/((-2)/7). Let 0*h - r*h**3 - 8/9 + 2/3*h**2 = 0. What is h?
-1, 2
Let w(o) be the first derivative of 0*o**2 - 39/4*o**4 + 78/5*o**5 - 15 + 0*o - 7/2*o**6 - 6*o**3. Solve w(l) = 0 for l.
-2/7, 0, 1, 3
Suppose 2 = 7*k - 6*k. Solve -15 + 15*r - 5*r**2 + 0*r**k + 5*r = 0 for r.
1, 3
Let t(h) = 24*h**4 - 15*h**3 - 36*h**2 - 27. Let g(o) = -o**4 + o**3 + o**2 + 1. Let s(j) = 27*g(j) + t(j). Factor s(u).
-3*u**2*(u - 3)*(u - 1)
Let n(q) be the second derivative of 2*q**7/3 + 46*q**6/15 + 27*q**5/5 + 13*q**4/3 + 4*q**3/3 + 62*q. Factor n(x).
4*x*(x + 1)**3*(7*x + 2)
Let d = 703 + -699. Let v(l) be the second derivative of 1/2*l**3 + 0 + l + 0*l**2 - 1/4*l**d. Factor v(p).
-3*p*(p - 1)
Suppose 5*g = -g - 150. Let f = g + 31. Suppose -5*i**3 + 2 + i**3 + 2*i**2 - f*i**2 + 4*i + 2 = 0. What is i?
-1, 1
Let o(y) be the third derivative of -y**6/120 - y**5/6 - 9*y**4/8 - 3*y**3 - y**2 - 10. Factor o(k).
-(k + 1)*(k + 3)*(k + 6)
Factor 24 + 188/3*o + 20/3*o**2.
4*(o + 9)*(5*o + 2)/3
Let g(y) = -7*y + y + y**2 + 7*y. Let o(l) = 4*l**2 + 37*l - 256. Let k(h) = -5*g(h) + o(h). Let k(n) = 0. What is n?
16
What is j in -78/7*j + 1521/7 + 1/7*j**2 = 0?
39
Let l be 20/130 + 74/26. Find z, given that -2*z**2 - 10*z - 4 - 3*z**2 - l + 2 = 0.
-1
Let u(n) be the third derivative of -3/100*n**5 + 1/5*n**3 - 1/40*n**4 + 0 + 1/200*n**6 + 0*n - 10*n**2 + 1/350*n**7. Suppose u(y) = 0. What is y?
-2, -1, 1
Let r be (46 + -43)/(-1 - 7/(-4)). Suppose r = 3*y - 2. Factor -2/3*m + 0 - 2*m**2 - 2/3*m**4 - y*m**3.
-2*m*(m + 1)**3/3
Let s(g) be the first derivative of -g**4/24 - 5*g**3/18 + 508. Factor s(m).
-m**2*(m + 5)/6
Let z(o) = -20*o**2 + 44*o - 10. Let b(t) = 7*t**2 - 15*t + 3. Let u(x) = 17*b(x) + 6*z(x). Let c be u(7). Fa